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The Advanced Algebra Tutor: Learning By Example DVD Series teaches students through step-by-step example problems that progressively become more difficult. This DVD covers the inverses of functions in algebra, including what inverses of functions are and why they are important in algebra. Grades 9-College. 22 minutes on DVD. |
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Show More geometry and beyond. This book provides the first comprehensive introduction to the circle of ideas developed around the program, the prerequisites being only a basic knowledge of algebraic geometry. It will be of great interest to graduate students and researchers working in algebraic geometry and related fields |
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This Textbook
Overview
A History of the "New Mathematics" Movement and its Relationship with Current Mathematical Reform provides a history of the "new mathematics" movement of the 1950s, 1960s, and early 1970s in the United States and relates it to current mathematics curricular reform. The history of the "new math" education movement is explained in terms of the general curriculum in schools, the mathematics curriculum, the teaching standards, and the pedagogical techniques used. A complete analysis of the history of the "new math" movement was accomplished by separately investigating major and minor "new math" projects. In conjunction, the aftermath of the "new math" movement is explained providing suggestions as to why this movement is often seen as having failed. A short history of reform from the 1970s to the present is provided. Finally, the book compares the "new mathematics" movement with the current mathematics reform movement led by the National Council of Teachers of Mathematics.
Related Subjects
Meet the Author
Angela Lynn Evans Walmsley is Assistant Professor in the Department of Research Methodology at Saint Louis University. Previously, she was a middle school and high school mathematics teacher. She holds a bachelor's degree in mathematics, a master's degree in mathematics education, and a doctoral degree in curriculum and instruction. Her interests include mathematics education, pre-service teacher education, and educational |
MAT 100 Mathematics Pathway
General Information: MAT 100 is a two-credit hour pass-fail course
requiring 150 minutes in the Lumberjack Mathematics Center each week through the completion of
all course materials. 75 minutes are scheduled on Tuesdays or Thursdays. A minimum of 75 minutes are spent during open lab time and are flexible. You have the
freedom to work at your own pace, within the constraints of established
deadlines, but you may choose to work ahead to complete the course early.
The
purpose of this course is to provide you with sufficient mathematical knowledge
so that you can take the Advancement Exam or the Mathematics Placement Exam (ALEKS) successfully and place into
another MAT/STA course. A
schedule is established for you to complete a set of material by the end of the
semester. You progress through the
material by demonstrating proficiency in stages. You are allowed to work ahead of this set
schedule. After completing course
requirements, you can if you wish work through more advanced material (not listed
in the student learning outcomes).
Prerequisites: Placement
in MAT 100 is based on the Placement Exam.
Catalog Description: Review of algebra
topics such as the simplification of algebraic expressions, solution of algebraic
equations, graphing of linear equations and factoring of polynomials. Prerequisite:
Placement insufficient for a credit bearing mathematics/statistics course
Course Description: MAT 100 is designed to enhance students' mathematics
skills so that they may exhibit proficiency at the level needed to enroll in another
mathematics or statistics course. Students are required to demonstrate
proficiency in material such as solving algebraic equations, graphing linear
equations, factoring polynomials, etc. |
Problem solving in meaningful contexts, language and communication, connections within and outside mathematics, and formal and informal reasoning underlie all content areas in mathematics. Throughout mathematics in Grades 6-8, students use these processes together with graphing technology and other mathematical tools such as manipulative materials to develop conceptual understanding and solve problems as they do mathematics These pages show some features of your book that will help you gain these skills and use them to master this year's topics |
a practical approach to arithmetic and beginning algebra and assumes no prior knowledge of mathematics. By thoroughly explaining various mathematical techniques, Proga helps students understand why a technique works so they'll remember how to use it. Well-known for its flexibility and complete coverage of arithmetic and algebra topics, Proga's text is perfectly suited for a combination arithmetic-elementary algebra course, for either an arithmetic or an algebra course, or for a two-term course sequence. |
APPLIED MATHEM ATICS /PURE MATHEM ATICS 3240
APPLIED GRAPH THEORY
AM/PM 3240: Applied Graph Theo
If the grid on the right represents a network of roads and the
numbers represent distances between intersections, what's
the shortest route from A to B? Are you sure?
Suppose you are the operator of a snow plough. After a
severe storm, you have to clear all the streets in the
network shown. Can you plan a route which avoids
travelling along a street you have already cleared? If not,
what route minimizes the total distance you have to travel?
Consider the grid from a different viewpoint. Suppose there
is a town at each intersection and the numbers represent
the distances between towns. Your job is to pave the roads
as economically as possible so that it is possible to travel
between any two towns along pavement. What roads should
be paved?
Graph theory is not like calculus or linear algebra, subjects you may have already studied. It is much less
structured; there are far fewer to learn. But it is a rich subject with many applications at least some of which
we hope will standard techniques intrigue you to the extent that you'll want to learn more about them.
Text. Discrete Mathematics by E. G. Goodaire and M. M. Parmenter has been used as a text for this
course.
Marks. Typically 55% of the final grade in this course is awarded for performance on a final examination,
30% to performance on a midterm and 15% for homework.
Calendar description. Algorithms and complexity, definitions and basic properties of graphs, Eulerian and
Hamiltonian chains, shortest path problems, graph coloring, planarity, trees, network flows, emphasis on
applications including scheduling problems, tournaments, and facilities design.
Prerequisite: Either M 2051 or PM 2320.
NOTE: Credit cannot be obtained for both AM/PM 3240 and Computer Science 3741.
Offered. Fall
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL, A1C 5S |
Considered a classic by many, A First Course in Abstract Algebra is an in-depth, introduction to abstract algebra. Focused on groups, rings and fields, this text gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures. The sixth edition of this text continues the tradition of teaching in a classical manner while integrating field theory and a revised Chapter Zero. New exercises were written, and previous exercises were revised and modified. [via]
The new edition of this linear algebra text includes an early introduction to key concepts, and optional integration of LINTEK and MATLAB. Features include: calculus-related examples; section summaries of key ideas, definitions and theorems; and exercise sets including "true or false" problems. [via] |
Make payment online after registration. Save a trip to the bookstore, It is simple, safe, and GREEN!
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eMath has been used by thousands of students in courses such as College Algebra,
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Text Size:
ACM115 - Applied Math & Measurement for Manufacturing
Credits: 2 Lab included: Yes
This course is designed to help students successfully transfer knowledge of math to the manufacturing floor. The focus will be on solving lab problems that require the use of math, including measurements and calculations. Students will work in both metric and U.S. standard measurement systems independently before learning conversions, building comfort with the language and instruments for measurement. Students will work in teams to find solutions to common plant problems and will work individually using Plato software to advance math skills according to customized plan. Students will develop a course notebook that contains notes, formulas, and examples that will become a reference book as they proceed through lab courses in their training and to assist them on the job. |
Pre-Algebra Essentials For Dummies
Overview
Many students worry about starting algebra. Pre-Algebra Essentials For Dummies provides an overview of critical pre-algebra concepts to help new algebra students (and their parents) take the next step without fear. Free of ramp-up material, Pre-Algebra Essentials For Dummies contains content focused on key topics only. It provides discrete explanations of critical concepts taught in a typical pre-algebra course, from fractions, decimals, and percents to scientific notation and simple variable equations. This guide is also a perfect reference for parents who need to review critical pre-algebra concepts as they help students with homework assignments, as well as for adult learners headed back into the classroom who just need to a refresher of the core concepts618387
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Saxon Math Grades 4-8
Grade 4
Saxon Math 54 teaches students the way they learn best... through
incremental development of new material and continual review of the
old. Following Math 3, concepts such as addition, place value and other
skills are reviewed, while new concepts such as fractions, decimals,
Roman Numerals and working with triple-digit numbers are introduced.
Lessons contain a warm-up, introduction to new material, lesson
practice where the new skill is practiced, and mixed practice, which is
comprised of new and old problems.
Math 54, Third Edition, Tests & Worksheets Retail Price: $24.00 CBD Price: $17.99Math 54, Third Edition, Solutions Manual Retail Price: $30.00 CBD Price: $22.49The solutions manual includes full step-by-step solutions for all lesson and investigation problems and for all 23 cumulative tests. Also includes answers to Supplemental Practice Problems and Facts Practice problems.
Grade 7
Math 87, Third Edition Retail Price: $103.60 CBD Price: $77.70
( In Stock ) The final stop for Saxon's middle school math, Math 8/7 continues
teaching students the way they learn best...through incremental
development of new material and continual review of the old. Following
Math 7/6, concepts such as arithmetic calculation, measurements,
geometry and other skills are reviewed, while new concepts such as
pre-algebra, ratios, probability and statistics are introduced as
preparation for upper level mathematics. Lessons contain a warm-up,
introduction to new concepts, lesson practice where the new skill is
practiced, and mixed practice, which is comprised of old and new
problemsGrade 8
Algebra 1/2 Home Study Kit includes the hardcover student text,
softcover answer key and softcover test booklet. Containing 123
lessons, this text is the culmination of pre-algebra mathematics, a full
pre-algebra course and an introduction to geometry and discrete
mathematics. Some topics covered include Prime and Composite numbers;
fractions & decimals; order of operations, coordinates, exponents,
square roots, ratios, algebraic phrases, probability, the Pythagorean
Theorem and more. Utilizing an incremental approach to math, your
students will learn in small doses at their own pace, increasing
retention of knowledge and satisfaction!
Need help with a specific homeschool question? Want to know some
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Math Basics for Healthcare Professionals (4th Edition)
9780133104158
ISBN:
013310415X
Edition: 4 Pub Date: 2013 Publisher: Prentice Hall
Summary: Michele Lesmeister is the author of Math Basics for Healthcare Professionals (4th Edition), published 2013 under ISBN 9780133104158 and 013310415X. Five hundred eighty one Math Basics for Healthcare Professionals (4th Edition) textbooks are available for sale on ValoreBooks.com, two hundred thirty five used from the cheapest price of $24.71, or buy new starting at $48.80 |
A comprehensive Calculus review app written by a Math PhD. Functions, Limits, Derivatives and Integrals are all covered with 55+ worked examples. For quick access to equations, the "Equations" tab displays commonly used properties and equations for derivatives and integrals |
Differentiate or Integrate
Tools
Screenshots
Developer Notes
Differentiate or Integrate allows you to differentiate and integrate mathematical functions.
You can also solve differential equations and plot graphs of your choice. You can also solve differential equations and plot graphs of your choice.
Now, do your homework easily when the app : |
You are here
A Primer for Mathematics Competitions
Publisher:
Oxford University Press
Number of Pages:
344
Price:
45.00
ISBN:
9780199539888
I like this book as an introduction to problem solving and as a source for general high school classroom enrichment. In the Preface, the authors state that the aim of this book is "not to equip you for the Himalayan heights of the IMO (International Mathematical Olympiad) but for the intermediate challenge of national Olympiads — say, of Welsh mountains, and moderately challenging Swiss Alps, North American Rockies, Peruvian Andes, South African Drakensberg, etc." The book originated in preparations for various African competitions; and, with respect to the quoted intent and its overall level, the book under review is very much like A First Step to Mathematical Olympiad Problems by Derek Holton.
The fairly standard topics ('toolchests') in this primer (see the Table of Contents) are handled with more than customary thoroughness. There are historical remarks, derivations of theorems and formulas, and connections with other tools. A typical chapter or section starts with motivating 'appetizer' problems, followed by exposition of theory, worked out examples, the solution to the appetizer problem, and a good selection of problems (with solutions) related to the subject matter of the chapter. Many of these end-of-chapter problems are multiple-choice. Although more topics are covered to a greater extent than in Holton's book, the book under review provides no actual IMO problems. The book's last two pages provide further resources for those interested in mathematical competitions, including a number of useful web sites. |
Find a Des PlainesAlgebra 2 (or Intermediate Algebra) revolves mainly around the introduction, classification, and manipulation of functions of an indeterminate variable (i.e. equations symbolized by 'f(x)'). Successful completion of the course serves as an essential foundation for the future calculus student. A... |
Mathematics A Discrete Introduction
9780534398989
ISBN:
0534398987
Edition: 2 Pub Date: 2005 Publisher: Thomson Learning
Summary: With a wealth of learning aids and a clear presentation, this book teaches students not only how to write proofs, but how to think clearly and present cases logically beyond this course. All the material is directly applicable to computer science and engineering, but it is presented from a mathematician's perspective.
Scheinerman, Edward R. is the author of Mathematics A Discrete Introduction, published 2005... under ISBN 9780534398989 and 0534398987. Two hundred six Mathematics A Discrete Introduction textbooks are available for sale on ValoreBooks.com, twenty eight used from the cheapest price of $6.34, or buy new starting at $57 |
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The Rules of Algebra: (Ars Magna) by Girolamo Cardano First published in 1545, this cornerstone in the history of mathematics contains the first revelation of the principles for solving cubic and biquadratic equations. Excellent translation, adapted to modern mathematical syntax.
Theory of Sets by E. Kamke Introductory treatment emphasizes fundamentals, covering rudiments; arbitrary sets and their cardinal numbers; ordered sets and their ordered types; and well-ordered sets and their ordinal numbers. "Exceptionally well written." — School Science and Mathematics.
Algebra by Larry C. Grove This graduate-level text is intended for initial courses in algebra that proceed at a faster pace than undergraduate-level courses. Subjects include groups, rings, fields, and Galois theory. 1983 edition. Includes 11 figures. Appendix. References. IndexSemi-Simple Lie Algebras and Their Representations by Robert N. Cahn Designed to acquaint students of particle physics already familiar with SU(2) and SU(3) with techniques applicable to all simple Lie algebras, this text is especially suited to the study of grand unification theories. 1984 edition.
Lie Groups, Lie Algebras, and Some of Their Applications by Robert Gilmore This text introduces upper-level undergraduates to Lie group theory and physical applications. It further illustrates Lie group theory's role in several fields of physics. 1974 edition. Includes 75 figures and 17 tables, exercises and problems.
Applied Matrix Algebra in the Statistical Sciences by Alexander Basilevsky This comprehensive text offers teachings relevant to both applied and theoretical branches of matrix algebra and provides a bridge between linear algebra and statistical models. Appropriate for advanced undergraduate and graduate students. 1983Elements of Abstract Algebra by Allan Clark Lucid coverage of the major theories of abstract algebra, with helpful illustrations and exercises included throughout. Unabridged, corrected republication of the work originally published 1971. Bibliography. Index. Includes 24 tables and figures.
Product Description: VolumeReprint of the W. H. Freeman and Company, San Francisco, 1985 |
Number 3: Algebra covers algebra from signed numbers to equation solving and working with polynomials. |
Reviews
.....the book is readable, concise, clear and well-organized. It is self-contained, including detailed, but not jumbly, discussions on basic aspects of the theory such as inversion or relationships between the real and complex case....... J.E. Galé, Mathematical Reviews |
From inside the book
LibraryThing Review
User Review - LibraryThing
Mathematical techniques used in solving technical problems that arise in electrical, mechanical, aeronautical, and thermal branches of engineering. Calculating machines and computers enable us to solve a greater range of problems requiring analytical formulations. Mathematical technology can be divided into four main categories and their combinations. (a) linear lumped systems; (2) linear distributed systems; (3) nonlinear lumped and distributed systems; (4) statistical methods and probability, although very little is provided on the latter theory. The chapters on matrix algebra, Fourier methods, variational methods, Laplace transforms, and nonlinear differential equations have been expanded. A section on Cartesian tensors was added to the chapter on vector analysis. |
,...
More, and probability, with a focus on applications of mathematics. Students will learn to recognize and describe important patterns that relate quantitative variables and develop strategies to make sense of real-world data. The course will develop students' abilities to solve problems involving chance and to approximate solutions to more complex probability problems by using simulation. The goal that will be addressed in this lesson is to review Algebra I fundamentals, more specifically mathematical models (price-demand model, formulas as models, and operations with real numbers) to lay the foundation for the semester.
Discussion for Applied Math Lesson Plan
Stefani Makowski
(Teacher (K-12))
Provides students an interesting way to learn required materials while relating math principles to everyday life. Uses Moodle as a collaboration tool in completing interactive weekly assignments. Materials can be adapted for different types of learners. Also uses novelty items (YouTube) to engage learners. |
Out of Stock
Description of 2013 SOS 7th Grade Math by Alpha Omega Publications
Shape up for geometry and algebra! Prepare your student for the world of shapes and formulas with SOS 7th Grade Math! Your student will be introduced to the fundamentals of geometry and algebra in preparation for more in-depth study in later grades.
Subjects include:
sets and number systems
place value
geometry
statistics and graphs
formulas
functions
ratios
proportions
Break your student's ideas of math being boring with SOS 7th Grade Math! This revolutionary, technologically-filled curriculum makes learning fun and not a chore. This course will solidify your student's math understanding by reviewing whole numbers; multiplication and division; and adding, subtracting, multiplying, and dividing fractions in an exciting, interactive format. Statistics and graphs are also covered. |
Mathematics
Honing your mathematical reasoning, proof-writing, problem-solving and presentation skills all are part of NMC's Mathematics Program. Build your self-confidence and enthusiasm for this field by enrolling in our courses, which will help prepare you for transferring to complete a bachelor's degree in mathematics. |
Welcome to Mathboat!
What do you need to fall in love with Calculus and get a 5 on AP Exam?
1. Informative Calculus Lectures in Powerpoint format.We offer you ppt lectures! 2. Practice problems!They are in your textbook.Do your homework!!! 3. Effective review before the AP Exam. We offer you a book with 6 full Multiple Choice Exams! 4. Practice with Free Responses Problems. Download some from AP Central - we'll give you the link to their site.
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Our Interactive Books provide all of the necessary materials and resources to hone your skills and get a 5 on the AP Test.Our books are written by a teacher who has been teaching AP Calculus BC for 15 years. She teaches 3 full AP Calculus BC classes per year and her students' AP scores speak for themselves: On average, 90 % of her students get fives and 100%pass the AP Calculcus BC Exam every year. Please read on and investigate our tools that are changing students' lives! |
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1) Introduction Real Functions and Graphs is a reminder of the principles underlying the sketching of graphs of functions and other curves.
2) Group Theory (A) Symmetry studies the symmetries of plane figures and solids, including the five 'Platonic solids', and leads to the definition of a group.
3) Linear Algebra Vectors and Conics is an introduction to vectors and to the properties of conic sections.
4) Analysis |
Introduction to MATLAB
时区:
In this webinar we provide an introduction to MATLAB, a high-level language and interactive environment for numerical computation, visualization, and programming.
MATLAB includes built-in mathematical functions fundamental to solving engineering and scientific problems, and an interactive environment ideal for iterative exploration, design, and problem solving. Through product demonstrations, you will see how this combination allows you to quickly explore ideas, gain insight into your data, and document and share your results.
This webinar features R2012b, the most recent release of MATLAB. R2012b features a redesigned desktop that organizes commonly used functionality, making it easier to get started using MATLAB.
A Q&A session will follow the presentation and demos.
About the Presenter: Bonita Vormawor earned a M.S. degree in Computer Science, from the National Technological University, and a B.A. degree for a double major in Computer Mathematics, and Natural Sciences, from the University of Pennsylvania. She has worked at Raytheon Company as a Senior Software Engineer II with Honors. Previously at Polaroid, she contributed as a Senior Software Engineer, Associate Scientist focused on near-infrared spectroscopy, Laboratory Administrator, and Database Developer. Earlier in her career she worked at Tufts University School of Dental Medicine, and the University of Pennsylvania School of Medicine. Bonita is a Senior Application Engineer at MathWorks with a focus of a LTC Generalist with a minor in Application Deployment. |
Think Like a Mathematician: A Companion to Undergraduate Mathematics
Looking for a head start in your undergraduate degree in mathematics? Maybe you've already started your degree and feel bewildered by the subject you previously loved? Don't panic! This friendly companion will ease your transition to real mathematical thinking. Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician |
The student must take the following modules:
Educational Aims: Knowledge, Understanding and Skills
Educational Aims
To create a
teaching and learning environment which supports all students in reaching
their full potential in their study of mathematics at BSc/BA level;
To offer a
high-quality teaching and learning programme, informed by staff research,
designed to train students in preparation for a wide range of postgraduate
education and employment.
The aims
of the BSc/BA Mathematics with Statistics programme are:
To provide
students with analytical techniques and problem-solving skills that can be
applied in many types of employment, especially those involving logical
skills, decision-making in complex circumstances, or advanced skills of
numeracy;
To offer
modules of study which, individually and collectively, enable students to
appreciate both the theoretical and problem-solving aspects of
mathematics;
To provide
students with enough core material, of sufficient depth and variety, in
the first two levels of study that they are adequately prepared and
informed for subsequent study in either or both of pure mathematics and
statistics;
to provide
a programme of study that allows students to take a coherent blend of
topics in pure mathematics and statistics at the third level of study of a
BSc/BA;
To maintain
a programme of study that introduces the background of current research in
pure mathematics and statistics;
To produce
alumni recognised for the distinctive value of their education on this
programme.
Learning Outcomes: Knowledge, Understanding and Skills
Learning Outcomes of the
Scheme of Study
Subject-specific Knowledge,
Understanding and Skills
On completing
the programme students should have acquired
A1. An understanding of and competence
in the key ideas and techniques, and knowledge of the statement and proof of
key results, both within the core areas of real and complex analysis, linear
and abstract algebra, and probability and statistics, and in the more advanced
topics chosen in the third level of study;
A2. An appreciation of the
hierarchical structure of mathematical knowledge;
A3. An understanding of mathematical
notation, and an ability to use it correctly and coherently;
A4. An appreciation of the importance
of proof, generalization and abstraction in the logical development of formal
theories;
A5. An ability both to follow and
correctly to construct mathematical proofs of appropriate degrees of
complexity;
A6. An understanding of the
mathematical and contextual basis of statistics as a science, and an
appreciation of the statistical paradigm, linking design and conduct of
experiments and observations with data analysis, modelling and inference;
A7. Experience of implementing the
statistical paradigm in a range of general applications;
A8. An ability to read and comprehend
mathematical literature at an appropriate level;
A9. An ability to use computers and
specialist software to investigate and solve practical mathematical problems.
General Knowledge,
Understanding and Skills
On completing
the programme students should have acquired
B1. An ability to learn from various
styles of presentation of material;
B2. An ability to apply
previously-acquired knowledge to new situations, both to gain understanding and
to solve problems;
B3. An ability to use information
skills to gain access to library and IT resources effectively in researching
topics;
B4. An ability to produce documents
which accurately and effectively communicate scientific material to the reader;
B5. An ability to make presentations
based on prepared material;
B6. An ability to work effectively
both independently and as part of a small group;
B7. An ability to work to deadlines,
and experience in time management when working to a range of deadlines. |
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Group Theory by W. R. Scott Here is a clear, well-organized coverage of the most standard theorems, including isomorphism theorems, transformations and subgroups, direct sums, abelian groups, and more. This undergraduate-level text features more than 500 exercises.
Rotations, Quaternions, and Double Groups by Simon L. Altmann This self-contained text presents a consistent description of the geometric and quaternionic treatment of rotation operators, employing methods that lead to a rigorous formulation and offering complete solutions to many illustrative problems.
Product Description:
dealing with techniques for applying characters to "pure" group theory, a large part of this book is devoted to the properties of the characters themselves and how these properties reflect and are reflected in the structure of the group. Chapter I consists of ring theoretic preliminaries. Chapters 2 to 6 and 8 contain the basic material of character theory, while Chapter 7 treats an important technique for the application of characters to group theory. Chapter 9 considers irreducible representations over arbitrary fields, leading to a focus on subfields of the complex numbers in Chapter 10. In Chapter 15 the author introduces Brauer's theory of blocks and "modular characters." Remaining chapters deal with more specialized topics, such as the connections between the set of degrees of the irreducible characters and structure of a group. Following each chapter is a selection of carefully thought out problems, including exercises, examples, further results and extensions and variations of theorems in the text. Prerequisites for this book are some basic finite group theory: the Sylow theorems, elementary properties of permutation groups and solvable and nilpotent groups. Also useful would be some familiarity with rings and Galois theory. In short, the contents of a first-year graduate algebra course should be sufficient preparation |
Product Description
Students will realize that the power of algebra can help them discover fascinating things about places and people through real-life examples. This series concentrates on the essentials of algebra plus provides a thorough breakdown of difficult concepts using step-by-step explanations and visual examples.Topics Covered: What is Algebra, anyway? Kinds of numbers Order of Operations - PEMDAS Rules of exponents Properties of operations Includes a DVD plus a CD-ROM with teacher's guide, quizzes, graphic organizers and classroom activities. Teaching Systems programs are optimized for classroom use and include "Full Public Performance Rights".Grade Level: 8-12. 26 minutes |
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Summary
Students and professors of an undergraduate course in differential geometry will appreciate the clear exposition and comprehensive exercises in this book that focuses on the geometric properties of curves and surfaces, one- and two-dimensional objects in Euclidean space. The problems generally relate to questions of local properties (the properties observed at a point on the curve or surface) or global properties (the properties of the object as a whole). Some of the more interesting theorems explore relationships between local and global properties.
A special feature is the availability of accompanying online interactive java applets coordinated with each section. The applets allow students to investigate and manipulate curves and surfaces to develop intuition and to help analyze geometric phenomena.
Table of Contents
Preface
Acknowledgements
Plane Curves: Local Properties
Parameterizations
Position, Velocity, and Acceleration
Curvature
Osculating Circles, Evolutes, and Involutes
Natural Equations
Plane Curves: Global Properties
Basic Properties
Rotation Index
Isoperimetric Inequality
Curvature, Convexity, and the Four-Vertex Theorem
Curves in Space: Local Properties
Definitions, Examples, and Differentiation
Curvature, Torsion, and the Frenet Frame
Osculating Plane and Osculating Sphere
Natural Equations
Curves in Space: Global Properties
Basic Properties
Indicatrices and Total Curvature
Knots and Links
Regular Surfaces
Parametrized Surfaces
Tangent Planes and Regular Surfaces
Change of Coordinates
The Tangent Space and the Normal Vector
Orientable Surfaces
The First and Second Fundamental Forms
The First Fundamental Form
The Gauss Map
The Second Fundamental Form
Normal and Principal Curvatures
Gaussian and Mean Curvature
Ruled Surfaces and Minimal Surfaces
The Fundamental Equations of Surfaces
Tensor Notation
Gauss's Equations and the Christoffel Symbols
Codazzi Equations and the Theorema Egregium
The Fundamental Theorem of Surface Theory
Curves on Surfaces
Curvatures and Torsion
Geodesics
Geodesic Coordinates
Gauss-Bonnet Theorem and Applications
Intrinsic Geometry
Bibliography
Author Bio(s)
Thomas F. Banchoff is a geometer and has been a professor at Brown University since 1967. Banchoff was president of the MAA from 1999-2000. He is published widely and known to a broad audience as editor and commentator on Abbotts Flatland. He has been the recipient of such awards as the MAA National Award for Distinguished College or University Teaching of Mathematics and most recently the 2007 Teaching with Technology Award.
Stephen Lovett is an associate professor of mathematics at Wheaton College in Illinois. Lovett has also taught at Eastern Nazarene College and has taught introductory courses on differential geometry for many years. Lovett has traveled extensively and has given many talks over the past several years on differential and algebraic geometry, as well as cryptography.
Editorial Reviews
… a complete guide for the study of classical theory of curves and surfaces and is intended as a textbook for a one-semester course for undergraduates …The main advantages of the book are the careful introduction of the concepts, the good choice of the exercises, and the interactive computer graphics, which make the text well-suited for self-study. …The access to online computer graphics applets that illustrate many concepts and theorems presented in the text provides the readers with an interesting and visually stimulating study of classical differential geometry. … I strongly recommend [this book and Differential Geometry of Manifolds] to anyone wishing to enter into the beautiful world of the differential geometry. —Velichka Milousheva, Journal of Geometry and Symmetry in Physics, 2012
Students and professors of an undergraduate course in differential geometry will appreciate the clear exposition and comprehensive exercises in this book … Some of the more interesting theorems explore relationships between local and global properties. A special feature is the availability of accompanying online interactive java applets coordinated with each section. The applets allow students to investigate and manipulate curves and surfaces to develop intuition and to help analyze geometric phenomena. —L'Enseignement Mathématique (2) 57 (2011)
… an intuitive and visual introduction to the subject is beneficial in an undergraduate course. This attitude is reflected in the text. The authors spent quite some time on motivating particular concepts and discuss simple but instructive examples. At the same time, they do not neglect rigour and precision. … As a distinguishing feature to other textbooks, there is an accompanying web page containing numerous interactive Java applets. … The applets are well-suited for use in classroom teaching or as an aid to self-study. —Hans-Peter Schröcker, Zentralblatt MATH 1200
Coming from intuitive considerations to precise definitions the authors have written a very readable book. Every section contains many examples, problems and figures visualizing geometric properties. The understanding of geometric phenomena is supported by a number of available Java applets. This special feature distinguishes the textbook from others and makes it recommendable for self studies too. … highly recommendable … —F. Manhart, International Mathematical News, August 2011
… the authors succeeded in making this modern view of differential geometry of curves and surfaces an approachable subject for advanced undergraduates. —Andrew Bucki, Mathematical Reviews, Issue 2011h
… an essential addition to academic library Mathematical Studies instructional reference collections, as well as an ideal classroom textbook. —Midwest Book Review, May 2011 |
This third article in the mathematical journey through open source takes you through the functional power of the bench calculator. After going through basic programming on the bench calculator, it's time to explore…
This second article on the mathematical journey through open source takes you through the basics of the bench calculator. Faced with the limitations of the shell command expr and other shell constructs, let's… |
Math 112: Project
Warning - this page is still under construction
Introduction
20% of your final marks for this course will come from work on
a project. This can be done individually, or in small groups. Each
person will be required to write up a report on the work.
Although this is 20% of the marks for the course, you are
not expected to write pages and pages. Quality counts more than
quantity. About 2 pages of writing, in a clear style should be
sufficient, together with additional work for mathematical
formulas, calculations, graphs, diagrams, pictures.
Since this is a short course, we do not have time to go into all
the details of applications of linear algebra.
The purpose of the project is to give you an opportunity to look
in more detail at some applications of the linear algebra we cover
in the course.
I am hoping that some groups of students will give short
presentation in class on their projects, so that we will all
benefit from each others work. Giving a presentation is not
compulsory, but if this is done, it will be taken into account
in the marking of the project. Such a presentation could be about
10 minutes long.
Deadline
The project is due to be handed in on 25th June.
You are encouraged to have at least a rough draft ready by the last
class, so that you are able to explain to others what your project is
about, and if you hand in a draft at that time, I will mark it and
give it back, so I can check that you are on the right track, and
you will find out if there's anything else you need to add or improve.
Marking Scheme
The marks will be awarded based on the following points:
10 marks: Evidence that the material has been understood. Make sure
your writing is clear and intelligible to any other member of class.
5 marks: Evidence that effort has been made to do some research or
independent thinking, eg,
reference to at least one other book or article than the text book
(This could be something on the web), or making up your own examples
(ie, not just copying everything from text book).
5 marks: Correct mathematics given in calculating examples.
5 marks: Presentation (to get full marks for presentation, you'll have to make sure this
clearly explains all the main points of your project).
Note: the above marks add up to 25, but the project is marked out of 20.
This means that if you do not do the presentation, it's still possible to
get full marks. If your marks add up to more than 20, you'll be given a
mark of 20 for the project.
I will also use the following checklist for marking:
Make it clear what the essay is about.
Clearly label and explain any graphs, diagrams, etc.
Define all terminology and notation used.
Explain briefly why mathematical results you use are true, or where they come from.
Give references and clearly state results.
Make sure the mathematics is correct.
Use correct spelling, punctuation, grammar.
In making calculations, make it clear
what the problem is,
How the math goes,
What the result is.
Outline of suggested form of essay
Background description, overview:
Not so much detailed
mathematical content needed here, mainly motivational or historical,
etc. The start of the chapters of the text book gives a good example.
Mathematical ideas:
This part should explain the mathematical content, explaining in words the
concepts, so that they can be easily understood.
Computations, formulas, or examples:
details of how these ideas are applied.
diagrams, graphs or pictures
Some visual component to the essay to convey the concepts in a clear way.
Note, you do not have to cover the above areas in the above
order, eg, you could start with some diagrams, and then explain their
meaning, importance, what they are about.
Method
Here is a suggested method of working:
Read the appropriate section or sections of the text book, and of the
study guide.
Read around a little if possible, or think up questions yourself,
so you are not just copying word
for word from the text book. (I can suggest things if you can't find anything,
or are not sure what to use.)
Make sure you understand what the topic is about, eg, by doing the exercises for that section of the book.
Work out in detail and write up about some example that uses the ideas.
Topics
The following is a list of possible topics to work on, with a
brief outline of what would be expected. Other topics are also
possible. Please let me know if you are thinking of working on
something else.
Basically the idea is to take a section of the book that we
will not be covering in class, and work through that section.
Some possible topics are not in our text book; if you choose one
of those, I will give you some appropriate reading material of
a similar level to that of the text book.
Note on extra reading material
For a different view on some of the topics presented in the text
book, you can look at sections from the following linear algebra
text books:
[BK] Introductory Linear Algebra with Applications, by Bernard Kolman
[CC] Linear algebra, and introductory approach by Charles Curtis
[GW] Computaional linear algebra with models, by Gareth Williams
the relevant sections are indicated below, and photocopies will be
available on reserve in Straufer library, with the other extras mentioned
below.
NOTE: you are not expected to read all of the extra material avaliable,
it's just to give you more choice about what examples to use, and what
applications to write about.
Markov chains:
Read: section 5.9
Write an essay about Markov chains. Describe what they
are and how linear algebra is involved. Give several examples
of their applications, and describe one example in detail.
Other material avaliable:
[BK] section 8-3, pages 439-449
[GW] section 1-7, pages 60-73
[GW] section
Powers of Matrices
Read: and
Write an essay on the applications of taking powers of matrices.
Write about what kinds of things can happen, eg, does the matrix
tend to infinity, or zero, or something else, when you keep
multiplying it by itself? Describe the meaning of different
kinds of behaviour in different problems. You can also describe
the geometric interpretation. Calculate what happens for several
examples, and make a table of some two by two matrices, and their
limits under taking large powers. Also tabulate their determinant
and trace. Are there any patterns? What is the relationship of
powers of matrices to the eigen values?
Other material avaliable:
Linear Algebra in Economics
Read: section 1.3 and 3.7
Write an essay on applications of linear algebra to problems in
economics. Include either a description of the Leontief method, or
something else. Which ever
case, write about possible applications, and describe one
example in detail.
Other material avaliable:
[GW] section 2-6 pages 151-156
Linear Algebra and Graph theory
Read: [BK]section 8.1, pages 417-434
Write an essay on the applications of linear algebra to
graph theory and network problems. Write how to use these
ideas to solve either the problem of the graph theory
game (which I'll describe in lectures), or some other problem.
Other material avaliable:
[GW] section 1-8 pages 73-97
"Scheduling conflict-free Parties for a dating service", Bryan L. Shader and Chanyoung Lee Shader, in the American mathematical Monthly, Feb 1997, Vol 104 #2. (This is probably a bit to much to look at properly, but it might give
you an idea of some other applications.)
Computer graphics
Read: section 3.8
Write an essay about the use of linear algebra in computer
graphics. Include a description of homogeneous coordinates,
what they are, and how they are used. Give examples of
calculations and applications.
Other material avaliable:
[BK] section 3.4, page 171-179
[GW] section 4-2, page 237
Differential Equations
Read: see index of text book for various examples
If you have previously learned calculus, you could write an
essay about solving differential equations using methods of
linear algebra, eg, diagonalization. Include examples and
write about applications.
Other material avaliable:
[BK] section 8.6, pages 469-479
[GW] section 3-7, pages 207-211 (This is about function spaces, not differential equations, but it may be of interest/use to refer to)
Recurrence relations
Read: section 5.8, also pages 89-90
We talked briefly about the Fibbonaci sequence in class.
This is an example of a recurrence relation (also called a difference equation). You can write an essay explaining what a recurrence relation is, and
giving some examples, eg, the Fibbonaci sequence. Use diagonalisation to
find a solution for the nth term.
Other material avaliable:
[BK] section 8.7, pages 480-484 (This is on the Fibbonaci sequence)
Game theory
Read: [BK] section 8.11
Write an essay about how linear algebra Can be used in game theory.
Explain what a pay off matrix is, and the concept of "saddle point".
Give some examples of applications.
Other material avaliable:
Least squares
Read: section 7.5
Write an essay how the method of least squares is used to find best possible
solutions to certain problems. give some examples of applications.
Other material avaliable:
[BK] section 8.4, pages 450-461
Symmetry of two and three dimensional objects
Read: section 2.6
Describing the symmetries of an object is a very interesting
question in mathematics and various branches of science.
Matrices can be used to describe symmetries, eg, if we take
a square, and put it's center at (0,0) in R2, then
the matrcies which map the square to itself are those
corresponding to rotations through 90 degrees, 180 degrees, and
270 degrees. We also have reflections in the lines y=0, x=0,
y=x, and y=-x. So together with the identity matrix, there are
8 matrices that map the square to itself. We say it has a
symmetry group of order 8. (order just means size). So this
gives us a number that will tell us how symmetric the object
is. We can look at the symmetries of other shapes, and see
if they are more or less symmetric. We can also do this for
three dimensional shapes, and for patterns that can be infinite.
For an essay on this topic, write about the concept of
symmetry, how matrices measure this. Give some examples
for various shapes, (preferably something more complicated than
the square should be included, eg, cube).
Other material avaliable:
[CC] chapter 4, pages 109-117
[CC] chapter 10, pages 292-293
Note the book [CC] is a little bit advanced, so you may need to pick out
which bits will be relevant, and ignore things you can't follow. I'll
try and find something better if anyone would be interested. |
Summary
THE PROGRAM STUDENTS NEED; THE FOCUS TEACHERS WANT!Glencoe Algebra 2is a key program in our vertically aligned high school mathematics series developed to help all students achieve a better understanding of mathematics and improve their mathematics scores on today's high-stakes assessments. |
Spivak or Apostol?
So does Spivak or Apostol have more content? I am learning this through self-learning, so I am looking for the most comprehensive one(s).
Apostol probably has more content. The other user was refering to a book on manifolds, which is sort of like Spivak's volume 2.
I would choose Spivak over Apostol. Apostol has a very good detailed history on calculus and all, but I don't like how he organizes the book. You can also get an answer book for Spivak. Either book is solid though. |
ALEX Lesson Plans Writing equations for parallel lines
Description:
Students 34: Write a function that describes a relationship between two quantities.* [F-BF1] [MA2013] (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8-EE5]
Subject: Mathematics (8 - 12) Title: Writing equations for parallel lines Description: Students
Title: Exponential Growth and Decay
Description:
ThisStandard(s): [MA2013] AL1 (9-12) 7: Interpret expressions that represent a quantity in terms of its context.* [A-SSE1] ALC (9-12) 3: Use formulas or equations of functions to calculate outcomes of exponential growth or decay. (Alabama) [MA2013] ALT (9-12) 12: Interpret expressions that represent a quantity in terms of its context.* [A-SSE1 25: Compare effects of parameter changes on graphs of transcendental functions. (Alabama)
Subject: Mathematics (9 - 12) Title: Exponential Growth and Decay Description: This
Title: Density
Description:
D CHE (9-12) 1: Differentiate among pure substances, mixtures, elements, and compounds. [S1] ENV (9-12) 1: Identify the influence of human population, technology, and cultural and industrial changes on the environment. 15: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. [A-CED4] [MA2013] AL1 (9-12) 17: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. [A-REI ALC (9-12) 1: Create algebraic models for application-based problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. (Alabama)
Subject: Mathematics (9 - 12), or Science (8 - 12) Title: Density Description: D
Title: What is the slope of the stairs in front of the school?
Description:
The purpose of this lesson is to help students apply the mathematical definition of slope to a concrete example. The students will learn to make the appropriate measurements and apply the formula to calculate the slope of the stairs experimentally 8: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. [8-EE6 1: Create algebraic models for application-based problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. GEO (9-12) 31: Prove the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). [G-GPE5]
Subject: Mathematics (8 - 12) Title: What is the slope of the stairs in front of the school? Description: The purpose of this lesson is to help students apply the mathematical definition of slope to a concrete example. The students will learn to make the appropriate measurements and apply the formula to calculate the slope of the stairs experimentally.
Title: Marathon Math
Description:
ThisStandard(s): CA2 (9-12) 11: Critique digital content for validity, accuracy, bias, currency, and relevance. [ELA] (9) 14: Use the research process to locate, select, retrieve, evaluate, and organize information to support a thesis on a nonliterary topic. [MA2013] DM1 (9-12) 3: Use the recursive process and difference equations to create fractals, population growth models, sequences, series, and compound interest models. (Alabama) [MA2013] DM1 (9-12) 2: Determine characteristics of sequences, including the Fibonacci sequence, the triangular numbers, and pentagonal numbers. (Alabama) 35: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* [F-BF2] [MA2013] AL1 (9-12) 27: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [F-IF3]
Subject: English Language Arts (9), or English Language Arts (9), or Mathematics (9 - 12), or Technology Education (9 - 12) Title: Marathon Math Description: This
Thinkfinity Lesson Plans
Title: Finding Our Top Speed
Description:
This Illuminations lesson sets the stage for a discussion of travel in the solar system. By considering a real-world, hands-on activity, students develop their understanding of time and distance. The mathematics necessary for the lesson relate to measuring time and distance as well as graphing to portray the data collected.
Standard(s): [S1] (6) 11: Describe units used to measure distance in space, including astronomical units and light years. [MA2013] (8) 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8-EE5,Science Title: Finding Our Top Speed Description: This Illuminations lesson sets the stage for a discussion of travel in the solar system. By considering a real-world, hands-on activity, students develop their understanding of time and distance. The mathematics necessary for the lesson relate to measuring time and distance as well as graphing to portray the data collected. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
Title: Apple Pie Recording Chart
Description:
This reproducible activity sheet, from an Illuminations lesson, prompts students to use strings and rulers to measure and record the distance around several round objects, as well as the distance across the middle of those objects.
Standard(s): [MA2013] (6) 1: Understand the concept of a ratio, and use ratio language to describe a ratio relationship between two quantities. [6-RP (7) 20: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. [7-SP Apple Pie Recording Chart Description: This reproducible activity sheet, from an Illuminations lesson, prompts students to use strings and rulers to measure and record the distance around several round objects, as well as the distance across the middle of those objects. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
Title: Building Bridges
Description:
In this lesson, from Illuminations, students attempt to make a transition from arithmetical to algebraic thinking by extending from problems that have single-solution responses. Values organized into tables and graphs are used to move toward symbolic representations. Problem situations involving linear, quadratic, and exponential models are employed
Subject: Mathematics,Professional Development Title: Building Bridges Description: In this lesson, from Illuminations, students attempt to make a transition from arithmetical to algebraic thinking by extending from problems that have single-solution responses. Values organized into tables and graphs are used to move toward symbolic representations. Problem situations involving linear, quadratic, and exponential models are employed. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
Title: Gallery Walk
Description:
In Gallery Walk Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Automobile Mileage: Age vs. Mileage
Description:
In this lesson, one of a multi-part unit from Illuminations, students plot data about automobile mileage and interpret
Subject: Mathematics Title: Automobile Mileage: Age vs. Mileage Description: In this lesson, one of a multi-part unit from Illuminations, students plot data about automobile mileage and interpret Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: To Fret or Not to Fret
Description:
In In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Exploring Measurement, Sequences, and Curves with Stringed Instruments
Description:
In this lesson, one of a multi-part unit from Illuminations, students measure lengths on stringed musical instruments. They Exploring Measurement, Sequences, and Curves with Stringed Instruments Description: In this lesson, one of a multi-part unit from Illuminations, students measure lengths on stringed musical instruments. They discuss how the placement of frets on a fretted instrument is determined by a geometric sequence. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Graphing What
Description:
This reproducible activity sheet, from an Illuminations lesson, is used by students to record independent and dependent variables as well as the function and symbolic function rule for a set of graphs.
Standard(s): [MA2013] (6) 17: Use variables to represent numbers, and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or, depending on the purpose at hand, any number in a specified set. [6-EE6 Graphing What Description: This reproducible activity sheet, from an Illuminations lesson, is used by students to record independent and dependent variables as well as the function and symbolic function rule for a set of graphs. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: To Fret or...
Description:
This reproducible activity, from an Illuminations lesson, features questions dealing with measuring distances on fretted stringed instruments Least Squares Regression
Description:
In interpret Least Squares Regression Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Not to Fret
Description:
This Not to Fret Description: ThisTitle: Graph Chart
Description:
This reproducible transparency, from an Illuminations lesson, contains the answers to the similarly named student activity in which students identify the independent and dependent variables, the function, symbolic function rule and rationale for a set of graphs.
Standard(s): 2: Recognize and represent proportional relationships between quantities. [7-RP2 26: Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess 1: Create algebraic models for application-based problems by developing and solving equations and inequalities, including those involving direct, inverse, and joint variation. (Alabama) [MA2013] AL2 (9-12) 12: Interpret expressions that represent a quantity in terms of its context.* [A-SSE1 12: Interpret expressions that represent a quantity in terms of its context.* [A-SSE1 Graph Chart Description: This reproducible transparency, from an Illuminations lesson, contains the answers to the similarly named student activity in which students identify the independent and dependent variables, the function, symbolic function rule and rationale for a set of graphs. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: To Fret or Not to Fret
Description:
This reproducible worksheet, from an Illuminations lesson, presents a series of questions related to fretted instruments and geometric sequences. In the lesson, students This reproducible worksheet, from an Illuminations lesson, presents a series of questions related to fretted instruments and geometric sequences. In the lesson, students compare geometric sequences with exponential functions. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Fretting
Description:
In this lesson, one of a multi-part unit from Illuminations, students use their discoveries from the first lesson to place frets on a fretless instrument. They then Fretting Description: In this lesson, one of a multi-part unit from Illuminations, students use their discoveries from the first lesson to place frets on a fretless instrument. They then compare geometric sequences with exponential functions. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Bathtub Water Levels
Description:
In from Bathtub Water Levels Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Seeing Music, Hearing Waves
Description:
Using Description: Using, Hearing Waves: Selected Answers and Solutions
Description:
This reproducible teacher sheet, from an Illumin: Selected Answers and Solutions Description: This reproducible teacher sheet, from an Illumin
Description:
In this Illuminations lesson, students calculate terms of a geometric sequence to determine frequencies of the chromatic scale. They then compare sine waves to see and hear the trigonometry behind harmonious and dissonant note combinations Description: In this Illuminations lesson, students calculate terms of a geometric sequence to determine frequencies of the chromatic scale. They then compare sine waves to see and hear the trigonometry behind harmonious and dissonant note combinations. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: The Effects of Outliers
Description:
This
Standard(s): 43: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [S-ID3 [MA2013] PRE (9-12) 44: Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [S-IC1]
Subject: Mathematics Title: The Effects of Outliers Description: This Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Traveling Distances
Description:
In
Standard(s): [MA2013] (8) 25: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between Traveling Distances Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Automobile Mileage: Comparing and Contrasting
Description:
In key Automobile Mileage: Comparing and Contrasting Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Hearing Music, Seeing Waves
Description:
This reproducible pre-activity sheet, from an Illuminations lesson, presents summary questions about the mathematics of music, specifically focused on sine waves and the geometric sequences of notes that are an octave apart.
Standard(s): [MA2013] AL1 (9-12) 27: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. [F-IF3T (9-12) 38: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. [F-TF2] [MA2013] ALT (9-12) 40: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.* [F-TF5 Linear Alignment
Description:
In
Standard(s): Linear Alignment Description: In Thinkfinity Partner: Illuminations Grade Span: 6,7,8,9,10,11,12
Title: Make a Conjecture
Description:
In this lesson, one of a multi-part unit from Illuminations, students explore rates of change and accumulation in context. They are asked to think about the mathematics involved in determining the amount of blood being pumped by a heart.
Standard(s): 13: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [A-CED2] [MA2013] AL1 (9-12) 14: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities and interpret solutions as viable or non-viable options in a modeling context. [A-CED 42: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [S-ID2 5: Determine approximate rates of change of nonlinear relationships from graphical and numerical data 37: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [S-MD6] [MA2013] AL2 (9-12) 38: (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [S-MD7] [MA2013] ALT (9-12) 12: Interpret expressions that represent a quantity in terms of its context.* [A-SSE1T (9-12) 37: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. [S-ID4] [MA2013] PRE (9-12) 44: Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [S-IC1] [MA2013] PRE (9-12) 45: Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. [S-IC2] [MA2013] PRE (9-12) 46: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [S-IC3] [MA2013] PRE (9-12) 49: Evaluate reports based on data. [S-IC6] [MA2013] ALT (9-12) 41: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [S-MD6] [MA2013] ALT (9-12) 42: (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [S-MD7 Health,Mathematics Title: Make a Conjecture Description: In this lesson, one of a multi-part unit from Illuminations, students explore rates of change and accumulation in context. They are asked to think about the mathematics involved in determining the amount of blood being pumped by a heart. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
Title: Exact Ratio
Description:
This
Standard(s): [MA2013] AL1 (9-12) 2: Rewrite expressions involving radicals and rational exponents using the properties of exponents. [N-RN 33: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [F-IF9 Mathematics Title: Exact Ratio Description: ThisWeb Resources
Interactives/GamesLearning Activities withThinkfinity Learning Activities
Title: Flowing Through Mathematics
Description:
This student interactive, from Illuminations, simulates water flowing from a tube through a hole in the bottom. The diameter of the hole can be adjusted and data can be gathered for the height or volume of water in the tube at any time.
Standard(s): GEO (9-12) 36: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* [G-GMD3] [MA2013] GEO (9-12) 39: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* [G-MG1]
Subject: Mathematics Title: Flowing Through Mathematics Description: This student interactive, from Illuminations, simulates water flowing from a tube through a hole in the bottom. The diameter of the hole can be adjusted and data can be gathered for the height or volume of water in the tube at any time. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 |
Product Description
Student will realize the power of algebra and that armed with knowledge of algebra, you can find out fascinating things about place, people and real-life situations. This series concentrates on the essentials of algebra plus provides a thorough breakdown of difficult concepts using step-by-step explanations and visual examples.The Standard Deviants Teaching Systems are simply the most effective method for students to learn and for teachers to teach. This educational programming is optimized for classroom use. Each module is a topic-based video accompanied with a digital workbook that uses a humorous and unique style and approach to difficult concepts with the learner's perspective in mind. Each video contains "Full Public Performance Rights" and a digital workbook which includes teacher's guides, classroom notes, quizzes, games, and graphic organizers. The subject matter correlates directly to state standards and is produced and designed by the Cerebellum Academic Team of professional scriptwriters, students, professors, actors, comedians, and teachers.Grade Level: 8 -12. 182 minutes |
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An article presenting a way that students of calculus and linear algebra can use both artistic and mathematical abilities to transform ordinary photographs into interesting pictures having mathematical content
This site includes two applets, one for visualizing the approximation of a square wave by trigonometric series, and the other for hearing successive approximations to the displacement curve of a sound wave.
This utility uses the free Flash player plug-in resident in most browsers to allow the user to plot parametrically defined surfaces in spherical coordinates. Many examples and directed exercises are included.
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major topics of modern enumerative and algebraic combinatorics with emphasis on partition identities, young tableaux bijections, spanning trees in graphs, and random generation of combinatorial objects. There is some discussion of various applications and connections to other fields. |
Math.NET aims to provide a self contained clean framework for symbolic mathematical (Computer Algebra System) and numerical/scientific computations, including a parser and support for linear algebra, complex differential analysis, system solving and more |
The Carson Algebra Series addresses two fundamental issues–individual learning styles and student comprehension of key mathematical concepts–to meet the needs of today's students and instructors. Carson's Study System, presented in the "To the Student" section at the front of the text, adapts to the way each student learns to ensure their success in this and future courses. The consistent emphasis on the big picture of algebra, with pedagogy and support that helps students put each new concept into proper context, encourages conceptual understanding. CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book. |
Mathematics End of Course Supports
Topic outline
General
Mathematics End-of-Course Supports
Welcome to the WA Mathematics End-of-Course Supports Moodle. This is a place for educators to share resources and collaborate as they prepare students for the End-of-Course (EOC) exams. Uploaded resources will not be reviewed by OSPI staff, but instead are the responsibility of the teacher to analyze resources and determine if they suit the needs of their students. If there are questions regarding the use of this site, please email Greta.Bornemann@k12.wa.us or Jennifer.Judkins@k12.wa.us.
This course contains the following sections:
Section 1: Discussion Forums
Section 2: Teacher-Created Resources Database
Section 3: Other Sources of Sample EOC items
Section 4: EOC Item Writing
Section 5: Calculator Policy
Section 6: Common Core Resources
Section 7: Mathematics Collection of Evidence
View each section by scrolling down the page or by clicking on the Section Links in the upper left corner of the page.
This is the PowerPoint presentation delivered at the WERA conference in December 2011. This presentation highlights EOC information, resources and key documents including EOC Updates for 2012 and 2011 Lessons from Scoring Student Work.
Other Sources of EOC Sample Items
The purpose of these documents is to identify sample items and previously released items that align to the 2008 Mathematics Standards assessed on the End-of-Course Exams. Links to released items, sample items and draft COE tasks are listed by PE so that teachers are able to easily locate items aligned to each Performance Expectation.
This document contains information for eductors about EOC Exams and Retake Exams as well as new EOC sample items for Year 1 and Year 2. Sample items for Year 1 begin on page 14; sample items for Year 2 begin on page 29.
This document contains sample EOC items in multiple choice, completion, and short answer formats, with solutions. Sample items for Year 1 begin on page 13; sample items for Year 2 begin on page 18.
EOC Item Writing
2012 Item Writing for End-of-Course Exams
The Office of Superintendent of Public Instruction Mathematics Assessment office held the end-of-course exams Item Writing Workshop February 28 - March 1, 2012.
Participants received instruction in writing multiple-choice, completion, and short-answer items aligned to Washington State Mathematics Standards, wrote sample EOC items for classroom use, and wrote exam items that will be used on the Washington Comprehensive Assessment Program. Participants described this experience as an excellent opportunity for professional development that provided them with insights for teaching and assessing standards.
The Powerpoint presentation: 2011 EOC Item Writing was used in March 2011 to train Washington State teachers to write items for the state-level end-of-course exams. The presentation was given over 3 days and represents approximately 10 hours of training. This is great information for a teacher who wants to know more about design, validity, and formatting considerations for the state-level end-of-course exams.
The Test & Item Specs Activity and EOC Item Spec Scavenger Hunts are activities that can help teachers delve deeper into the format of and information in the Test and Item Specifcations. We suggest using these as group activities and discussing your responses for each activity.
The Word Problems vs. Process Items helps distinguish the difference between items assessing content Performance Expectations that ask students to solve word problems and items assessing process Performance Expectations that require problem solving strategies. Teachers can use these examples to classify the work they are asking students to do to ensure students have practice both solving word problems and solving problems.
These item templates are used as general guidelines for the format of EOC assessment items. Examples of EOC assessment items can be found in the Item Writing Guidelines document (link above) and in the EOC Sample Item Booklet, EOC Updates to 2012, EOC Updates to 2011, and the Released Item Documents and Quick Guides (links at the top of this page under OSPI Links and Resources).
These rubric templates are used as general guidelines for the format of rubrics for EOC short-answer items. Examples of completed EOC item rubrics based on the new standards can be found in the Item Writing Guidelines document (link above) and in the Sample EOC Short-Answer Items documents below.
Calculator Policy and Resources
Approved calculators may be used on the EOC exams. A scientific calculator is sufficient for all items on all end-of-course (EOC) mathematics assessments, but students may use any calculator that does not have any of the prohibited features listed in the calculator policy. Proctors must clear calculator memory both before and after each testing session. Follow the link above to view the complete calculator policy.
The Illustrative Mathematics Project will provide guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards, and by publishing other tools that support implementation of the standards.
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Mathematics Collection of Evidence (COE)
Please click here for information regarding the Mathematics Collection of Evidence, eligibility requirements, and tasks for Algebra and Geometry. |
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Table of Contents
1. The Nature of Differential Equations.2. First Order Equations. 3. Second Order Linear Equations. 4. Qualitative Properties of Solutions. 5. Power Series Solutions and Special Functions. 6. Fourier Series and Orthogonal Functions. 7. Partial Differential Equations and Boundary Value Problems. 8. Some Special Functions of Mathematical Physics. 9. Laplace Transforms. 10. Systems of First Order Equations. 11. Nonlinear Equations. 12. The Calculus of Variations. 13. The Existence and Uniqueness of Solutions. 14. Numerical |
1568581114
9781568581118
Math Behind Wall Street:Useful both for novice and experienced investors on Wall Street eager to minimize their risks, a comprehensive guide explains the elements of statistics and probability, the concept of the riskless portfolio, and more |
AWM Electronic Newsletter
Mathematics Foundation of America (MFOA)
posted Jun 17, 2010, 10:29 PM by Glenna Buford
The purpose of MFOA is to ensure that the mathematically talented high school student receives mathematics education appropriate for a future mathematician by providing suitable mathematics summer programs and mathematics mentors. |
Basic Mathematics - 8th edition
Summary: For the modern student like you--Pat McKeague's BASIC MATHEMATICS, 8E--offers concise writing, continuous review, and contemporary applications to show you how mathematics connects to your modern world. The new edition continues to reflect the author's passion for teaching mathematics by offering guided practice, review, and reinforcement to help you build skills through hundreds of new examples and applications. Use the examples, practice exercises, tutorials, videos, and e-Book sec...show moretions in Enhanced WebAssign to practice your skills and demonstrate your knowledgesoftcover >>> annotated teacher edition with publisher notations on cover & New book no writing or marks has All Students content and all answers. text only no access code or other supplements. ship...show more immediately - Expedited shipping available ...show less
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This book in graph theory is intended the typical freshman or sophomore in computer science and related disciplines with a first exposure to the mathematical topics essential to their study of computer science or digital logic.There is an introduction of graph and tree in this book.This focus on the description of basic problems involving graph and tree and their applications. |
Improper Riemann Integrals is the first book to collect classical and modern material on the subject for undergraduate students. The book gives students the prerequisites and tools to understand the convergence, principal value, and evaluation of the improper/generalized Riemann integral. It also illustrates applications to science and engineeringThe first derivative of a particle coordinate means its velocity, the second means its acceleration, but what does a fractional order derivative mean? Where does it come from, how does it work, where does it lead to? The two-volume book written on high didactic level answers these questions. Fractional Derivatives for Physicists and Engineers—... more...
The book "Single variable Differential and Integral Calculus" is an interesting text book for students of mathematics and physics programs, and a reference book for graduate students in any engineering field. This book is unique in the field of mathematical analysis in content and in style. It aims to define, compare and discuss topics in... more... |
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Epstein presents the fundamental concepts of modern differential geometry within the framework of continuum mechanics. Divided into three parts of roughly equal length, the book opens with a motivational chapter to impress upon the reader that differential geometry is indeed the natural language of continuum mechanics or, better still, that the latter is a prime example of the application and materialisation of the former. In the second part, the fundamental notions of differential geometry are presented with rigor using a writing style that is as informal as possible. Differentiable manifolds, tangent bundles, exterior derivatives, Lie derivatives, and Lie groups are illustrated in terms of their mechanical interpretations. The third part includes the theory of fiber bundles, G-structures, and groupoids, which are applicable to bodies with internal structure and to the description of material inhomogeneity. The abstract notions of differential geometry are thus illuminated by practical and intuitively meaningful engineering applications. |
Student Life
Welcome to the Math Zone
On behalf of
the College of Science and Technology and Department of Mathematics, we
welcome you to the website for
the Southern Miss Math Zone. Education in basic mathematics is critical
for success in life. The Math Zone is an interactive, computer-based,
mathematics learning environment. Starting in Spring semester 2007 the
Southern Miss mathematics department is using this new approach to
teach basic mathematics. The College believes that the establishment of
this innovative learning environment will enable introductory students
to learn more math.
Learning Through Technology
Students are introduced to a new method of learning through technology
Teaching Through Interaction
One-on-one interactions between students and teachers personalize the learning experience
New Facility
Newly rennovated facility provides more space and a better atmosphere for students to learn |
This free algebra textbook from Boundless Learning is based off openly available educational resources such as "government resources, open educational repositories, and other openly licensed websites." The textbook...
Created by David Liao, this site offers a way for scientists, educators and others to investigate biological systems using a physical sciences perspective. On the site, visitors will find video tutorials, classroom fact...
The Mathematical Association of America (MAA) provides a range of high-quality educational resources for educators all across the United States and the world. Recently, they completed digitizing over 114 years of their...
This NASA site provides an introduction to black holes, including how black holes form and how they can be detected. Numerous links provide additional information. The site also contains a fun multiple-choice quiz, cool...
Understanding Algebra is a textbook written by James Brennan of Boise State University. The entire contents of the textbook are located on this site, and a PDF version is also available through the author?s Website. B... |
Art And Craft of Problem Solving
9780471789017
ISBN:
0471789011
Edition: 2 Pub Date: 2006 Publisher: John Wiley & Sons Inc
Summary: You' ve got a lot of problems. That's a good thing. Across the country, people are joining math clubs, entering math contests, and training to compete in the International Mathematical Olympiad. What's the attraction? It's simple--solving mathematical problems is exhilarating! This new edition from a self-described "missionary for the problem solving culture" introduces you to the beauty and rewards of mathematical p...roblem solving. Without requiring a deep background in math, it arms you with strategies and tactics for a no-holds-barred investigation of whatever mathematical problem you want to solve. You'll learn how to: get started and orient yourself in any problem. draw pictures and use other creative techniques to look at the problem in a new light. successfully employ proven techniques, including The Pigeonhole Principle, The Extreme Principle, and more. tap into the knowledge gained from folklore problems (such as Conway's Checker problem). tackle problems in geometry, calculus, algebra, combinatorics, and number theory. Whether you're training for the Mathematical Olympiad or you just enjoy mathematical problems, this book can help you become a master problem-solver! About the Author PaulAmerican
Zeitz, Paul is the author of Art And Craft of Problem Solving, published 2006 under ISBN 9780471789017 and 0471789011. Five hundred thirty seven Art And Craft of Problem Solving textbooks are available for sale on ValoreBooks.com, one hundred thirty seven used from the cheapest price of $41.50, or buy new starting at $53 newly revised Second Edtion of this distinctive text uniquely blends interesting problems with strategies, tools, and techniques to develop mathematical skill and intuiti [more]
The newly revised Second Edtion of this distinctive text uniquely blends interesting problems with strategies, tools, and techniques to develop mathematical skill and intuition necessary for problem solving. Readers are encouraged to do math rather |
VISUAL MATH DICTIONARY
Price:$16.95 Available Qty: 13
Qty:
The most accessible and useful guide to math terms and procedures available, this reference has over 600 definitions and scores of additional resources including tables, rules and symbols. Math terms are explained simply and visually with ample examples in two colors and clear, concise wording. Hundreds of illustrations make it easy for students to acquire and retain key knowledge. Visual descriptions of many important concepts abound, including rules for finding area and volume, data representation, financial math, rational numbers equivalents, factors, figurative numbers, the international system, transformations, prime and composite numbers and much more. A wonderful desktop resource for students in grades 5 and up or for anyone who needs a ready reference for math. 128 pages, paperback. |
Discovery Math was designed to meet 21 century learning and meet common core standards. This version was specifically designed for Kindergarten students, but with some curriculum modification it can... More > be applied to 1st grade and special education.< Less
Discover Physics is a conceptual physics textbook intended for students in a nonmathematical one-semester general-education course. For more information about the book, see its web page. The new... More > version of Discover Physics is Conceptual Physics. I'm no longer actively maintaining Discover Physics, and I recommend that new adopters use Conceptual Physics instead.< Less |
Using and Understanding Mathematics - 4th edition
Summary: Most students taking this course do so to fulfill a requirement, but the true benefit of the course is learning how to use and understand mathematics in daily life. This quantitative reasoning text is written expressly for those students, providing them with the mathematical reasoning and quantitative literacy skills they'll need to make good decisions throughout their lives. Common-sense applications of mathematics engage students while underscoring the practical, esse...show morential uses of math.
Features
Practical Matters. Focusing on matters of high practical importance, this feature highlights common-sense applications of math such as avoiding credit card trouble and spotting a bad cell phone deal.
A Brief Review. This feature reviews key mathematical skills students should have learned previously, but which many students still need review and practice. They appear in the book wherever a particular skill is first needed, and exercises based on the review boxes can be found at the end of the unit.
Thinking About. Building upon the main narrative, this feature reaches beyond to a deeper level of mathematical understanding. Examples include boxes on the proof of the Pythagorean theorem and on Zeno's paradox.
Time Out to Think. Appearing throughout the book, the Time Out to Think features pose short conceptual questions designed to help students reflect on important new ideas. They also serve as excellent starting points for classroom discussions.
Margin Features. A wide margin leaves room for students to make notes while studying. The margin also contains material that spurs student interest in three basic forms:
By the Way features contain interesting notes and asides relevant to the topic at hand
Historical Note remarks give historical context to the ideas presented in the chapter
Technical Notes contain details that are important mathematically for students looking for more depth
Now Try Exercises. At the end of every in-text example students are directed to Now Try a specific exercise, immediately testing their comprehension of the material.
Does It Make Sense? These qualitative exercise questions test conceptual understanding by asking whether given statements are sensible and asking students to explain why or why not.
Basic Skills and Concepts. Covering concepts from the unit, these exercises can be used for homework assignments or for self-study. Answers to most odd-numbered exercises appear in the back of the book.
Web Projects. The Web Projects require students to search for data or other information online. They can be used for extended projects, discussions, group activities, or essays.
In the News. In these exercises, students are challenged to find examples of unit concepts in the news or in their daily lives. These questions may be assigned as homework or used for class discussions. |
The equation parser-calculator for COMPLEX number math expressions with parse-tree builder and user-friendly interface for parsing and calculation a run-time defined math complex expression. The math expressions... |
Calculus: Early Transcendentals
What's the ideal balance? How can you make sure students get both the computational skills they need and a deep understanding of the significance of ...Show synopsisWhat's the ideal balance? How can you make sure students get both the computational skills they need and a deep understanding of the significance of what they are learning? With your teaching--supported by Rogawski's "Calculus Second Edition"--the most successful new calculus text in 25 years! Widely adopted in its first edition, Rogawski's "Calculus" worked for instructors and students by balancing formal precision with a guiding conceptual focus. Rogawski engages students while reinforcing the relevance of calculus to their lives and future studies. Precise mathematics, vivid examples, colorful graphics, intuitive explanations, and extraordinary problem sets all work together to help students grasp a deeper understanding of calculus. Now Rogawski's "Calculus" success continues in a meticulously updated new edition. Revised in response to user feedback and classroom experiences, the new edition provides an even smoother teaching and learning experience.Hide synopsis
Reviews of Calculus: Early Transcendentals
Good thorough examples Feb 3, 2011
This is a great book and it is very easy to understand. But the only downfall of it is I wish the answers to the selected answers showed each step to finding the solution because even though the problems are based on the same concept, some questions are harder. But it's an overall good back and totally worth it :) |
There is a student and parent section at this website that has a variety topics of interest for students taking AP classes.
ARC (Academic Resource Corporation)
This is a for hire tutorial site. I have viewed this site but I am not an expert on all the services they offer. My first impression was it could be helpful for students needing remedial work on prerequisite skills.
Dictionary
This is an on-line dictionary
Discovering Advanced Algebra textbook
You can acess your Algebra 2 textbook on-line.
Graph Paper
Printable graph paper.
Graph Paper
Printable graph paper, include graph for precalculus and calculus.
Graphing Calculator
This is a graphing calculator.
Interactivate: Lessons in Math and Science
The subjects covered include geometry, algebra, probability,
and discrete functions. Within each activity, visitors can read more about
the intended audience for each one, and also learn about the prerequisites
and objectives for each lesson.
Math Resources
Internet Resources for the Mathematics Students [Last reviewed on
September 1, 1999]. This is a great resource for all kinds of math topics.
mathmistakes.info
Look here for extra practice in Algebra, Trigonometry and Calculus. You will find flashcards, common mistakes that are made and problems or to test yourself. Also you will find additional links for tutoring.
Precalculus with Limits AGA 4e
Select problems from our book can be printed to save you from copying a complex graph. Scroll down until you see our book cover and click on it. |
Description:
The American Mathematical Association of Two-Year Colleges (AMATYC) has compiled a collection of mathematics resources related to various subjects and disciplines. "Math Across the Community College Curriculum" is the title of the collection, which includes great math resources and applications for educators and students alike. Carol Hay and Jessie Klein from Middlesex Community College created this resource for elementary education majors. A course overview provides a description of the goals, learning outcomes, and activities associated with the resource. Four activities are provided here for use in the classroom. They include "Alien Genetics" (an activity centered around the determination of genotypes and phenotypes of offspring), "Fast Plant Genetics," "Cell Size," and "Skin Color Genetics." These are great resources to incorporate in the classroom, and enhance the learning experiences of students. |
MA 150 Precalculus Mathematics Scagliola, David consideration of those topics in algebra and trigonometry necessary for the calculus. Topics include: mathematical analysis of the line, the conic sections, exponential and logarithmic functions, circular functions, polynomial and rational functions, mathematical induction, and theory of equations. Pre-requisite: MA131 or equivalent. 3:0:3
Educational Philosophy: My educational philosophy is based on interaction and active involvement--learning by doing. This course will be primarily lecture based, however, students are always encouraged/required to: ask and answer questions, accomplish reading assignments, and practice/practice...practice... In addition, there will be opportunities for students to demonstrate their understanding of materials covered.
Instructor Learning Outcomes
Demonstrate understanding of Functions and Graphs
Improve problem solving skills
Demonstrate their ability to solve: linear equations, quadratic equations and systems of equations
Prepare a foundation for more advanced courses
Class Assessment: Students are expected to read the sections to be discussed in class prior to the class and be prepared to work examples and ask questions. Mathematics can only be learned through practice, therefore, 10% of your grade will be based on homework. All examinations will be modeled from homework problems, so there should be no surprises to students who have done the required homework. SHOW ALL OF YOUR WORK on homework assignments and exams! An answer with no work shown is either right or wrong; but, an answer showing your work may get some credit, even if it is not completely correct.
Grading: Homework - 10%
Project - 20%
Midterm - 30%
Final - 40%
Late Submission of Course Materials: Homework will be collected daily. All homework must be turned in NLT the final exam.
Make-Up Examinations: on a case by case basis
Classroom Rules of Conduct: While in class, the class should be your primary focus. Disruptions of class due to communications devices have become so prevalent that they are a major distraction in class (to you, to the instructor and to other students). For this reason such devices must not be brought to class or must be inactivated during the class lecture. Eating and drinking beverages (other than water) is not allowed in the halls or |
A book that is designed to cover all the mathematics required for physics being studied at undergraduate level (at least first and second year). It does what it says on the cover. It is very comprehensive, however, reading it is not easy. The print is small, and the book is so large, that not only is it physically difficult, but you become depressed by the fact that no matter how fast you read or understand, it'll take a while to get through it!! Probably two years! Probably the only book you need for the maths involved in undergraduate physics, if only for reference.
This review is from: Mathematical Methods for Physics and Engineering (3rd edition): A Comprehensive Guide (Paperback)
This book is simply the best. It is lightyears better than Boas (the most often suggested alternative), and it basically contains all the maths You'll ever need in all but the most theoretical undergraduate course of any natural science (well, except maths, if that's a science ;-) ).
In fact, now slowly finishing my PhD in physics, I think I can say that unless You are doing actual theoretical/mathematical physics, it probably contains all or most of the maths You'll need for the rest of Your life.
This book is a watershed in the teaching of calculus and the essential mathematical methods required by undergraduate mathematicians, physicists and engineers.It will easily become the standard reference for methods courses , if it has not done so already.It starts right at the beginning with a refresher in basic calculus etc , and then proceeds to carefully develop multi-variable calculus, linear differential equations,complex variables, calculus of variations , tensors, representations, numerical analysis and prob&stats.What I really like about this book is the way general curvilinear coordinate transformations are explained at the end of the vector calculus section, to which you can refer when reading the chapter on tensors.I know of no other methods textbook which introduces tensors like this:many lesser texts (and that means all the rest) seem to feel that it is sufficient to teach people about raising indices, and give readers some vague hand-waving about coordinate transformations.This book is one to buy for this alone, as you will then have a firm grasp of why the tensor notation is like it is.Indeed, I would say that this book makes most other methods textbooks look the half-arsed disgrace that they are.Jacobians could be more carefully introduced, and the writing style can be a little Enid Blyton (phrases like 'one can consult the many excellent textbooks on such and such' can become rather monotonous), but apart from tiny niggles like this, this really is a truly comprehensive methods book, which really starts from the beginning and takes you well into the foothills of genuinely advanced techniques, and which you will keep through your professional life.An instant classic.
This review is from: Mathematical Methods for Physics and Engineering (3rd edition): A Comprehensive Guide (Paperback)
I phrased the title of this review carefully. Riley, Bence and Hobson is a standard text for many engineering and physics undergraduate courses with good reason. It covers the majority of topics required to complete a physics degree and will remain useful after you graduate. I bought mine in my first year (now in year 2) and it looks like i'll be using it for a long time yet.
There are plenty of derivations, discussions and perhaps most importantly for physics/engineering students, examples that are related to the course. This could be relating partial derivatives and heat transfer, fourier transforms and Fraunhofer diffraction - you get the idea. There are plenty of general maths examples and enough problems to keep you busy for a few nights.
On the downside, this is - for me at any rate - a reference text first and foremost. Students looking for a lucid account of the mathematics behind the physics should look no further, but it isn't necessarily the book to buy if you want lots of simple problems for practice. The solutions manual goes a little way towards sort this out, you can buy it them both as a pack (recommended) and it covers many of the examples in depth. If you just want a book for practising your vector calculus or ironing out your calculus worries, look to one of Schaum's outlines instead.
Whilst the discussion is, on the whole, pretty lucid, it does move quickly. A certain amount of reading between the lines is required for some topics and this isn't necessarily a bad thing, but it might put some people off. I found better explanations of things like Fourier transforms in books on digital signal processing, for instance. What you will find is that almost all the maths you'll ever do on a science course is in the book, even if it doesn't have a lengthy paragraph explaining it.
Mainly it is important to understand where the maths is coming from instead of blindly applying the required formula to set situations. Inevitably there will come a time when you actually have to know what the symbols are doing, rather than what process to apply to them. When that time comes, this is what you look to.
The verdict: It's a great book, it covers all the bases and has just the right amount of explanation to jog your memory on a forgotten topic. I would not recommend it for learning new principles from though, unless you really need to and stick to Schaum's for general practise - and for that I'd give it a 4.5.
This review is from: Mathematical Methods for Physics and Engineering (3rd edition): A Comprehensive Guide (Paperback)
I have been looking for a complete guide to higher level Mathematics (for revision of a wide range of methods such as Fourier Transforms, Calculus, Group Theory etc.) and spent a considerable time looking at the various choices on Amazon. This book seemed to have the most consistent set of 5 star reviews - so I took the plunge.
I am delighted - it is well written, thoroughly comprehensive, has every topic I was looking for, and, although HUGE (well over 1300 pages!), is clearly laid out and easy to read.
I wish I had had this book when I was younger (I am now over half a century old!). I am a Computer Science PhD, rather than an Engineer or Physicist - but this book is the one for me!
This review is from: Mathematical Methods for Physics and Engineering (3rd edition): A Comprehensive Guide (Paperback)
This review is from: Mathematical Methods for Physics and Engineering (3rd edition): A Comprehensive Guide (Paperback)
I am a games developer and I was looking for a good textbook that I could turn to for the math involved in advanced rendering and physics. I am very pleased to have bought the third edition of this excellent work. For me this book is an absolute winner. It covers a huge range of topics, from quadratic equations to spherical harmonics, differential equations and quantum operators; yet the treatment does not feel hurried and terse like it does in some other books that cover such a scope (Kreyszig for example). It's written in a clear and engaging style and the print is not small - presumably profquantum is refrerring to an earlier edition in his/her review. Run, don't walk, to buy this book
This review is from: Mathematical Methods for Physics and Engineering (3rd edition): A Comprehensive Guide (Paperback)
Contains most (if not all) of the mathematical material needed for and undergrade physics course (definitely up to Yr3, possibly after) whilst at the same time being very accessible for first/ second year ability. Each chapter starts from the basics , and gradually builds up to required level. Very useful to have answers at the back, useless otherwise (cant check whether you are correct or not). Exceptionally good section on vector calculus, as well as applications to different parts of physics.
This review is from: Mathematical Methods for Physics and Engineering (3rd edition): A Comprehensive Guide (Paperback)
This is simply the best maths textbook for physicists. By the best I mean the easiest to understand, the easiest to find what your looking for and the most comprehensive. There are worked examples and the questions in the book are also good with answers for the odd numbered questions. Yes it may look like a door stop but you do need alot of maths!! anyway it is easy to find what your looking for so thie size isn't an issue.
This review is from: Mathematical Methods for Physics and Engineering (3rd edition): A Comprehensive Guide (Paperback)
I ordered this to refresh my mathematics 40 years after taking a degree in physics. I was looking for a book to cover all the techniques that I vaguely remember with a practical approach that starts with the very basics but includes all the detail needed. This book does just that. The emphasis is on the application of mathematical techniques and examples from physics and engineering are frequently explored to illustrate the theory. |
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Overview
Mathematics for Economists, a new text for advanced undergraduate and beginning graduate students in economics, is a thoroughly modern treatment of the mathematics that underlies economic theory.
An abundance of applications to current economic analysis, illustrative diagrams, thought-provoking exercises, careful proofs, and a flexible organization-these are the advantages that Mathematics for Economists brings to today's classroom.
Related Subjects
Meet the Author
Carl P. Simon is professor of mathematics at the University of Michigan. He received his Ph.D. from Northwestern University and has taught at the University of California, Berkeley, and the University of North Carolina. He is the recipient of many awards for teaching, including the University of Michigan Faculty Recognition Award and the Excellence in Education Award.
Lawrence Blume is professor of economics at Cornell University. He received his Ph.D. from the University of California, Berkeley, and has taught at Harvard University's Kennedy School, the University of Michigan, and the University of |
More About
This Textbook
Overview
R. L. Moore: Mathematician & Teacher presents a full and frank biography of a mathematician recognized as one of the principal figures in the 20th Century progression of the American school of point set topology. He was equally well known as creator of the Moore Method (no textbooks, no lectures, no conferring) in which there is a current and growing revival of interest and modified application under inquiry-based learning projects in both the United States and the United Kingdom.
Parker draws on oral history, with first-person recollections from many leading figures in the American mathematics community of the last half-century. The story embraces some of the most famous and influential mathematical names in America and Europe from the late 1900s in what is undoubtedly a lively account of this controversial figure, once described as Mr. Chips with Attitude. He was the first American to become a Visiting Lecturer for the American Mathematical Society, was a member of the National Academy of Sciences, published 68 papers and a book that is still referred to seventy years later and that has been the subject of literally hundreds of papers by other mathematicians around the globe.
Three of Moore's students followed him as president of the American Mathematical Society, and three others became vice-presidents. Five served as president of the Mathematical Association of America, and three became members of the National Academy of Sciences.
What People Are Saying
Paul R. Halmos
"Some say that the only possible effect of the Moore Method is to produce research mathematicians-but I don't agree. The Moore Method is, I am convinced the right way to teach anything and everything-it produces students who can understand and use what they have learned. It does, to be sure, instill the research attitude in the student-the attitude of questioning everything and wanting to learn answer actively-but that's a good thing in every human endeavor, not only in mathematical research."
—Santa Clara University
Richard D. Anderson
"I first studied under Moore in 1941. I found him to be an inspirational kind of teacher, and a man totally dedicated to his students, more so than any other teacher I've known."
—Boyd Professor Emeritus, Louisiana State |
LiveMath Labs is a collection of interactive mathematics laboratories providing hands-on experience with mathematical concepts and skills. Each lab is completely self-contained with interactives powered by LiveMath Maker and accompanying lab sheets full of descriptions, directions, leading questions, thought provoking hypotheses, and investigative report areas. The labs can be used for individual investigation or group explorations. They are ready to supplement any mathematics textbook, by bringing the text examples to life and allowing learners to manipulate the situation as their curiosity guides them. The labs can also be edited by any instructor and quickly tailored to energize the classroom discussion or activity. LiveMath Labs have been designed with student experience in mind.
Active students have a much better chance to acquire new skills and understand underlying concepts. Encouraging passive students to become active students requires an environment where they can be active. LiveMath Labs creates this environment. Enrich your current textbookıs presentation with an environment where students can control the examples. Here students can change prominent settings and compare the results. Here students can grab a hold of 3D representations and graphs and examine the shapes and regions in real time. Here students can extend the interactive situations to explore their own interests. Here students can experiment and investigate. Here students get experience. Here students learn.
Each LiveLabs Lab consists of one lab sheet, which guides the student through the investigation, and supporting interactives. The lab sheet begins with description and background and then provides step-by-step instructions on how to modify the values in the interactive followed by resources for collecting and comparing the resulting information or data. Each lab then follows up with a guided comparison from which students can describe their own hypotheses concerning the material. Finally, the student may check their hypotheses and further shape the interactive to explore their own thoughts and questions.
After gaining hands-on experience, viewing multiple representations, and authoring their own hypotheses students are much better prepared to read the textbook presentation, follow a teacherıs explanation, discuss concepts and skills with their classmates, or tackle homework problem...activities in which only active students can participate |
Key to Algebra - Student Book 2. Paperback student workbook of 37 pages. A great Algebra supplement for the homeschool student. New concepts are presented in simple language, making them easy to understand, with easy to follow examples. Book 2 Focus - Variables, Terms, and Expressions. |
Chapter Zero Fundamental Notions of Abstract Mathematics
9780201437249
ISBN:
0201437244
Edition: 2 Pub Date: 2000 Publisher: Addison-Wesley
Summary: Chapter Zero is designed for the sophomore/junior level Introduction to Advanced Mathematics course. Written in a modified R.L. Moore fashion, it offers a unique approach in which students construct their own understandings. However, while students are called upon to write their own proofs, they are also encouraged to work in groups. There are few finished proofs contained in the text, but the author offers proof ske...tches and helpful technique tips to help students as they develop their proof writing skills. This book is most successful in a small, seminar style class.
Schumacher, Carol is the author of Chapter Zero Fundamental Notions of Abstract Mathematics, published 2000 under ISBN 9780201437249 and 0201437244. Five hundred eighty five Chapter Zero Fundamental Notions of Abstract Mathematics textbooks are available for sale on ValoreBooks.com, one hundred thirty eight used from the cheapest price of $49 |
0941355, Grades 3-4 (Math by All Means)
The lessons in this book actively involve students in exploring geometric ideas through hands-on investigations with two- and three-dimensional shapes. Students also develop greater proficiency in logic, number, and measurement.
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William Briggs
"Briggs's book is in some sense an update of Polya's classic, How to Solve It. Certainly Briggs pays due homage to the master, cites his four main principles of problem solving, and organizes his text in a manner that at least pays homage to Polya. But Briggs goes much further. His writing style is lively and attractive. He gets in the reader's face and stays in his/her face from page one. He does this in a friendly way, one that gets the reader involved and keeps him/her involved as the work progresses. …The student will be carried along by this book, and ever anxious to learn the next new idea. I like Briggs's book so well that I would certainly make considerable use of his text the next time that I teach problem-solving." -- Steven G. Krantz, Washington University in St. Louis.
Mathematics educators agree that problem solving is one of the essential skills their students should possess, yet few mathematics courses or textbooks are devoted entirely to developing this skill. Supported by narrative, examples, and exercises, Ants, Bikes, and Clocks: Problem Solving for Undergraduates is a readable and enjoyable text designed to strengthen the problem-solving skills of undergraduate students. The book, which provides hundreds of mathematical problems, gives special emphasis to problems in context, often called story problems or modeling problems, that require mathematical formulation as a preliminary step. Both analytical and computational approaches, as well as the interplay between them, are included.
With its lively and engaging writing style and interesting and entertaining problems, Ants, Bikes, and Clocks will strengthen students' mathematical skills, introduce them to new mathematical ideas, demonstrate for them the connectedness of mathematics, and improve both their analytical and computational problem solving. One of the remarkable and unusual features of this text is that it encourages students to use the computer for experimentation. In fact, Briggs uses a variety of tricks that encourage students to use any tool at hand to test their ideas.
Audience
Ants, Bikes, and Clocks is an excellent text for an undergraduate problem-solving course or as a resource for mathematics educators, providing hundreds of mathematical problems that can be used in any course. Mathematically the book relies on two semesters of calculus, although much of the book requires only precalculus skills. |
Problem Solving Approach to Mathematics - With CD - 10th edition
Summary: The new edition of this best-selling text includes a new focus on active and collaborative learning, while maintaining its emphasis on developing skills and concepts. With a wealth of pedagogical tools, as well as relevant discussions of standard curricula and assessments, this book will be a valuable textbook and reference for future teachers. With this revision, two new chapters are included to address the needs of future middle school teachers, in accordance to the NCTM Focal Poin...show morets document94VeryGood
Bookmonger.Ltd Hillside, NJ
2009 Hardcover Very good *** CD-ROM INCLUDED *** |
Course Learning Outcomes The student will: • Use the concepts of definite integrals to solve problems involving area, volume, work, and other physical applications. • Use substitution, integration by parts, trigonometric substitution, partial fractions, and tables of anti-derivatives to evaluate definite and indefinite integrals. • Define an improper integral. • Apply the concepts of limits, convergence, and divergence to evaluate some classes of improper integrals. • Determine convergence or divergence of sequences and series. • Use Taylor and MacLaurin series to represent functions. • Use Taylor or MacLaurin series to integrate functions not integrable by conventional methods. • Use the concept of parametric equations and polar coordinates to find areas, lengths of curves, and representations of conic sections. • Apply L'hôpital's Rule to evaluate limits of indeterminate forms.
Calculator: Graphing Calculator required. TI 83, TI 84 or TI 86 series calculators recommended. Calculators capable of symbolic manipulation will not be allowed on tests. Examples include, but are not limited to, TI 89, TI 92, and Nspire CAS models and HP 48 models. Neither cell phones nor PDA's can be used as calculators. Calculators may be cleared before tests.
Differentiation and Integration Formulas: Students are expected to memorize the differentiation formulas on the last page inside the back cover of the text and integration formulas 1- 20 in the attached chart.
Textbook Sections (for Fall, 2013 only)
Preliminaries
3.8 Derivatives of Logarithmic and Exponential Functions
3.9 Derivatives of Inverse Trigonometric Functions
4.7 L'Hopital's Rule
6.8 Logarithmic and Exponential Functions Revisited
6.9 Exponential Models
6.10 Hyperbolic Functions
Chapter 7. Integration Techniques
7.1 Basic Approaches
7.2 Integration by Parts
7.3 Trigonometric Integrals
7.4 Trigonometric Substitution
7.5 Partial Fractions
7.6 Other Integration Strategies
7.7 Numerical Integration
7.8 Improper Integrals
Chapter 8. Differential Equations
8.1 Basic Ideas
8.3 Separable Differential Equations
Chapter 9. Sequences and Infinite Series
9.1 An Overview
9.2 Sequences
9.3 Infinite Series
9.4 The Divergence and Integral Tests
9.5 The Ratio, Root and Comparison Tests
9.6 Alternating Series
Chapter 10. Power Series
10.1 Approximating Functions with Polynomials
10.2 Properties of Power Series
10.3 Taylor Series
10.4 Working with Taylor Series
Chapter 11. Parametric and Polar Curves
11.1 Parametric Equations
11.2 Polar Coordinates
11.3 Calculus in Polar Coordinates
11.4 Conic Sections
Textbook Sections (Effective Spring, 2014)
Chapter 6. Appliations of Integration
6.1 Velocity and Net Change
6.2 Regions Between Curves
6.3 Volume by Slicing
6.4 Volume by Shells
6.5 Lengths of Curves
6.6 Surface Area
6.7 Physical Applications (cover work and density and mass; all other topics optional) |
Geometric Algebra 2: ApplicationsPresentation Transcript
Geometric Algebra
Part 2: Applications and the state of the art
"... provides a single, simple mathematical framework which
eliminates the plethora of diverse mathematical descriptions and
techniques"
[McRobie and Lasenby, 1999]
Vitor Fernando Pamplona |
Synopses & Reviews
Please note that used books may not include additional media (study guides, CDs, DVDs, solutions manuals, etc.) as described in the publisher comments.
Publisher Comments:
The purpose of Glimpses of Algebra and Geometry is to fill a gap between undergraduate and graduate mathematics studies. It is one of the few undergraduate texts to explore the subtle and sometimes puzzling connections between Number Theory, Classical Geometry and Modern Algebra in a clear and easily understandable style. Over 160 computer-generated images, accessible to readers via the World Wide Web, facilitate an understanding of mathematical concepts and proofs even further. Glimpses also sheds light on some of the links between the first recorded intellectual attempts to solve ancient problems of Number Theory and Geometry and twentieth century mathematics. GLIMPSES will appeal to students who wish to learn modern mathematics, but have few prerequisite courses, and to high-school teachers who always had a keen interest in mathematics, but seldom the time to pursue background technicalities. Even postgraduate mathematicians will enjoy being able to browse through a number of mathematical disciplines in one sitting. This new edition includes invaluable improvements throughout the text, including an in-depth treatment of root formulas, a detailed and complete classification of finite Möbius groups a la Klein, and a quick, direct, and modern approach to Felix Kleins "Normalformsatz," the main result of his spectacular theory of icosahedron and his solution of the irreducible quintic in terms of hypergeometric functions. Gabor Toth is the Chair and Graduate Director of the Department of Mathematical Sciences at Rutgers University, Camden. His previous publications include Finite Mobius Groups, Spherical Minimal Immersions and Moduli (2001), Harmonic Maps and Minimal Immersion Through Representation Theory (1990) and Harmonic and Minimal Maps with Applications in Geometry and Physics (1984). Professor Toths main fields of interest involve the geometry of eigenmaps and spherical minimal immersions and the visualization of mathematics via computers.
Synopsis:
Synopsis:
"Synopsis"
by Springer,"Synopsis"
by Springer, |
Math Introduction to Using Formulas
Overview: A math formula is shorthand for expressing a relationship between quantities, numbers or variables. Common mathematical formulas make experimental data useful and meaningful. What Is a Formula? A mathematical formula is used to mirror a relationship between quantities. Some of those quantities are fixed (such as the speed of light in Einstein's famous E […]
Math Introduction to Solving Number Patterns
Overview: One problem-solving strategy in mathematics is to look for a pattern that will predict the next number in a sequence. That is often the first step to writing an equation that describes how to find each number. Some famous patterns, such as Fibonacci numbers and Pascal's triangle, play an important role in number theory. […]
Math Review of Operations with Matrices
Overview: Matrices, like other numbers, variables, and expressions, can be involved in mathematical operations. The rules are different, as every element of each matrix must be included. Also, only certain types of matrices can be combined. How Are Matrices Added? In order to add matrices, both matrices must be of the same dimensions so that […]
Math Introduction to Matrices
Overview: A matrix is an array of rows and columns that contain numbers or variables. Each position in the matrix is specific and serves a distinct purpose. Matrices can be defined by their size and shape. How Is A Matrix Defined? A matrix is defined by the number of rows and columns it has. Those rows and […]
Math Introduction to Fractals
Overview: The world of fractal geometry is usually pictured in beautiful images of self-similarity. Although the images are intricate, they are based on relatively simple calculations and replacements. What Is Self-Similarity? Self-similarity means that the pattern is the same or nearly the same no matter what scale is examined. The instructions (or equations) to create […] |
Arguing that computers are essential to teaching mathematics, Kemeny discusses not only how to use computers in the classroom, but also which mathematical topics should be taught in the age of computers. He explains his philosophy of using computers to teach mathematics and illustrates this philosophy with a number of concrete examples. (Atlanta, GA, 1988) |
Precalculus
MAT 110 with minimum grade of C or appropriate score on the Mathematics Placement Test, and MAT 080 or geometry proficiency.
III. Course (Catalog) Description
This course focuses on the study of functions including polynomial, rational, exponential, logarithmic and trigonometric functions. Additional topics include the conic sections, series, parametric equations, and polar equations. Use of technology is integrated throughout. lectures, discussions, demonstrations, experimentation, audio-visual aids and regularly assigned homework. Calculators/computers will be used when appropriate. Course may be taught as face-to-face, media-based, hybrid or online course. graphics calculator is required. A TI-83/84 will be used for instructional purposes.
X. Methods of Evaluating Student Progress
(To be completed by instructor.)
Evaluation methods can include grading homework, chapter or major tests, quizzes, individual or small group projects and a final exam |
Basic Math and Pre-Algebra For Dummies Education Bundle
Book Description: Get the skills you need to solve problems and equations and be ready for algebra class., and percents, you'll build necessary skills to tackle more advanced topics, such as imaginary numbers, variables, and algebraic equations. Look inside and discover topics such as:Understanding fractions, decimals, and percentsUnraveling algebra word problemsGrasping prime numbers, factors, and multiplesWorking with graphs and measuresSolving single and multiple variable equationsWant more? Let Basic Math & Pre-Algebra Workbook For Dummies help you out even further. You'll find 280+ pages with hundreds of practice problems featuring ample workspace to work out the problems. Each problem includes a step-by-step answer set to identify where you went wrong (or right). This helpful workbook will get you up to speed with basic math and pre-algebra before you know it! |
View Career Major Course
Course Information
Division
Trade & Industrial Education
Course Code
TI00526
Course Title
Construction Math
Suggested Course Hours
15.00
Course Description
This course is an introduction to basic math functions: addition, subtraction, division, multiplication, whole numbers, fractions and decimals, math applications for the construction industries, decimal-fraction conversions, metric system, and basic geometry and its applications to common shapes and forms.
Contact Information
Larry Bullock
405-743-5147
lbull@okcareertech.org
Prerequisites
Knowledge & Skills
-Demonstrate basic math functions that include addition, subtraction, division, multiplication, whole numbers, fractions, and decimals as they apply to the construction industry.
-Demonstrate the steps required to calculate decimals to fractions.
-Demonstrate an understanding of the metric system and basic geometry and its applications to common shapes and forms.
Construction Trainee Skill Standards - Aligns with the National Center for Construction Education and Research standards |
MATH 175:
INQUIRY-BASED INTRODUCTION TO CRYPTOLOGY
T. KYLE PETERSEN
"That student is taught the best who is told the least."
–R. L. Moore
1. Introduction
1.1. About the method. If you're reading this, you're probably a
good teacher. (At the very least, you have a non-vanishing interest
in teaching.) Did you ever have the sneaking suspicion that your stu-
dents, even the "good" ones, who get the best grades on exams, don't
really know the material you've been trying to teach them? What
percentage of your last calculus class would you say could recite that
d
dx
[xn ] = nxn−1 ? What percentage could tell you why? My answers
to these questions would be about 99 and about 15, respectively. If
your numbers are higher, congratulations, but I'd wager anyone with
an answer of more than 25 to the second question is an outlier.
Most students are led to believe mathematics consists of memoriza-
tion of facts and simple algorithmic exercises. Inquiry-based learning
(IBL, or the "modified Moore method", after R. L. Moore) seeks to
counteract this tendency. The pitfalls of the shallow view include the
inability to assess the correctness of a written solution, the belief that
there is one "right way" to solve a problem, and the idea that all prob-
lems can be addressed in just a few minutes. With an inquiry-based
approach, students learn that many worthwhile questions have answers
that can take hours, or even days (weeks!) to conquer, they see that
a solution can often come from several different directions, and they
develop a sharp eye for logical flaws in an argument. In short, IBL
tries to makes students think like mathematicians. Once students have
traced on their own all the steps and missteps1 leading to the claim
d
" dx [xn ] = nxn−1 ", they understand the statement in a way that is sim-
ply not possible from memorization alone. The need for memorization
of further facts falls by the wayside as students realize that so many
1And there are lots of steps! What is a limit? What is a derivative? The
definitions of a function and of continuity probably also crop up. . .
1
2 T. K. PETERSEN
ideas follow from true knowledge of the rules of the game and how to
apply them.
But how do we get students to reach this point? R. L. Moore adopted
a Socratic approach. There is no textbook, but rather the instructor
gives students a list of problems and some statements of definitions and
theorems, but with no exposition and no proofs. The course consists
of students doing the problems and attempting to prove the theorems.
During class meetings students present their findings at the board while
the other students ask questions. The instructor largely lurks in the
background, acting as moderator and cheerleader, but rarely, if ever,
as judge. There are many variations on the theme, almost a spectrum,
from "hard-core Moore"2 on one extreme to, at the other extreme,
something much closer to a typical lecture-style course, with written
homework, exams, and even textbooks. The specific structure of Math
175 is discussed in the next section.
There are several possible reasons why more courses are not taught
in the IBL style. One reason is that this method requires different
skills than lecturing does, and it can be easy for things to go very
wrong—more about this in the "Difficulties and Advice" section. Even
when done properly some still criticize the method; the main reason
given is lack of coverage. It does seem to be generally true that the list
of topics students see in a one-semester IBL course is shorter than the
same list for a course taught in the lecture style. One counter-argument
I have heard is that the learning curve for IBL students is exponential,
whereas the curve for lecture style students is linear. So while after one
semester the lecture class may be ahead, by the end of two semesters
the IBL class will have overtaken them.
I prefer the following analogy. The main theorems and definitions
from a course are like flowers. In a lecture course students pluck the
flowers one by one and put them in a pretty vase to admire. In an IBL
class, the students get down in the dirt to plant seeds, water them, and
watch the flowers grow. A year later, the flowers in the vase will have
wilted and died. With a little care, though, the IBL students will still
have a flower garden.
1.2. About this document. My aim with this note is to give an idea
of how this course has been run for the past couple of years, along with
some general advice about my version of the IBL method. It is not
an instruction manual. It is not a detailed syllabus. While it contains
2One rumor—almost surely false—is that he once brought a revolver to class as
extra motivation for a particularly recalcitrant group of students: "Today someone
will prove Theorem X."
MATH 175: INQUIRY-BASED INTRODUCTION TO CRYPTOLOGY 3
information about the the structure of the course and the running of
day-to-day operations, you will find little here that is specific to num-
ber theory or cryptography. (You can find that in the worksheets.)
Difficulties in teaching this course are more likely to come from unfa-
miliarity with the method than from content.
For me, there is something paradoxical about trying to teach some-
one how to teach a course in which the guiding principle is that students
teach themselves. Shouldn't I just wish you luck and let you go figure
it out for yourself? Maybe. But maybe you can learn something from
my experience and opinions as well. (Really, the best thing I can rec-
ommend for someone interested in teaching an IBL course is to attend
a workshop, or to sit in on a class taught by an experienced IBLer.)
My point is that whatever I say, you need to make the material your
own before you put it into practice. To be sure, I hope that the ad-
vice in this note saves you headaches and wasted time, but your own
experiments and mistakes will teach you better than I ever could, and
ultimately will make you a better teacher.
Good Luck!
2. History and Structure of Math 175
Math 175 was originally conceived by Phil Hanlon in the late 1980s
as a "problems course" for honors freshmen. He gave students a list
of fifty or so problems, usually discrete, but with no obvious unifying
theme. He would lecture on various topics, and every few days a student
would present a solution to a problem from the list. Grades were based
purely on the number of solutions presented. This was classic Moore
method.
While some students relished the open-ended nature of the course,
many of their classmates disliked the fact there was no specific content
for the course. With this in mind, Hanlon tried to tie the problems
to some specific content. First he tried graph theory, then cryptology,
which stuck. Prodded by student interest, he and several collaborators
later developed an entire "coursepack" with some historical motivation
and exposition on cryptographic methods and related mathematical
topics.
Hanlon taught the course each year through the late 1990s and in-
termittently thereafter. (He took a job in the Provost's office.) From
1999–2005 several people taught the course, in several different for-
mats. At one point a hardcover textbook, Invitation to Cryptology,
was added to the required course materials. In general, the course lost
almost all connection to the Moore method.
4 T. K. PETERSEN
When I was hired in 2006, it was with the understanding that I would
help revive the IBL character of Math 175. In the fall of that year,
a
Kirsten Eisentr¨ger and I designed and co-taught the course. We still
had the textbook and coursepack that fall, but in 2007 and 2008 those
materials were dropped in favor of the materials contained in this folder.
Otherwise, the structure, grading procedures, and content is largely un-
changed from 2006, including, notably, the co-teaching model. In 2007
undergraduate teaching assistant Thomas Fai attended class meetings
c
and helped to answer student questions. In 2008, Fran¸ois Dorais and
I co-taught the course.
Math 175 is a "freshman honors seminar," which means that it is
a small class intended for first-year students in the honors program.
Each section is capped at 20 students. I have had between 15 and 19
students in the four sections I've taught. The students are generally
from the LSA honors program, though there are usually a few from
Engineering and from general LSA. Very few students have a desire
to major or minor in mathematics before taking the course. Part of
the aim of the course is to get students excited about mathematics.
Hopefully some of them will go on to take further math courses.
Students not in the honors program are required to have instructor
approval to enroll in Math 175. I never turned away an interested
freshman, but I always declined requests from upperclassmen. I think
it is important that the class be fairly homogeneous. Students should
feel as equals with their classmates and thus be unafraid to express their
opinions. With this in mind, I think it is also important to identify and
gently nudge out students who are too good. For example, in fall 2008
there were three students in one section of Math 175 who were also
taking math 295 ("super honors" calculus). They were good students
but they upset the egalitarian dynamic of the classroom.
The course meets four days a week for fifty minutes. Monday, Tues-
day, and Wednesday class is held in a seminar room with individual
desks and several chalkboards. Thursday meetings are held in a com-
puter lab. Attendance is absolutely mandatory. I've used a very effec-
tive carrot-and-stick approach. As reward for coming to class, partic-
ipation makes up a full 20% of their final grade. The punishment for
missing class is severe. Each student gets three "free" absences. Each
subsequent absence results in the final grade dropping by a full letter,
e.g., an A student with five unexcused absences receives a C.
2.1. Group work. On a typical class day, we randomly arrange stu-
dents in groups of two or three, and hand out one of the worksheets.
MATH 175: INQUIRY-BASED INTRODUCTION TO CRYPTOLOGY 5
Students stay with their group until completion of the worksheet; of-
ten three or four class meetings. These worksheets are meant to be
done (only) in class. The pace of the course overall is dictated by stu-
dent progress through the worksheets. When one worksheet is finished,
there is usually some sort of "wrap up" discussion and new groups are
formed to begin a new worksheet. It is a real luxury that Math 175
is not a prerequisite for any subsequent course. This means you can
really wallow in a topic if it seems to be the right thing for the students.
As students dig into the worksheets, we circulate to listen to student
ideas, and to ask and answer questions.3 Students are periodically
invited to the board to present solutions to the problems on the work-
sheets. Usually one or two students will be selected to present in the
second half of the class period. Be sure to allow at least ten minutes
for a presentation; fifteen or twenty is better. Too often in my first
year I found myself rushing students through their presentations. This
is frustrating for everybody. Keeping an eye on the clock is any easy
solution to this problem. More on answering student questions, mo-
tivating students when stuck, and managing student presentations is
discussed in the "Difficulties and Advice" section.
The design of the worksheets is as follows. Like a section of a text-
book, a given worksheet usually has one main idea. A "goal theorem",
say. The worksheet builds gradually toward this goal theorem, in-
troducing definitions as necessary. There is a mix of numerical and
abstract problems, all of which are meant to guide students to the idea
of the goal theorem.
My approach for designing such a worksheet is straightforward. Be-
ginning with the goal theorem, I first write my own proof. Then I
ask, "what would a student need to know to understand and construct
this proof?" First off, they probably need a lemma or two. Now, what
would they need to be able to prove these lemmas? Is it possible to
guide students (with examples) to the idea of the lemma before they've
seen its statement? There are also some definitions that should prob-
ably appear along the way, and they too should be motivated with
examples. In the end, a typical goal theorem will come at the end of a
sequence of fifteen or more problems. Along the way there is no such
thing as a problem that's "too small" for the students.
If you plan to teach this course you should go through the worksheets
and modify them to suit your own tastes. If you prefer a different path
3Don't give them any free answers! I like to use the psychiatrist's old trick of
answering a question with a question. Student: "There are infinitely many primes,
right?" Instructor: "Do you think there are infinitely many primes?"
6 T. K. PETERSEN
to a particular goal theorem, map it out! If there is a topic omitted
that you really like (Pollard's ρ method for instance), make a new
worksheet!
The students should keep notes on the worksheet problems in a sepa-
rate folder, or in a composition notebook. This will be their "textbook"
for the course and helpful when it is time to do homework or study for
exams.
2.2. Computer lab. The computer lab is generally fun for everyone.
Students get into groups of two or three to complete a day's task.
Sometimes the goal is very narrow ("decode this message"), other times
it is wide open ("find the largest integer you can with the following
properties. . . "). Often the lab activities are phrased in terms of a
competition, with bonus points for the winning team. Whereas the
homeworks and in-class worksheets encourage students to think deeply
and methodically, the lab activities often reward speed and following
hunches—different kinds of problem solving skills.
Sometimes the lab topics are closely related to the worksheets from
earlier in the week, e.g., implementing the Euclidean algorithm. Other
times the lab has little to do with the classwork. In either case the
topic should be engaging and most students should be able to finish
within an hour. Students find the labs a nice respite from the hard
work they are putting in on the class worksheets.
Maple is the default program for most of these activities, though
there are some web-based activities as well. An added benefit of using
software like Maple is that students can begin to use it when working
on homework problems.
The computer lab activities have changed much more from year to
year when compared with the worksheets. Dorais is working to redesign
the computer labs (making them more cohesive) for fall 2009.
2.3. Homework and exams. In some IBL courses there is no home-
work and there are no exams. Grades are based solely the number
and quality of solutions presented, for example. In other IBL courses,
there is written homework, but no exams, and presentations make up a
large part of a student's grade. Math 175 has both written homework
and exams, and we don't grade presentations. One advantage of this
approach is that it makes grading straightforward for the instructor.
No different from a typical lecture course, really. Also, it feels more
"normal" for the students. The class is different enough for them al-
ready, and if they were to be graded on presentations, that would only
add anxiety to a situation they already find stressful. I have considered
MATH 175: INQUIRY-BASED INTRODUCTION TO CRYPTOLOGY 7
dropping the final exam in favor of some sort of final project, but for
now this is a vague idea.
During the semester the students have nine homework assignments,
two midterms, and a final exam. Students are encouraged to work
together on the homework, though they must acknowledge their col-
laborators and write up their own solutions. The way the homeworks
and exams are currently written reflects the timing of the most recent
semester's students. If you find your class moving faster or slower, you
may need to move some problems accordingly or change due dates to
match the pace of the worksheets.
The homeworks have two parts. The first contains problems and
exercises based on material presented in the worksheets. The second,
called "outside the box" (OTB) questions, are often quite challenging.
The exams are meant to be fairly straightforward, with problems drawn
from worksheet material and of difficulty comparable to the first part
of the homework.
The purpose of the OTB questions is to help students develop their
problem solving skills. These problems may or may not (more often
not) be related to the worksheets. Often they have many layers so that
students can see progress without necessarily reaching the final answer.
Usually a student can receive half credit or more on these problems for
some carefully worked out examples and a nice conjecture. Rarely will
a student be able to tackle all the OTB questions on a homework (and
they are not required to do so).
Apart from developing good problem solving skills, the homework
can help students develop their skill at communicating complex ideas.
Thus the standard for written homework is very high. As is to be
expected, their writing is generally horrible at the beginning of the
semester. But they do improve! Early and often, you can show them
what good mathematics writing looks like, and cheerfully encourage
them to achieve that goal. They need to be told that yes, complete
sentences in proper English are required, and no, three examples do not
prove a universal statement. Then they need to be told again. And
again. But if you are patient, and encourage them to talk about it with
one another, they get it eventually.
Each year I am struck by the quality of written work at the end of the
semester compared to that of the beginning. While still not perfect, I
would compare it favorably to the writing found in a junior-level linear
algebra class.
8 T. K. PETERSEN
3. Difficulties and Advice
Run well, this course can be the most fun you've ever had in a
classroom. (Certainly that has been my experience.) However, there
are many places where it can go off the rails if you're not careful. The
results can be painful for everyone involved.
3.1. Marketing the method. One of the best ways to ensure a suc-
cessful semester has nothing to do with mathematics. Here is a terrific
quote from a former student, when asked what he would tell future
students taking the class:
You may think that Professor Petersen does not lecture
because he does not know what he's doing, or is a bad
teacher. This is false. I learned some of the best critical,
logical thinking skills from him because of the specific
way in which this class is taught.
Consider the first sentence. If you don't convince the students other-
wise, this is their most common assumption. You're lazy, a bad teacher,
you don't know what you're doing. Before you have even given them
the first handout they are skeptical of the method or worse.
First impressions matter. On the first day of class try to tackle the
"perception problem" head-on. Explain to them why you think the
class is taught as it is: that they will learn the material better, that
they will have ownership of the ideas, that they will experience the joy
of discovery of new ideas, and so forth.
Analogies can also help. Ask the students what their hobbies and
extracurricular interests are. Any basketball players? Any cellists? Ask
them how they became proficient. Did you become a good basketball
player by watching your coach dribble around and do lay-up drills?
by watching Michael Jordan? No. Did you learn to play the cello by
watching your teacher do scales? by listening to Yo-Yo Ma? Of course
not.
To become good at something you need to do it yourself. This makes
sense to students. In this class you, the instructor, will play the role of
coach.
If you hit the students early and often with these ideas—I probably
bring it up in one way or another at least once a week for the first
month—you can convince them that at least there is a good philosophy
behind the structure of the course. This gets you as far as the second
sentence in the student quote above. Bringing each student all the way
to the final sentence is subtler, and, perhaps, not always possible.
MATH 175: INQUIRY-BASED INTRODUCTION TO CRYPTOLOGY 9
The problem is that unlike playing basketball or playing music,
most students don't inherently derive joy from "playing" mathemat-
ics. Therefore the hard work involved in getting better and learning
will tend to feel like work for them. It is good to remember this point
of view throughout the semester so that, whenever possible, you show
students what a great game this math stuff can be!
3.2. Developing a positive culture. One of the simplest ways to
get students to enjoy themselves while working hard is to get them
to enjoy coming to class. It is easy for students to be excited about
the days in the computer lab. On days spent in the classroom with
the worksheet it takes more effort. In general the time spent in class
should be friendly and open so that students feel comfortable offering
their opinions without fear of looking foolish. Students need to make
mistakes and discuss the dead ends to get the most out of class time.
If they are too shy or embarrassed to speak openly everyone loses out.
A certain passiveness or apathy in the mathematics classroom is
something that, for many students, has been reinforced for years. The
standard model has them sit quietly at desks listening to a lecture and
passively taking notes. Few are engaged mentally. They are rarely, if
ever, challenged to think in the moment. Part of the difficulty early in
the semester is to overcome their habits.
In a similar vein, consider Schoenfeld's observation [?] that U.S. high
school students average about two minutes of thinking per homework
problem. Two minutes! You either get it immediately or it's hope-
less. To the average student, working on the same problem for fifteen
minutes is an eternity. This is probably tied to the notion that math-
ematical ability is something innate, rather than something attained
through hard work. They are shocked when I tell them that I, as a
research mathematician, am stuck more than 95% of the time. I have
no idea what the answer is or how to get there. What do I do then?
Work more examples. Ask a narrower question. Ask a broader ques-
tion. Change the parameters and do even more examples. These ideas
don't occur naturally to most students. So tell them. They need to
learn that it is the struggle that matters, and that the struggle is often
a necessary precursor to that five percent of insight and progress.
What is rewarded in the classroom is the struggle, not only the so-
lution. Every attempt is to be applauded. Most of the students are
likely to be unsure of themselves in the beginning. For these students
the first few experiences should always end on a positive note, even if
what the student says is nonsense mathematically. Thank the student
for speaking up. Smile. Locate the kernel of truth in what the student
10 T. K. PETERSEN
said and point out its brilliance to the rest of their group or to the
class.
It's also fun to point out that while some approaches are "incorrect
solutions", they are theorems themselves, and the students are still
creating mathematics! Say students analyze a certain function and find
f (1) = 2, f (2) = 4, f (3) = 8, f (4) = 16. At this point the conjecture
f (n) = 2n emerges and students spend a good deal time and effort to
proving the conjecture, to no avail. Finally, someone, for lack of any
better ideas, works out the case n = 5 and finds f (5) = 31. Most
students will despair—they don't even have a good conjecture now!
Suppose class is ending and you want to end on a positive note. You
can take the chalk and write the following on the board (the group of
students is Sarah, Jimmy, and Eva):
Theorem 1 (Sarah, Jimmy, Eva). We have f (n) = 2n for n = 1, 2, 3, 4,
and f (5) = 31.
Corollary 1. The function f (n) is not generally equal to 2n .
This is progress! Make them believe it!
3.3. Presentations at the board. Over the course of the semester all
the students should spend roughly the same amount of time presenting
at the board. While walking around the classroom, identify which
groups "get it" and which groups are having more trouble. Anywhere
from ten to thirty minutes from the end of class ask a particular student
to go to the board and present a solution to a particular problem. In
the beginning especially, I like to pick students who seem to have a
good handle on the problem. For students who seem more shy or less
confident, I pick an easier problem to help their chances for a positive
experience.
When the student has written their solution on the board, call the
class to attention, "All right, now we have Eva presenting her solution
to problem 3," and take a seat at the back of the classroom. (Phys-
ically moving to the back of the room and sitting down removes you
from a position of authority and places Eva, at the chalkboard, in that
position.) When Eva has finished her explanation, there will be si-
lence. Probably the class will turn in their seats to look to you for
approval/disapproval. Smile. Say nothing yet of your thoughts of the
solution. Ask if there are questions for the speaker. Once any questions
are answered, if you think the presentation was complete and correct,
say so—"Great job, Eva! I especially like the part where. . . "—and give
the speaker a round of applause.
MATH 175: INQUIRY-BASED INTRODUCTION TO CRYPTOLOGY 11
What if a student presents a solution and there is an obvious flaw in
the argument? You ask, "Does anyone have a question for Eva?" and
you wait. Don't. . . say. . . anything. Wait! Don't say anything. Wait
longer! Two minutes of silence is not unusual. It is very likely that
someone in class sees the error but is too shy or too polite to point
it out. Eventually someone will speak up, and then it is your job to
facilitate discussion. It is not your job to point out the mistake, and it is
certainly not your job to show them how to fix it. This is where the cool
stuff happens, because, believe it or not, they will figure things out for
themselves. You "helping" here just steals the thunder from someone
who could have thought of the idea for themselves. The confidence
that students gain at this time is invaluable.
3.4. When students are stuck. It is possible there will be times that
nobody but you sees the fatal flaw in an argument. You've asked for
questions, waited two full minutes, and still nothing but blank stares.
What to do? Hint at it. The more oblique the suggestion, the better. I
like starting this approach by having the presenter read their solution
aloud again. Then I ask for questions and wait again. Still nothing? I
focus in a bit more. "Could you please read the second paragraph once
more?" Still nothing? "Could you please read that paragraph one more
time? There's still something that I don't quite understand." You can
also ask someone in the audience to describe their approach. "Anna,
could you tell us how this compares to your group's solution?" Still
nothing? (I can't actually think of time when I got this far and there
were still no fruitful comments from the audience.) Well, have them
read it again: "Okay, one more time, from the top. . . ." It's sort of like
the the shampoo algorithm: Lather. Rinse. Repeat as necessary.
But of course you don't have unlimited time and students don't have
unlimited patience and determination. Sometimes you really are beat-
ing a dead horse, or it's nearly the end of the hour and you want to end
on an upbeat note. This is a very delicate situation. I would argue that
it's okay to leave a problem on the board unresolved, provided that you
can cast off any air of defeat before dismissing the class. "Okay, Jimmy,
unfortunately we're near the end of the hour, so we'll have to pause
here and begin again tomorrow. I think we made some real progress
today, though! This must just be a real tough nut to crack. . . We'll all
sleep on it and see what we can come up with tomorrow. Remember
it took two hundred years to prove Fermat's last theorem!"
Managing situations like this require the most skill on the part of
the instructor. First you need to realize that time is running away and
12 T. K. PETERSEN
nobody is going to have answer. Then you need to disengage everyone
in a way that doesn't feel like giving up. It's not easy.
Students can also use help before getting to the chalkboard. When
stuck during group work the "Read it. Read it again." approach isn't
usually appropriate. There are many other suggestions that you can
give students to get them past a hurdle though. Prompt them without
giving away too much. "Which examples have you tried? Hmm. . . what
about an example where n is prime?" Sometimes students throw up
their hands and ask a question that in essence says "Can you tell us
the answer please?" These include gems like "I don't get it," and "I
don't know what I'm supposed to do." My favorite approach to these
questions is to answer with my own question: "What part of the prob-
lem don't you get?" or "What do you think you should do here? Did
you try an example?" Also, "Do you understand all the words in the
statement of the problem?" (This can be a legitimate concern!)
In general, just remember that the goal is to have the students iden-
tify and correct mistakes without your help. The less you say to get
them to do that, the better. Once they've done it, go bananas! "That
is so awesome! That's the most incredible thing I've ever seen!" It re-
ally is exciting to watch when it works well, so chances are your praise
will be genuine. If not, fake it.
4. Some Reading
The Legacy of R. L. Moore Project website [?] is a good resource for
all things inquiry-based, and can put you in touch with a large network
of practitioners and proponents of the method. They have an annual
meeting in Austin, Texas. Paul Halmos' article [?] is great reading and
makes a compelling argument for teaching what he calls a "problems
course". For convenience it is included in this folder. Alan Schoenfeld
is a leading math education researcher and proponent of inquiry-based
methods. The article cited below [?], and included in this folder, points
out several problems arising in lecture-based courses that he feels are
corrected in an inquiry-based environment.
References
[H] P. R. Halmos, What is Teaching? Amer. Math. Monthly 101 (1994),
848–854.
[RLM] The Legacy of R. L. Moore Project,
[S] A. H. Schoenfeld, When Good Teaching Leads to Bad Results: The
Disasters of 'Well-Taught' Mathematics Courses, Educational Psy-
chologist, 23 (1988), 145–166 |
0030295580
9780030295584
An Introduction to the History of Mathematics:This classic best-seller by a well-known author introduces mathematics history to math and math education majors. Suggested essay topics and problem studies challenge students. CULTURAL CONNECTIONS sections explain the time and culture in which mathematics developed and evolved. Portraits of mathematicians and material on women in mathematics are of special interest.
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Rent An Introduction to the History of Mathematics 6th edition today, or search our site for Howard Whitley textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by CENGAGE Learning. |
The difference between precalculus and trigonometry?
OK at the 2 year college here, they offer ONLY trig , and you take that after college algebra, and before you take calculus, and the counselors at the 2 year college all say that, trig and precalculus mean the same thing there, which is weird, because, then if you look at the classes offered at another nearby 2 year college, strangely, they offer trig AND precalculus, so what's the difference between the two?
The difference between precalculus and trigonometry?
This is all I could agree on about trigonometry since I've never taken it before.
However, for Precalculus, I can say that it includes only the "essentials" of trigonometry, such as graphs of all six functions and the inverse functions, right-triangle trig., analytic trigonometry, the very basics of vector analysis, and the very basics of Analytic Geometry. Also, the other material that is discussed that pretty much has nothing to do with trig. includes functions and their graphs, linear, absolute-value, quadratic, polynomial, exponential, logarithmic and rational functions, sequences and series, matrices, conics, and an introduction to limits. All the material needed to get you ready for the world of Calculus.
Jurrasic
#5
Apr16-11, 03:16 PM
P: 101
Quote by frozenguy
At my 2 year, they have trig and pre-calculus separate. Trig was straight trig. Functions, identities, graphing, deriving, etc. Pre calculus if I remember correctly was mainly analyzing functions and their graphs. Exponential, logarithmic, polynomial, rational, trig functions mainly. Touch on conic sections and vectors as well I think. Maybe some complex numbers.
That explains quite a bit. Thanks :)
Chunkysalsa
#6
Apr16-11, 05:58 PM
P: 311
at my school Precalculus = college algebra + trig. Though trig usually only has like a couple of sections while precalc and algebra have millions.
QuarkCharmer
#7
Apr16-11, 06:19 PM
P: 1,035
Check the syllabus for the course and see what is included?
Jurrasic
#8
May4-11, 12:04 AM
P: 101
Quote by Chunkysalsa
at my school Precalculus = college algebra + trig. Though trig usually only has like a couple of sections while precalc and algebra have millions.
Yeah thanks that's really helpful. They actually have the same thing at this school with hardly any trig classes but tons of college algebra, and about 4 different calculus classes.
Jurrasic
#9
May4-11, 12:06 AM
P: 101
Quote by QuarkCharmer
Check the syllabus for the course and see what is included?mege
#10
May4-11, 12:34 AM
P: 192
Quote by JurrasicIs there a Course Catalog/Bulletin which has descriptions seperately from the Course Schedule? (there should be, the bulletin/catalog usually is good for a year or more, whereas the schedule is only good for the single term) |
Course Description: See Math 135 for calculus topics covered. Algebraic and elementary function topics are covered throughout, as needed. Math 131 and Math 132 together are equivalent to Math 135. The sequence Math 131-132 is designed for students whose manipulative skills in the techniques of high school algebra and precalculus may be inadequate for Math 135. Prer., 4 years high school math (algebra, geometry, trigonometry or their equivalents). Credit not granted for this course and Math 135.
(always check with your current instructor for most up-to-date information) |
Instructor
Notes
More Information
Section Description
This course is the third semester of a three semester sequence in calculus for engineers, physical scientists and mathematicians. It is basically calculus done in several variables, with the emphasis on the case of two independent variables; e.g. z = f(x, y). After studying differentiation and integration we will cover vector calculus; e.g. the theorems of Gauss, Green and Stokes. These are higher dimensional analogs of the fundamental theorem of calculus. The material in this course is important, elegant and (to be frank) difficult. We will move rapidly through the first (easier) part of the course in order to give ample time to the last two chapters (the difficult part of the course).
Section Expectation
The goals are first to learn the material and obtain a good grade and second have some fun along the way. You should have a good knowledge of Calculus 1 and Calculus 22 (math 021 and math 022) as well as the needed time to spend on this course.
Evaluation
There will be two exams, about 5 quizzes and computer graded homework. Bonus points will be given for attendance |
Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for). |
Customer Reviews for AB Publishing Practical Arithmetics Book 1
This series of books aims to give the child the ability to compute easily and accurately, and to enable him to interpret and solve the quantitative situations which he will meet in everyday life. In the achievement of this aim, these books incorporate the most valuable findings of modern experimentations in the teaching of arithmetic, including the results of important researches conducted by the authors themselves. These books present only those methods and materials which have been thoroughly tested in the classroom by many experienced teachers. Full provision has been made for pupils varying levels of ability. For those of superior ability more difficult exercises, marked with a star, are provided. For pupils of average and below-average ability additional exercises may be prescribed if needed; the diagnostic tests indicate whether extra work is necessary and also give references to suitable materials. This book covers two years of instruction. Includes addition, subtraction, multiplication, division, and introduces geometry, fractions, and measurement. Answer key included at the back of the book Practical Arithmetics Book 1
Review 1 for Practical Arithmetics Book 1
Overall Rating:
4out of5
Date:May 25, 2011
MamaBrown
This book give students the math skills they need, with no frills to get in the way. It offers many fun activities to gives students practice on a variety of skills.
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1of1voted this as helpful.
Review 2 for Practical Arithmetics Book 1
Overall Rating:
5out of5
Excellent Math Program!!!
Date:January 23, 2011
Mary
Location:Melbourne, Florida
Age:45-54
Gender:female
Quality:
5out of5
Value:
5out of5
Meets Expectations:
5out of5
My daughter is in third grade and is using this book for her arithmetic lessons. I cannot say enough good things about this program (there is 2nd and 3rd book as well). There is enough repetition to learn each new concept, but not too much as to make it boring for the student. The concepts and lessons are designed to be applicable to real life situations.
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Review 3 for Practical Arithmetics Book 1
Overall Rating:
5out of5
Date:September 6, 2008
Kellee B.
I have used many math books with my son, this is by far the greatest. My son has been able to do most of it on his own. If your child can read and follow directions they can do most of the work independently. It is written to the child and explains all new concepts in an easy, understandable manner. They use real everyday problems. Your child doesn't just learn to parrot back facts but gains much understanding as they always have them apply the new concepts. I find no need to supplement this program at all. I'm so glad to have found this arithmetic book. I plan to use the all three books with each of my children. Kellee
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Review 4 for Practical Arithmetics Book 1
Overall Rating:
4out of5
Date:March 17, 2008
Vickie Madrigal
I have tried many arithmetic products & this is my favorite. These books are small in size but packed full of practical/every day math that children can relate to. I also like that there are word problems that are easy to read & understand. This is mixed in with regular problems. I have found that even though my children knew all of their "facts" on paper they sometimes did not know how to relate it to everyday uses. This book has some black & white illustrations & problems in black type. I bought all 3 books in this series & I am glad I did because this will be my math program for some time. Practical, easy to understand. I would give it an A.
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Review 5 for Practical Arithmetics Book 1
Overall Rating:
5out of5
Date:October 19, 2005
Vik
Don't let the size of this book, or the other two in the series, fool you! There is no wasted space in these books, you need no separate answer key (they're in the back), my children love the vintage pictures, the explanations are good without being wordy, and this is very thorough. Problems do need to be copied into a spiral notebook and worked out (not a workbook). Being non-consumable, it's great for multiple children and very inexpensive.Be sure your children know arithmetic forward and backwards before moving on to mathematics. I'm amazed at the number of people I know who can do algebra but can't balance a checkbook or figure interest! |
Mathematics for Elementary Teachers: A Contemporary Approach,...Mathematics for Elementary Teachers: A Contemporary Approach, 10th Edition makes readers motivated to learn mathematics. With new-found confidence, they are better able to appreciate the beauty and excitement of the mathematical world. The |
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Show More helps readers master the big ideas in each chapter through Concept Checks and Conceptual Problems, as well as Concept Explorations and Strategy Problems that challenge students to think step by step and not rush for a numerical answer |
Chapter 1 (part 1): State Standards Order of Operations ●Write algebraic expressions. Textbook Textbook: Dolciani
Foundations for A1.1.1a ●Simplify expressions involving assignments "The Classic"
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and Evaluating A1.2.1b Properties of Real numbers. Section Quizzes Prentice-Hall
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the Number Line Real Numbers. McDougal
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Decimal Operations Standards simplify expressions. Concepts and
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Franklin County Community School Corporation ● Franklin County High School ● Brookville, IN
COMMON CORE STANDARDS
UNIT 1 – COMMON CORE
N.Q.1 Use units as a way to understand problems and to guide the solution of multi-step
problems; choose and interpret units consistently in formulas; choose and interpret the
scale and the origin in graphs and data displays.
N.Q.2 Define appropriate quantities for the purpose of descriptive modeling.
N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when
reporting quantities.3 Represent constraints by equations or inequalities, and by systems of
equations and/or inequalities, and interpret solutions as viable or non-viable options in a
modeling context. For example, represent inequalities describing nutritional and cost
constraints on combinations of different foods1 Explain each step in solving a simple equation as following from the equality of
numbers asserted at the previous step, starting from the assumption that the original
equation has a solution. Construct a viable argument to justify a solution method.
A.REI.3 Solve linear equations and inequalities in one variable, including equations with
coefficients represented by letters.
Franklin County Community School Corporation ● Franklin County High School ● Brookville, IN
UNIT 2 – COMMON CORE
N.RN.1 Explain how the definition of the meaning of rational exponents follows from
extending the properties of integer exponents to those values, allowing for a notation for
radicals in terms of rational exponents. For example, we define 51/3 to be the cube root
of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.
N.RN.2 Rewrite expressions involving radicals and rational exponents using the
properties of exponents.
A.REI.5 Prove that, given a system of two equations in two variables, replacing one
equation by the sum of that equation and a multiple of the other produces a system with
the same solutions.
A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with
graphs), focusing on pairs of linear equations in two variables.
A.REI.10 Understand that the graph of an equation in two variables is the set of all its
solutions plotted in the coordinate plane, often forming a curve (which could be a line).
A.REI.11 Explain why the x-coordinates of the points where the graphs of the equations
y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the
solutions approximately, e.g., using technology to graph the functions, make tables of
values, or find successive approximations. Include cases where f(x) and/or g(x) are
linear, polynomial, rational, absolute value, exponential, and logarithmic functions.★
A.REI.12 Graph the solutions to a linear inequality in two variables as a half-plane
(excluding the boundary in the case of a strict inequality), and graph the solution set to a
system of linear inequalities in two variables as the intersection of the corresponding
half-planes.
F.IF.1 Understand that a function from one set (called the domain) to another set (called
the range) assigns to each element of the domain exactly one element of the range. If f
is a function and x is an element of its domain, then f(x) denotes the output of f
corresponding to the input x. The graph of f is the graph of the equation y = f(x).
F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret
statements that use function notation in terms of a context.
F.IF.3 Recognize that sequences are functions, sometimes defined recursively, whose
domain is a subset of the integers. For example, the Fibonacci sequence is defined
recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1Franklin County Community School Corporation ● Franklin County High School ● Brookville, INe. Graph exponential and logarithmic functions, showing intercepts and end
behavior, and trigonometric functions, showing period, midline, and amplitude2 Write arithmetic and geometric sequences both recursively and with an explicit
formula, use them to model situations, and translate between the two forms.★LE.1 Distinguish between situations that can be modeled with linear functions and
with exponential functions.
a. Prove that linear functions grow by equal differences over equal intervals; and
that exponential functions grow by equal factors over equal intervals.
Franklin County Community School Corporation ● Franklin County High School ● Brookville, IN
b. Recognize situations in which one quantity changes at a constant rate per unit
interval relative to another.
c. Recognize situations in which a quantity grows or decays by a constant
percent rate per unit interval relative to another.
F.LE.2 Construct linear and exponential functions, including arithmetic and geometric
sequences, given a graph, a description of a relationship, or two input-output pairs
(include reading these from a table).
F.LE.3 Observe using graphs and tables that a quantity increasing exponentially
eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a
polynomial function.
F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context.
Franklin County Community School Corporation ● Franklin County High School ● Brookville, IN
UNIT 3 – COMMON CORE
S.ID.1 Represent data with plots on the real number line (dot plots, histograms, and box
plots).
S.ID.2 Use statistics appropriate to the shape of the data distribution to compare center
(median, mean) and spread (interquartile range, standard deviation) of two or more
different data sets.
S.ID.3 Interpret differences in shape, center, and spread in the context of the data sets,
accounting for possible effects of extreme data points (outliers).
S.ID.5 Summarize categorical data for two categories in two-way frequency tables.
Interpret relative frequencies in the context of the data (including joint, marginal, and
conditional relative frequencies). Recognize possible associations and trends in the
data.
S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how
the variables are related.
a. Fit a function to the data; use functions fitted to data to solve problems in the
context of the data. Use given functions or choose a function suggested by the
context. Emphasize linear and exponential models.
b. Informally assess the fit of a function by plotting and analyzing residuals.
c. Fit a linear function for a scatter plot that suggests a linear association.
S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear
model in the context of the data.
S.ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.
S.ID.9 Distinguish between correlation and causation.
Franklin County Community School Corporation ● Franklin County High School ● Brookville, IN
UNIT 4 – COMMON CORESSE.2 Use the structure of an expression to identify ways to rewrite it. For example,
see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be
factored as (x2 – y2)(x2 + y2).
A.SSE.3 Choose and produce an equivalent form of an expression to reveal and
explain properties of the quantity represented by the expression.★
a. Factor a quadratic expression to reveal the zeros of the function it defines.
b. Complete the square in a quadratic expression to reveal the maximum or
minimum value of the function it defines.
c. Use the properties of exponents to transform expressions for exponential
functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈
1.01212t to reveal the approximate equivalent monthly interest rate if the annual
rate is 15%.
A.APR.1 Understand that polynomials form a system analogous to the integers,
namely, they are closed under the operations of addition, subtraction, and multiplication;
add, subtract, and multiply polynomials4 Solve quadratic equations in one variable.
Franklin County Community School Corporation ● Franklin County High School ● Brookville, IN
a. Use the method of completing the square to transform any quadratic equation
in x into an equation of the form (x – p)2 = q that has the same solutions. Derive
the quadratic formula from this form.
b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots,
completing the square, the quadratic formula and factoring, as appropriate to the
initial form of the equation. Recognize when the quadratic formula gives complex
solutions and write them as a ± bi for real numbers a and b.
A.REI.7 Solve a simple system consisting of a linear equation and a quadratic equation
in two variables algebraically and graphically. For example, find the points of
intersection between the line y = –3x and the circle x2 + y2 = 3.
Franklin County Community School Corporation ● Franklin County High School ● Brookville, IN
UNIT 5 – COMMON CORE
N.RN.3 Explain why the sum or product of two rational numbers is rational; that the sum
of a rational number and an irrational number is irrational; and that the product of a
nonzero rational number and an irrational number is irrationalb. Graph square root, cube root, and piecewise-defined functions, including step
functions and absolute value functions.
F.IF.8 Write a function defined by an expression in different but equivalent forms to
reveal and explain different properties of the function.
a. Use the process of factoring and completing the square in a quadratic function
to show zeros, extreme values, and symmetry of the graph, and interpret these in
terms of a context.
b. Use the properties of exponents to interpret expressions for exponential
functions. For example, identify percent rate of change in functions such as y =
(1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing
exponential growth or decayFranklin County Community School Corporation ● Franklin County High School ● Brookville, INBF.4 Find inverse functions.
a. Solve an equation of the form f(x) = c for a simple function f that has an
inverse and write an expression for the inverse. For example, f(x) = 2 x3 or f(x) =
(x+1)/(x-1) for x ≠ 1.
F.LE.3 Observe using graphs and tables that a quantity increasing exponentially
eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a
polynomial function.
Franklin County Community School Corporation ● Franklin County High School ● Brookville, IN
Indiana Academic Standards
Unit-Quarter 1 :: Topic-Reasoning with Equations and Inequalities
A1.1.3a Simplify expressions by using the associative and commutative properties to
combine like terms.
A1.1.3b Simplify linear expressions by using the distributive property.
A1.2.1a Determine which inverse operations should be applied and in what order to
solve a given linear equation.
A1.2.1b Solve linear equations that require the use of commutative and associative
properties to combine like terms.
A1.2.1c Solve linear equations that require the use of the distributive property to remove
grouping symbols.
A1.2.1d Solve linear equations with the variables on both side of the equation.
A1.2.2a Solve equations and formulas for a specified variable.
A1.2.3 Find solution sets of linear inequalities when possible numbers are given for the
variable.
A1.2.4a Solve linear inequalities that require the use of commutative and associative
properties to combine like terms.
A1.2.4b Solve linear inequalities that require the use of the distributive property to
remove grouping symbols.
A1.2.4c Solve linear inequalities with the variables on both side of the inequality.
A1.2.4d Graph the solution set of a linear inequality in one variable (on a number line).
A1.2.5a Solve compound linear inequalities.
A1.2.5b Graph the solution set of combined linear inequality in one variable (on a
number line).
A1.2.6a Solve word problems that involve linear equations.
A1.2.6b Solve word problems that involve formulas.
A1.2.6c Solve word problems that involve linear inequalities.
A1.7.2a Solve algebraic proportions that lead to linear equations.
Franklin County Community School Corporation ● Franklin County High School ● Brookville, IN
Unit-Quarter 1 :: Topic-Algebraic Modeling - Linear Functions
A1.3.3e Translate between a table, an equation, a graph and a verbal description, given
at least one of the representations.
A1.4.1a Graph a linear equation given slope-intercept form.
A1.4.1b Graph a linear equation given in standard form.
A1.4.1c Graph a linear equation in any form.
A1.4.2a Find the slope of a line given its graph.
A1.4.2b Find the slope of a line given its equation.
A1.4.2c Find the slope of a line given two points on the line.
A1.4.2d Find the x-intercept and the y-intercept of a line given its graph.
A1.4.2e Find the x-intercept and the y-intercept of a line given its equation.
A1.4.2f Find the x-intercept and the y-intercept of a line given two points on the line.
A1.4.3a Write the equation of a line in slope-intercept form, given the slope and the y-
intercept.
A1.4.3b Write the equation of a line in slope-intercept form, given a graph.
A1.4.3c Demonstrate how the slope and y-intercept of the graph are related to an linear
equation in slope-intercept form.
A1.4.3d Write the equation of a line in slope-intercept form, given the standard form.
A1.4.3e Write the equation of a line in slope-intercept form, given a table.
A1.4.3f Write the equation of a line in slope-intercept form, given a verbal description.
A1.4.4a Write the equation of a line given two points on the line.
A1.4.4b Write the equation of a line given one point on the line and an equation of a
parallel line.
A1.4.4c Write the equation of a line given one point on the line and an equation of a
perpendicular line.
A1.4.4d Write the equation of a line, given a combination of points on the line, x- or y-
intercepts, or the slope of the line.
Unit-Quarter 1 2 :: Topic-Reasoning with Equations and Inequalities
A1.3.3e Translate between a table, an equation, a graph and a verbal description, given
at least one of the representations.
A1.4.5a Write the equation of a line that models a data set.
A1.4.5b Use the equation of a line or the graph of the equation to make predictions with
a given data set.
Franklin County Community School Corporation ● Franklin County High School ● Brookville, IN
A1.4.5c Find the slope of the line described by a given data set.
A1.4.5d Determine the rate of change for a specified measure based on the equation or
graph for a given set of data.
A1.4.6a Graph a linear inequality in two variables.
A1.5.1a Explain that the solution of a pair of linear equations in two variables is the
intersection of their graphs.
A1.5.1b Estimate the solution of a pair of linear equations in two variables by graphing.
A1.5.2a Graph a pair of linear inequalities on the same coordinate plane.
A1.5.2b Shade the region of the graph that represents the solution set of a pair of linear
inequalities.
A1.5.2c Identify the solution set of a pair of linear inequalities in two variables given their
graphs.
A1.5.3a Solve a pair of linear equations in two variables by using the substitution
method.
A1.5.4a Solve a pair of linear equations in two variables by elimination using addition or
subtraction.
A1.5.5a Solve a pair of linear equations in two variables by elimination using
multiplication with addition or subtraction.
A1.5.6a Write a pair of linear equations from information provided in a word problem.
A1.5.6b Determine whether graphing, substitution, or elimination would be the most
appropriate technique for given set of linear equations.
A1.5.6c Solve word problems involving pairs of linear equations.
Unit-Quarter 2 :: Topic-Interpreting Functions
A1.3.1a Apply appropriate labels and intervals to each axis.
A1.3.1b Sketch a reasonable graph for a given relationship.
A1.3.2a Describe relationships between two measures on the horizontal and vertical
axes
A1.3.2b Explain what is going on at a specific point or during a particular interval on a
graph.
A1.3.3a Identify the criteria for a relationship to be considered a function.
A1.3.3b Determine whether a list or table of ordered pairs represents a function
A1.3.3c Determine whether a given graph represents a function
A1.3.3d Determine whether a given equation represents a function
A1.3.3e Translate between a table, an equation, a graph and a verbal description, given
at least one of the representations.
A1.3.4a Find the domain and range of a list or table of ordered pairs
A1.3.4b Find the domain and range of a given graph
A1.3.4c Find the domain and range of a given equation
Franklin County Community School Corporation ● Franklin County High School ● Brookville, IN
Unit-Quarter 2 3 :: Topic-Arithmetic with Polynomials and Rational Expressions
A1.1.1a Evaluate real number expressions
A1.1.1b Order real number expressions
A1.1.3a Simplify expressions by using the associative and commutative properties to
combine like terms.
A1.1.3d Simplify polynomial expressions by using the distributive property.
A1.1.4a Identify root and power of rational exponents
A1.1.4b Simplify real number expressions with rational exponents.
A1.1.4c Simplify algebraic expressions with rational exponents.
A1.6.1a Define and identify monomial and polynomial.
A1.6.1b Add and subtract monomials.
A1.6.1c Add and subtract polynomials.
A1.6.2a Multiply and divide monomials.
A1.6.3a Find powers of monomials.
A1.6.3b Find roots of monomials (only when the answer has an integer exponent).
A1.6.4a Multiply monomials by binomials.
A1.6.4b Multiply monomials by polynomials.
A1.6.4c Multiply binomials by binomials.
A1.6.4d Multiply polynomials by polynomials.
A1.6.5a Divide polynomials by monomials.
Unit-Quarter 3 :: Topic-Reasoning with Equations and Inequalities
A1.1.3c Simplify quadratic expressions by using the distributive property.
A1.6.6a Find the greatest common monomial factor in a polynomial and rewrite the
polynomial in factored form.
A1.6.7a Factor quadratics that are a difference of two squares.
A1.6.7b Factor quadratic equations.
A1.7.2b Solve algebraic proportions that lead to quadratic equations.
A1.8.2a Explain the Zero Product Rule in relation to solving factored quadratic
equations.
A1.8.2b Solve quadratic equations by factoring completely and then applying the Zero
Product rule.
A1.8.3a Solve quadratic equations in which a perfect square equals a constant.
A1.8.3b Solve quadratic equations in which a binomial squared equals a constant.
Franklin County Community School Corporation ● Franklin County High School ● Brookville, IN
A1.8.4a Identify perfect square trinomials
A1.8.4b Construct a perfect square trinomial by completing the square, given the first
two terms of the trinomial.
A1.8.4c Factor perfect square trinomials and rewrite as a quantity squared.
A1.8.4d Complete the square to solve quadratic equations
Unit-Quarter 3 4 :: Topic-Seeing Structure in Expressions
A1.1.2a Simplify square roots using factors
A1.1.2b Simplify rational expressions with square roots.
A1.8.5a Derive the quadratic formula by completing the square.
A1.8.6a Simplify expressions that contain radicals.
A1.8.6b Determine the decimal approximation of expressions with radicals.
A1.8.6c Determine the value of a, b and c from a quadratic equation.
A1.8.6d Solve quadratic equations by using the quadratic formula.
Unit-Quarter 4 :: Topic-Algebraic Modeling - Quadratic Functions
A1.6.8a Identify the x-intercepts and zeros of a given quadratic graph.
A1.6.8b Identify the solutions of quadratic equations.
A1.6.8c Identify the zeros of quadratic functions.
A1.6.8d Solve a quadratic equation by graphing.
A1.6.8e Describe the relationships among the x-intercepts of a quadratic graph, the
solutions of a quadratic equation, the zeros of a quadratic function, and the factors of a
quadratic expression.
A1.8.1a Graph quadratic equations both with positive and with negative leading
coefficients.
A1.8.1b Graph cubic equations both with positive or with negative leading coefficients.
A1.8.1c Identify the basic shape of the graph of a radical function.
A1.8.1d Graph radical equations with positive or negative leading coefficients
A1.8.7a Solve word problems that involve quadratic equations.
A1.8.8a Solve equations that contain radical expressions equal to a constant.
A1.8.8b Solve equations that contain radical expressions equal to the variable in the
expression.
A1.8.9a Use graphing technology to find approximate solutions of quadratic equations.
A1.8.9b Use graphing technology to find approximate solutions of cubic equations.
Franklin County Community School Corporation ● Franklin County High School ● Brookville, IN
Unit-Quarter 4 :: Topic-Arithmetic with Polynomials and Rational Expressions
A1.1.5a Use dimensional unit analysis to organize conversions and computations
A1.7.1a Simplify algebraic ratios.
A1.7.2a Solve algebraic proportions that lead to linear equations.
A1.7.2b Solve algebraic proportions that lead to quadratic equations.
A1.7.2c Solve algebraic proportions that lead to polynomial equations.
Unit-Quarter 4 for and make use of structure.
SMP8. Look for and express regularity in repeated reasoning |
I have limited time to spend on the resource (3-6 hours) and never done any proofs and I need to be able to apply deductive, inductive and other proof techniques to some relatively easy propositions (basic number theory, trees etc.).
Please recommend a resource (website, or short book) that will meet these objectives.
Not exacxtly "quick and dirty", but the best resource for learning to prove stuff is Polya's How To
–
user22805Sep 2 '12 at 4:38
This is a strange request. What is limiting your time?
–
SnowballSep 2 '12 at 4:50
1
@Snowball: My work schedule is pretty busy and I am getting my CPA. Maybe I can accommodate more time, but it will be hard to invest too much into it. The purpose of my request is for an online/distance learning class I am enrolled in (algorithms) that has proofs in homework problems.
–
Wuschelbeutel KartoffelhuhnSep 2 '12 at 4:56
1
Learning how to prove things is a skill you learn yourself through practice...there is no book that will make you create your own proofs of things. This is not just a "topic of maths" that can be learned in a few hours but the basis of all mathematical thought!
–
frettySep 2 '12 at 9:04
This skill takes a little time to cultivate, but you should be able to make rapid progress if you are determined! You can probably get helpful feedback on your proof-work here, too.
–
rschwiebSep 2 '12 at 13:20
2 Answers
How to Prove It (this could be used by anyone in highschool or a bit before)
For basic number theory stuff you have several options depending upon your background:
If you don't have any abstract algebra, then I would reccomend Elementry Number theory by Strayer. It does use some algebra, but very little. There is also the Rosen book, which is widely used. Rosen is supposed to be simple and straight forward.
For graph theory stuff, any introductory discrete math book would be fine, enless you want to learn a lot about the subject. In the case that you do want to learn a fair amount about it, then I would reccomend Graphs and Digraphs by Chartrand, Lesinak, and Zhang. The 2nd option is much more involved. You can also find plenty of free introductory number theory books online, by googling "free number theory." Apperently, number theory is stuck in jail.
thank you very much for the recommendations. however, it would be overkill to get a book for each type of problem i am trying to solve (they are relatively elementary - its more about the introductory application of proof techniques, rather than the mathematical domain of the problems). i am at the college level and the types of problems i want to be able to solve are "show directly that this tree has n-1 nodes", "show that this expression(x) is larger than that expression(x) via induction"
–
Wuschelbeutel KartoffelhuhnSep 2 '12 at 5:01
In all honestly, I think that if you're just looking for one source, you're better off getting a general discrete math book. These books always cover some number theory and graph theory. Just search "discrete math" on amazon or w/e and find a book that appeals to you. These books usually have an intro proof section too.
–
Chris DugaleSep 4 '12 at 5:13
I'm kind of amazed that no one's pointed out the tricki yet. Also if you search for the type of question you're thinking of you should be able to find great examples of simple proof techniques (induction, telescopy, etc.) on this very site. And if you know the names of techniques I think google will be your friend: searching explain proof by induction turns up some useful results and nice examples.
thanks for those tips. i checked out tricki but im specifically looking for a nice and easy intro/overview, and the proofs there seem to be more advanced (analysis etc). i will keep in mind to search for simple proofs on the web and on this site.
–
Wuschelbeutel KartoffelhuhnSep 2 '12 at 21:01 |
More About
This Textbook
Overview
Probability Models is designed to aid students studying probability as part of an undergraduate course on mathematics or mathematics and statistics. It describes how to set up and analyze models of real-life phenomena that involve elements of chance. Motivation comes from everyday experiences of probability via dice and cards, the idea of fairness in games of chance, and the random ways in which, say, birthdays are shared or particular events arise. Applications include branching processes, random walks, Markov chains, queues, renewal theory, and Brownian motion. No specific knowledge of the subject is assumed, only a familiarity with the notions of calculus, and the summation of series. Where the full story would call for a deeper mathematical background, the difficulties are noted and appropriate references given. The main topics arise naturally, with definitions and theorems supported by fully worked examples and some 200 set exercises, all with solutions.
Editorial Reviews
From the Publisher
From the reviews:
MATHEMATICAL REVIEWS
"…gives a concise non-measure theoretic introduction to the basics of probability theory and shastic processes. The overall level is that of a first university course on the subject, given that the students have had introductory courses on linear algebra and real analysis. Numerous examples make the text fairly light reading…the mathematically less trained reader will find the language (and terminology) used pleasant: no unnecessary pedantic notation is wasted. The more mathematically inclined reader will learn form both the examples and pedagogic line of approach. In summary, I find [this book] a useful text to have on my shelves and would consider using it as a textbook for science and engineering students. Mathematics students would benefit from it as a first contact with the world of randomness before delving deeper using a measure theoretic approach."
ISI SHORT BOOK REVIEWS
"What makes this book so interesting is the fact that, in only two hundred and fifty pages, the reader is brought from the very beginning to a fairly high level in the knowledge of probability theory. ... There is a wealth of about two hundred exercisis, with solutions, which makes the book useful for teaching."
ISI Short Book Reviews, Vol. 22/3, December 2002
"'The purpose of this book is to provide a sound introduction to the study of real-world phenomena that possess random variation'. … this one is a nice choice, written in a broad and lively style." (P. Schmitt, Monatshefte für Mathematik, Vol. 143 (1), 2004)
"A clear treatment of probability theory … it has a great deal to recommend it. … there is a real attempt to provide a readable account of the material without getting too bogged down in analytical detail and … without ignoring the issues or resorting to over-simplification. … It is good to have such specialized material in what is essentially a text for undergraduates, and I can recommend this stimulating book to anybody who is looking for a way to spice up their knowledge." (Gerry Leversha, The Mathematical Gazette, Vol. 88 (512), 2004)
"What makes this book so interesting is the fact that, in only two hundred and fifty pages, the reader is brought from the very beginning to a fairly high level in the knowledge of probability theory. … The author deals in an elegant way with important theorems such as the central limit theorem and the laws of large numbers. … There is a wealth of about two hundred exercises, with solutions, which makes the book useful for teaching." (N.D.C. Veraverbeke, Short Book Reviews, Vol. 22 (3), |
More About
This Textbook
Overview
This volume celebrates the first decade of the Computer Algebra system Magma. With a design based on the ontology and semantics of algebra, Magma enables users to rapidly formulate and perform calculations in the more abstract parts of mathematics. This book introduces the reader to the role Magma plays in advanced mathematical research through 14 case studies which, in most cases, describe computations underpinning new theoretical results. The authors of the chapters were chosen both for their expertise in the particular field and for their innovative use of Magma. Although by no means exhaustive, the topics range over much of Magma's coverage of algorithmic algebra: from number theory and algebraic geometry, via representation theory and group theory to some branches of discrete mathematics and graph theory. A basic introduction to the Magma language is given in an appendix. The book is simultaneously an invitation to learn a new programming language in the context of contemporary research problems, and an exposition of the types of problem that can be investigated using computational algebra.
Table of Contents
Preface.- Magma: the project.- About this volume.- How to read the Magma code?- W.Bosma: Some computational experiments in number theory.- C.Fieker: Applications of the class field theory of global fields.- N.Bruin: Some ternary Diophantine equations of signature (n,n,2).- W.Stein: Studying the Birch and Swinnerton-Dyer conjecture for modular abelian varieties using Magma.- P.B.van Wamelen: Computing with the analytic Jacobian of a genus 2 curve.- G.Brown: Graded rings and special K3 surfaces.- D.E.Taylor: Constructing the split octonions.- J.F.Carlson: Support varieties for modules.- J.F.Carlson: When is projectivity detected on subalgebras?- D.F.Holt: Cohomology and group extensions in Magma.- C.M.Roney-Dougal, W.R.Unger: Computing the primitive permuation groups of degree less than 1000.- V.Gebhardt: Computer aided discovery of a fast algorithm for testing conjugacy in braid groups.- M.Grassl: Searching for linear codes with large minimum distance.- P.Lieby: Colouring planar graphs.- G.Bailey: Appendix: The Magma Language.- |
Western science relies on mathematics as a powerful language for expressing the character of the observed world. Mathematical models allow predictions, more or less, of complex natural systems, and modern computing has both magnified the power of those models and helped shape new models that increasingly influence 21st-century decisions. Computer science, the constructive branch of mathematics, relies on mathematics for its culture and language of problem solving, and it also facilitates the construction of mathematical models.
In this program, we will explore connections between mathematics, computer science, and the natural sciences, and develop mathematical abstractions and the skills needed to express, analyze, and solve problems arising in the sciences. The regular work of the program will include seminars, lectures, problem solving workshops, programming labs, problem sets, and seminar papers. The emphasis will be on fluency in mathematical thinking and expression along with reflections on mathematics and society. Topics will include concepts of algebra, functions, algorithms, computer programming, and problem solving, with seminar readings about the role of mathematics in modern education and in society.
This program is intended for students who want to gain a fundamental understanding of mathematics and computing before leaving college or before pursuing further work in the sciences. |
concept of understanding in mathematics with regard to mathematics education is considered in this volume, the main problem for mathematics teachers being how to facilitate their students' understanding of the mathematics being taught. |
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Mathematics Curriculum Guide Revised 2007. Available at Roanoke County Public Schools does not discriminate with regard to race, color, national ...
High School Precalculus Course Aims To expand on concepts found in geometry and advanced algebra, introduce new topics related to trigonometry, and develop a solid ... school/Math/pre calc.pdf
AP Calculus BC Syllabus Course Overview My objective in teaching AP Calculus BC is to enable students to appreciate the usefulness and beauty of calculus while ... |
College of the Redwoods
OPTIMATH
Online Practice and Testing in Mathematics Spring/Summer 2012
Practice Exercises for course Math 376
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Mathematics Principles Teachers Pack V10
Overview
Mathematics Principles V10 Teachers Pack. A combined eBook and educational site licence software package at a tiny fraction of the previously published price. Now published as a portable, learning, reference and subject revision guide, students, teachers and hobbyists can have their own low-cost portable version as an eBook. For easy reading, a comprehensive list of hundreds of topics each with a graphic image and explanatory text act as a useful exam revision reminder or reference tool for professionals. The accompanying software which brings all these images to life can be downloaded at no extra charge thereby providing an additional computer based interactive learning resource as an easy and enjoyable way to study. Unlock the accompanying software with your eBook receipt. Chapters (250 topics):- Mathematics Tools, Number Systems, Number Conversion, Number Types, Compound Measures, Roots, Angles and Parallels, Triangle Ratios, Triangle Angles, Percentages, Ratios, Fractions, Vectors, Geometry, Circle Angles, Area, Surface Area and Symmetry, Volume, Laws, Algebra 0., Algebra 1., Algebra 2., Mathematical Rules, Powers and Indices, Simplifying, Linear Equations, Graphing, Slope and Translation, Curves and Angle Conversion, Personal Finance, Data Analysis, Binary Numbers, Binary Arithmetic, Additional Notes. |
Math.NET Numerics
Numerics is the numerical foundation of the Math.NET project, aiming to provide methods and algorithms for numerical computations in science, engineering and every day use. Covered topics include special functions, linear algebra, probability models, random numbers, interpolation, integral transforms and more. |
books.google.pl - This... Mathematics
Concrete Mathematics: Foundation for Computer Science
This discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline.
Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories. Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study.
Major topics include:
Sums
Recurrences
Integer functions
Elementary number theory
Binomial coefficients
Generating functions
Discrete probability
Asymptotic methods
This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them.
0201558025B04062001
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Oceny użytkowników
Z 5 gwiazdkami
15
Z 4 gwiazdkami
4
Z 3 gwiazdkami
3
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Review: On to C++
Recenzja użytkownika - Thom - Goodreads
A good introduction to C++ which requires no prior programming experience. Using the concept of a train, object oriented concepts are hit fairly soon, before C standards such as call by reference ...Przeczytaj pełną recenzję
Review: Concrete Mathematics: A Foundation for Computer Science
Recenzja użytkownika - Avinash K - Goodreads
Really good! Well written. But really, a very good text book. If you don't want to solve the exercises (at least 40% what is called the Warm Ups and The Basics) you are better of with a book meant for ...Przeczytaj pełną recenzję
Informacje o autorze (1994 |
Note: This page contains sample records for the topic mathematics stem subjectsWithin the literature there has been a call for the integration of science, technology, engineering, and mathematics (STEM) disciplines. Little research has been conducted to investigate the effects of integrative approaches among STEMsubjects. The purpose of this study was to synthesize findings from existing research on the effects of…
|The generative economic power and social influence of Science, Technology, Engineering, and Mathematics (STEM) has made the production of a capable science and engineering workforce a priority among business and policy leaders. They are rightly concerned that without a robust STEM workforce, the nation will become less competitive in the global…
The mathematical models prevalently used to represent stem cell proliferation do not have the level of accuracy that might\\u000a be desired. The hyperbolastic growth models promise a greater degree of precision in representing data of stem cell proliferation.\\u000a The hyperbolastic growth model H3 is applied to experimental data in both embryonic stem cells and adult mesenchymal stem\\u000a cells. In the
|Science, Technology, Engineering, and Mathematics (STEM) occupations are critical to the nation's continued economic competitiveness because of their direct ties to innovation, economic growth, and productivity, even though they will only be 5 percent of all jobs in the U.S. economy by 2018. The disproportionate influence of STEM raises a…
A STEM teacher is one who teaches in the fields of science, technology, engineering, and mathematics. In K-12 schooling, most STEM teachers instruct mathematics and science classes, which continue to be critical shortage areas. As part of a comprehensive human capital strategy, designing recruitment initiatives to attract qualified STEM teachers…
This paper describes a mathematical model for use in analyzing single case replication series. First, a mathematical model of two adjacent single subject design phases is developed with some mathematical rigor. Then, a comparative data analysis is performed, comparing the information produced by a classical pretest-posttest design analysis, a classical single subject visual analysis, and an analysis employing components of
|Over the past eight years or so, educators have struggled to make sense of the many views and definitions of science, technology, engineering, and mathematics (STEM) education and what constitutes quality in STEM practices. The multitude of recent STEM funding opportunities has done little to create a common understanding about how to best engage…
\\u000a In Chapters 2 and 3 I sought to question the past primacy of notions of psychology centred on individuals apprehending mathematical\\u000a objects. Objects, whether mathematical or artistic, develop meaning relationally to other objects, and in relation to the\\u000a persons apprehending them. Objects do not have meaning in themselves. They are accessed through stories told about them. These\\u000a stories structure theScholars have theorized and examined women's underrepresentation in science, technology, engineering and mathematics (STEM) fields for well over thirty years. However, much of this research has paid little attention to issues of racial and ethnic diversity among women, suggesting that all women have the same experiences in STEM. Women of color…
|This paper addresses the issue of subjectivity in the context of mathematics education research. It introduces the psychoanalyst and theorist Jacques Lacan whose work on subjectivity combined Freud's psychoanalytic theory with processes of signification as developed in the work of de Saussure and Peirce. The paper positions Lacan's subjectivitysubject areas, and/or between a STEMsubject…
We have been investigating the applicability of fuzzy mathematics in safety assessments (PSAs). It is a very efficient approach, both in terms of methodology development time and program execution time. Most importantly, it processes subjective information subjectively, not as if it were based on measured data. One of the most useful results of this work is that we have shown the potential for significant differences (especially in perceived margin relative to a decision threshold) between fuzzy mathematics analysis and conventional PSA analysis. This difference is due to subtle factors inherent in the choice of probability distributions for modeling uncertainty. Since subjective uncertainty, stochastic variability, and dependence are all parts of most practical situations, a technique has been developed for combining the three effects. The methodology is based on hybrid numbers and on Frechet inequality dependency bounds analysis. Some new results have also been obtained in the areas of efficient disjoint set representations and constrained uncertainty and variability analysis.
|This study investigates whether students' approach to studying their main honours degree subject differs from how they approach studying mathematics as a service subject. It builds upon work by Crawford, Nicholas, Gordon and Prosser that looked at mathematics students' approaches to studying mathematics and their conceptions of mathematics. Two…
The need for high quality science, technology, engineering, and mathematics (STEM) education has been touted by numerous reports that link our Nation's future economic success and security to a highly skilled STEM workforce. National studies and internati...
Recently, adult stem cells have become a focus of intensive biomedical research, but the complex regulation that allows a small population of stem cells to replenish depleted tissues is still unknown. It has been suggested that specific tissue structures delimit the spaces where stem cells undergo unlimited proliferation (stem cell niche). In contrast, mathematical analysis suggests that a feedback control
|This text, occasioned by a critical reading of "Mathematics Education and Subjectivity" (Brown, "2011") and constituting a response to the book, aims at contributing to the building of (post-structuralist) theory in mathematics education. Its purpose was to re/write two major positions that "Mathematics Education and Subjectivity" articulates:…
STEM (science, technology, engineering and mathematics) has been a powerful engine of prosperity in the US since World War II. Currently, American students' performances and enthusiasm in STEM education are inadequate for the US to maintain its leadership in STEM professions unless the government takes more actions to motivate a new generation of…
The cancer stem cell (CSC) hypothesis states that only a small fraction of a malignant cell population is responsible for tumor growth and relapse. Understanding the relationships between CSC dynamics and cancer progression may contribute to improvements in cancer treatment. Analysis of a simple discrete mathematical model has suggested that homeostasis in developing tissues is governed by a "quorum sensing" control mechanism, in which stem cells differentiate or proliferate according to feedback they receive from neighboring cell populations. Further analysis of the same model has indicated that excessive stem cell proliferation leading to malignant transformation mainly results from altered sensitivity to such micro-environmental signals. Our aim in this work is to expand the analysis to the dynamics of established populations of cancer cells and to examine possible therapeutic avenues for eliminating CSCs. The proposed model considers two populations of cells: CSCs, which can divide indefinitely, and differentiated cancer cells, which do not divide and have a limited lifespan. We assume that total cell density has negative feedback on CSC proliferation and that high CSC density activates CSC differentiation. We show that neither stimulation of CSC differentiation nor inhibition of CSC proliferation alone is sufficient for complete CSC elimination and cancer cure, since each of these two therapies affects a different subpopulation of CSCs. However, a combination of these two strategies can substantially reduce the population sizes and densities of all types of cancer cells. Therefore, we propose that in clinical trials, CSC differentiation therapy should only be examined in combination with chemotherapy. Our conclusions are corroborated by clinical experience with differentiating agents in acute promyelocytic leukemia and neuroblastoma. PMID:22210402
|There is a widespread awareness in the American culture that women do not pursue careers in mathematics-related fields in equal numbers to men. Efforts to address this disparity by reforming mathematics education have met with some success; recent research shows that girls' achievements in mathematics stay on par with those of boys through…
There is growing concern that the United States is not preparing a sufficient number of students, teachers, and practitioners in the areas of science, technology, engineering, and mathematics (STEM). A large majority of secondary school students fail to r...
This report responds to a request from Representative Frank Wolf (VA) for the National Science Foundation (NSF) to identify highly successful K-12 schools and programs in science, technology, engineering, and/or mathematics (STEM). In response to a reques...
A system dynamics model was developed in response to the apparent decline in STEM candidates in the United States and a pending shortage. The model explores the attractiveness of STEM and STEM careers focusing on employers and the workforce. Policies such as boosting STEM literacy, lifting the H-1B visa cap, limiting the offshoring of jobs, maintaining training and a combination
|Science, technology, engineering, and mathematics (STEM) are cultural achievements that reflect our humanity, power our economy, and constitute fundamental aspects of our lives as citizens, consumers, parents, and members of the workforce. Providing all students with access to quality education in the STEM disciplines is important to our nation's…
There is increasing evidence for the "cancer stem cell hypothesis" which holds that cancers originate in tissue stem cells\\u000a or progenitor cells. As a result of this, cancers are driven by a cellular subcomponent that retains stem cell properties.\\u000a Among these properties are self-renewal and multi-lineage differentiation. The biological processes which account for stem\\u000a cell properties are currently being elucidated.
|In this study I have investigated how alternative ways of teaching mathematics influence and affect Early Childhood Education (ECE) students' attitudes towards maths and how they understand their own subjectivities as more or less mathematical during a 10-week alternative maths course. The investigated course adopts a feminist post-structural…
A mathematical model is presented for a group of circular cylinders subject to crossflow. The fluid-force coefficients in the model are determined from available experimental data. It is found that there are three dynamic instability mechanisms: galloping...
|The teaching of scientific subjects usually require laboratories where students can put the theory they have learned into practice. Traditionally, electronic programmable calculators, dedicated software, or expensive software simulation packages, such as MATLAB have been used to simulate scientific experiments. Recently, spreadsheet programs have…
\\u000a While myelodysplastic syndromes (MDS) are commonly observed nowadays, the underlying mechanisms remain unclear, not to mention\\u000a mathematical models for MDS. In this work, by incorporating the concept of stem cell niches, we proposed a minimal mathematical\\u000a model that can be used as a platform for studying the formation and treatment of MDS. Our model includes two main compartments:\\u000a bone marrow
Science, mathematics, engineering, and technology (STEM) are fundamental aspects of everyone's lives as citizens, consumers, parents, and workers. Providing all students with access to high-quality education in STEM is important to their futures and that of the U.S. What can schools do to meet this goal for their students? Successful K-12 STEM Education tackles this question, focusing on the science and mathematics parts of STEM and on criteria for identifying effective STEM schools and practices. The report gives an overview of the landscape of K-12 STEM education by considering different school models, highlighting research on effective STEM education practices, and identifying some conditions that promote and limit school- and student-level success in STEM. It can serve as a guide for those involved in K-12 education at all levels: policy makers; decision makers at the school and district levels; local, state, and federal government agencies; curriculum developers; educators; and parent and education advocacy groups. Free download of this publication is available to registered users of National Academies Press.
|In this volume, Wolff-Michael Roth provides a critical but partial reading of Tony Brown's book "Mathematics Education and Subjectivity". The reading contrasts Brown's approach with Roth's own conception of subjectivity as derived from the work of Vygotsky, in which Roth aims to "reunite" psychology and sociology. Brown's book, however, focuses…
|This article focuses on science, technology, engineering, and mathematics (STEM) education in secondary inclusive classrooms. Co-teaching is increasingly used in inclusive practice by administrators to provide effective instruction in inclusive classrooms. The practical and successful instructional strategies in the article focus on one…
Mathematics is a basic subject in primary and secondary schools. Early exposure to mathematics is very important since it will affect the student perception towards this subject for their entire life. Therefore, a program called 'Mini Hari Matematik' was conducted to expose the basic mathematics concept through some games which fit the knowledge of Standard four and five students. A questionnaire regarding student perception towards this subject was distributed before and after the program. From the analysis, the program has positively changed the student's perception towards mathematics.
|The overarching goal of the Science, Technology, Engineering, and Mathematics (STEM) Education Initiative is to foster effective STEM teaching and learning throughout the educational system at the local, state, and national levels, thereby producing science literate citizens and a capable STEM workforce. To contribute to achieving this goal, we… primary teachers' subject knowledge in mathematics and considers the relevance of an audit of higher-level subject knowledge to the subject knowledge required for teaching primary mathematics. Questionnaires and interviews were carried out to determine the views of generalist…
This article explores, through interview data with 125 respondents in Canada, whether the study of foreign languages can be considered as important as the study of the "core" STEMM (science, technology, engineering, mathematics, medicine) subjects in school and university curricula. Five categories of interviewees, including those involved and not…
Based on the Bureau of Labour and Statistics (BLS) employment projections, more and more technology-driven jobs will be created and, therefore, demand for highly-skilled technologically-trained professionals will increase. What is being done in the United States (US) to ensure a steady flow in the dwindling pipeline of Science, Technology, Engineering and Mathematics (STEM) workforce? The US has a number of
Mathematical and statistical image analysis methods and systems are applied to enhance and refine the process of reprogramming cells, for example, to modify cells from patients into custom-matched stem cells.
|Many scholars claimed the integration of science, technology, engineering and mathematics (STEM) education is beneficial to the national economy and teachers and institutes have been working to develop integrated education programs. This study examined a project-based learning (PjBL) activity that integrated STEM using survey and interview…
|The author examined enrollment differences at postsecondary institutions between students with and without disabilities in science, technology, engineering, and mathematics (STEM) majors to investigate the extent to which students with disabilities, compared with their counterparts, pursue highly demanded STEM careers that require postsecondary…
|This study examined the characteristics of 10 science, technology, engineering and mathematics (STEM) focused high schools that were selected from various regions across the United States. In an effort to better prepare students for careers in STEM fields, many schools have been designed and are currently operational, while even more are in the…
Chemo-irradiation induced oxidative damage to vascular endothelium may contribute to pulmonary complications of hematopoietic stem cell transplantation (HSCT). We compared antioxidants, markers of oxidative stress and the ability of plasma to handle an oxidative stress in plasma or serum from 24 sub...
STEM fields. In order to increase the representation of women in the STEM fields, it is important to understand the developmental factors that impact girls' interest and confidence in STEM academics and extracurricular programs. Research indicates that greater confidence leads to greater interest and vice versa (Denissen et al., 2007). This study identifies factors that impact girls' interest and confidence in mathematics and science, defined as girls' STEM development. Using Bronfenbrenner's (2005) bioecological model of human development, several factors were hypothesized as having an impact on girls' STEM development; specifically, the macrosystems of region of residence and race/ethnicity, and the microsystems of extracurricular STEM activities, family STEM influence, and math/science teacher influence. Hierarchical regression analysis results indicated that extracurricular STEM involvement and math teacher influence were statistically significant predictors for 6--12th grade girls' interest and confidence in mathematics. Furthermore, hierarchical regression analysis results indicated that the only significant predictor for 6--12th grade girls' interest and confidence in science was science teacher influence. This study provides new knowledge about the factors that impact girls' STEM development. Results can be used to inform and guide educators, administrators, and policy makers in developing programs and policy that support and encourage the STEM development of 6--12th grade girls.
Over the past decade most, if not all, university departments of mathematics, science and engineering have talked about a decline in the mathematical capabilities of their entry cohorts. Anecdotal evidence from the universities and the press has blamed this drop on a lowering of standards at A level. However, it may be due to the lowering of admission requirements to
This was a study to explore the persistence and success of underrepresented minorities in undergraduate science, technology, engineering, and mathematics (STEM) majors. Specifically, the effect of the precollege STEM curriculum on the preparation and persistence of undergraduate STEM students was examined. National statistics continue to illuminate the need for increasing the number of underrepresented minority students attaining STEM degrees, emphasizing that a large percentage of these students have enrolled in these majors. The persistence of traditional and nontraditional students was considered in the study. The following research questions were used to determine the types of data that was collected and analyzed: (a) How does the precollege STEM curriculum affect the persistence or non-persistence of underrepresented minorities in undergraduate STEM majors? (b) How can curriculum reform motivate underrepresented minority learners to persist to undergraduate STEM degrees? (c) What types of instructional methods aid in nontraditional STEM students persistence and degree attainment? A qualitative approach was identified as the appropriate methodology to address the research questions, and the data collecting tool, consisting of semi-structured interviews gave rich descriptions into the STEM students' preparation, persistence, and success. Findings from this research will help to improve understandings about underrepresented minorities' precollege STEM preparation and its effect on their postsecondary STEM success, thus adding to the growing body of knowledge about improving underrepresented minorities' persistence and degree attainment in STEM programs. The findings of this study suggest that the most important factor for underrepresented minority in undergraduate STEM programs to succeed and persist is their precollege STEM preparation.
|A series of activities were undertaken to understand the underrepresentation and increase the participation of people with disabilities in science, technology, engineering, and mathematics (STEM) careers. These activities were funded by the Research in Disabilities Education (RDE) program of the National Science Foundation (NSF). They were…
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|In this paper, based on a project funded by the UK Economic and Social Research Council considering how people position themselves in relation to popular representations of mathematics and mathematicians, we explore constructions of mathematicians in popular culture and the ways learners make meanings from these. Drawing on an analysis of popular…
In this paper, based on a project funded by the UK Economic and Social Research Council considering how people position themselves in relation to popular representations of mathematics and mathematicians, we explore constructions of mathematicians in popular culture and the ways learners make meanings from these. Drawing on an analysis of popular…
Summary and Conclusions 1.This report deals with the effect of brain stem transection on glucose tolerance over a period of several weeks postoperatively. Of 23 rats and 12 dogs subjected to this operation, all showed a reduction of glucose tolerance regardless of the level of transection, whether pontile, midbrain, or hypothalamic. In 8 rats and 1 dog in which the
|In 2004, the pattern in academic pathways for high school students in the USA showed that students were completing more demanding mathematics courses. Despite the upward pattern in advanced-level mathematics course-taking, disparities among racial/ethnic groups persisted between 1982 and 2004. Using data from the Education Longitudinal Study of…
In 2004, the pattern in academic pathways for high school students in the USA showed that students were completing more demanding mathematics courses. Despite the upward pattern in advanced-level mathematics course-taking, disparities among racial\\/ethnic groups persisted between 1982 and 2004. Using data from the Education Longitudinal Study of 2002 (ELS: 2002; Ingels et al., 2007), the current study sought to
Federal STEM education policy concerns center on issues that relate to STEM education as a whole, such as governance of the federal effort and broadening participation of underrepresented populations, as well as those that are specific to STEM education a...||In this study, we explored the experience of Asian international doctoral students in the Science, Technology, Engineering, and Mathematics (STEM) fields at one research-extensive university. We found that Asian international doctoral students in the STEM fields at this institution were often isolated from their peers and faculty, faced an array…
To date, models for simulating sap flow dynamics in individual trees with a direct link to stem diameter variation include only the diameter fluctuation driven by a change in stem water storage. This paper reports results obtained with a comprehensive flow and storage model using whole-tree leaf transpiration as the only input variable. The model includes radial stem growth based on Lockhart's equation for irreversible cell expansion. It was demonstrated that including growth is essential to obtaining good simulation results. To model sap flow dynamics, capacitance of storage tissues was assumed either constant (i.e., electrical analogue approach) or variable and dependent on the water content of the respective storage tissue (i.e., hydraulic system approach). These approaches resulted in different shapes for the desorption curve used to calculate the capacitance of storage tissues. Comparison of these methods allowed detection of specific differences in model simulation of sap flow at the stem base (F(stem)) and stem diameter variation (D). Sensitivity analysis was performed to select a limited subset of identifiable parameters driving most of the variability in model predictions of F(stem) and D Both the electrical analogue and the hydraulic system approach for the flow and storage model were successfully calibrated and validated for the case of a young beech tree (Fagus sylvatica L.). Use of an objective model selection criterion revealed that the flow and storage model based on the electrical analogue approach yielded better predictions. PMID:16356899
Acquiring abundant and high-purity cancer stem cells (CSCs) is an important prerequisite for CSC research. At present, researchers usually gain high-purity CSCs through flow cytometry sorting and expand them by short-term sphere culture. However, it is still uncertain whether we can amplify high-purity CSCs through long-term sphere culture. We have proposed a mathematical model using ordinary differential equations to derive the continuous variation of the CSC ratio in long-term sphere culture and estimated the model parameters based on a long-term sphere culture of MCF-7 stem cells. We found that the CSC ratio in long-term sphere culture presented as gradually decreased drift and might be stable at a lower level. Furthermore, we found that fitted model parameters could explain the main growth pattern of CSCs and differentiated cancer cells in long-term sphere culture.
A mathematical model is presented for a group of circular cylinders subject to crossflow. The fluid-force coefficients in the model are determined from available experimental data. It is found that there are three dynamic instability mechanisms: galloping controlled by fluid damping, flutter controlled by fluidelastic force, and coupled galloping-flutter instability controlled by both fluid damping and fluidelastic force. Closed-form solutions of the critical flow velocity for galloping and flutter are obtained based on constrained modes. Experimental data are found to be in good agreement with the analytical results.
This paper describes the results of a series of human-subjects experiments to test how people think about spatial relations between lines and regions. The experiments are centered on a formal model of topological spatial relations, called the 9-intersection. For unbranched lines and simply-connected regions, this model identifies 19 different spatial relations. Subjects were presented with two or three geometrically-distinct drawings
Linear lumped parameter models of the apparent masses of human subjects in standing positions when exposed to vertical whole-body vibration have been developed. Simple models with a single degree-of-freedom (d.o.f.) and with two (d.o.f.) were considered for practical use. Model parameters were optimised using both the mean apparent mass of 12 male subjects and the apparent masses of individual subjects measured in a previous study. The calculated responses of two (d.o.f.) models with a massless support structure showed best agreement with the measured apparent mass and phase, with errors less than 0.1 in the normalised apparent mass (i.e., corresponding to errors less than 10% of the static mass) and errors less than 5° in the phase for a normal standing posture. The model parameters obtained with the mean measured apparent masses of the 12 subjects were similar to the means of the 12 sets of parameters obtained when fitting to the individual apparent masses. It was found that the effects of vibration magnitude and postural changes on the measured apparent mass could be represented by changes to the stiffness and damping in the two (d.o.f.) models.
Hierarchical organized tissue structures, with stem cell driven cell differentiation, are critical
Hierarchical organized tissue structures, with stem cell driven cell differentiation, are critical PMID:23990931
Blood recirculating devices, such as ventricular assist devices and prosthetic heart valves, are burdened by thromboembolic complications requiring complex and lifelong anticoagulant therapy with its inherent hemorrhagic risks. Pathologic flow patterns occurring in such devices chronically activate platelets, and the optimization of their thrombogenic performance requires the development of flow-induced platelet activation models. However, existing models are based on empirical correlations using the well-established power law paradigm of constant levels of shear stress during certain exposure times as factors for mechanical platelet activation. These models are limited by their range of application and do not account for other relevant phenomena, such as loading rate dependence and platelet sensitization to high stress conditions, which characterize the dynamic flow conditions in devices. These limitations were addressed by developing a new class of phenomenological stress-induced platelet activation models that specifies the rate of platelet activation as a function of the entire stress history and results in a differential equation that can be directly integrated to calculate the cumulative levels of activation. The proposed model reverts to the power law under constant shear stress conditions and is able to describe experimental results in response to a diverse range of highly dynamic stress conditions found in blood recirculating devices. The model was tested in vitro under emulated device flow conditions and correlates well with experimental results. This new model provides a reliable and robust mathematical tool that can be incorporated into computational fluid dynamic studies in order to optimize design, with the goal of improving the thrombogenic performance of blood recirculating devices. PMID:23359062
The expression of the transcription factors Oct4, Sox2, and Nanog is commonly associated with pluripotency of mouse embryonic stem (ES) cells. However, recent observations suggest that ES cell populations are heterogeneous with respect to the expression of Nanog and that individual ES cells reversibly change their Nanog expression level. Furthermore, it has been shown that cells exhibiting a low Nanog
New technologies and virtual environments are emerging globally, yet the way these tools can impact the learning and future career paths of students who are gifted is limited in the literature at this time. The purpose of this article is to provide a summary of how a science, technology, engineering, and mathematics (STEM) summer camp, based on virtual and simulated
|Schools that give students access to STEM (science, technology, engineering and mathematics) studies are accomplishing several objectives: introducing students to higher-level academic and career studies, expanding project-based learning in the curriculum, enticing students to remain in school until graduation, and preparing students for…
A study was conducted to evaluate the feasibility of using item response theory (IRT) equating to reduce test form overlap of the Graduate Record Examinations (GRE) Subject Test in Mathematics. Monte Carlo methods were employed to compare double-part equating with 20-item common item blocks to triple-part equating with 10-item common item blocks.…
Interlinked gene regulatory networks (GRNs) are vital for the spatial and temporal control of gene expression during development. The hematopoietic transcription factors (TFs) Scl, Gata2 and Fli1 form one such densely connected GRN which acts as a master regulator of embryonic hematopoiesis. This triad has been shown to direct the specification of the hemogenic endothelium and emergence of hematopoietic stem cells (HSCs) in response to Notch1 and Bmp4-Smad signaling. Here we employ previously published data to construct a mathematical model of this GRN network and use this model to systematically investigate the network dynamical properties. Our model uses a statistical-thermodynamic framework to describe the combinatorial regulation of gene expression and reconciles, mechanistically, several previously published but unexplained results from different genetic perturbation experiments. In particular, our results demonstrate how the interactions of Runx1, an essential hematopoietic TF, with components of the Bmp4 signaling pathway allow it to affect triad activation and acts as a key regulator of HSC emergence. We also explain why heterozygous deletion of this essential TF, Runx1, speeds up the network dynamics leading to accelerated HSC emergence. Taken together our results demonstrate that the triad, a master-level controller of definitive hematopoiesis, is an irreversible bistable switch whose dynamical properties are modulated by Runx1 and components of the Bmp4 signaling pathway. PMID:23623899
Research into women's underrepresentation in science, technology, engineering, and mathematics (STEM) disciplines has become a topic of interest due to the increasing need for employees with technical expertise and a shortage of individuals to fill STEM jobs. The discrepancy in women's representation between STEM and other fields cannot adequately be explained by factors such as women's need to balance work and family (medicine and law are both extremely demanding careers), women's fear of competition (admissions into medical and law schools are highly competitive), or women's inability to excel in science (e.g., entry into medicine requires excellent achievement in the basic sciences). The purpose of this study is to gain a deeper understanding of the role and/or impact a sense of belonging has inside and outside of STEM classrooms. Research questions focused on the role and/or impact of belonging contributes to students' self-efficacy beliefs as a STEM major. Bandura's self-efficacy theory serves as the theoretical framework. Data sources include close-ended surveys of 200 sophomore- and junior-level college students majoring in a STEM discipline. A quantitative exploratory approach allowed participants' responses to be analyzed using both correlation and multiple regression analyses to understand whether a student's sense of belonging is associated with his or her self-efficacy beliefs. Findings suggested that positive support systems impact students' self-efficacy and play a role in fostering students' motivation and decision to major in STEM disciplines. This study contributes to positive social change by providing empirical evidence faculty and administrators may use to promote university-based STEM support programs reflecting the impact belonging has on students' self-efficacy and potentially increasing the number of students majoring in STEM disciplines.
The paper introduces the pest belief model and Fishbein and Ajzen's theory of reasoned action to analyze farmers' decisions in stem b|Incorporating business skills such as problem-solving, public presentations, collaboration, and self-direction into STEM (science, technology, engineering and mathematics) subjects is an excellent way to build students' enthusiasm for these disciplines. When educators add workplace internships to the learning experience, they are well on their… study sought to examine the effects of an expressive talking intervention for 58 caregiving partners of hematopoietic stem cell transplant survivors, persons known to experience distress. Caregivers were randomly assigned to a 3-session emotional expression (EE) or control condition. Subjective, objective and physiologic indicators of emotion were assessed. Relative to controls, EE participants experienced more negative emotion, uttered more negative emotion words, and perceived the exercises as more helpful and meaningful. The trajectory of skin conductance and the use of cognitive mechanism words increased across EE sessions, suggesting sustained emotional engagement. Future research is warranted to determine the optimal dose and timing of EE for this population.
Quality STEM education is the key in helping the United States maintain its lead in global competitiveness and in preparing for new economic and security challenges in the future. Policymakers and professional societies emphasize STEM education by legislating the addition of engineering standards to the existing science standards. On the other hand, the nature of the work of most STEM professionals requires people to actively apply STEM knowledge to make critical decisions. Therefore, using an integrated approach to teaching STEM in K-12 is expected. However, science teachers encounter numerous difficulties in adapting the new STEM integration reforms into their classrooms because of a lack of knowledge and experience. Therefore, high quality STEM integration professional development programs are an urgent necessity. In order to provide these high quality programs, it is important to understand teachers' perceptions and classroom practices regarding STEM integration. A multiple-case study was conducted with five secondary school science teachers in order to gain a better understanding of teachers' perceptions and classroom practices in using STEM integration. This study addresses the following research questions: 1) What are secondary school science teachers' practices of STEM integration? 2) What are secondary science teachers' overall perceptions of STEM integration? and 3) What is the connection between secondary science teachers' perceptions and understanding of STEM integration with their classroom practices? This research aims to explore teachers' perceptions and classroom practices in order to set up the baseline for STEM integration and also to determine STEM integration professional development best practices in science education. Findings from the study provide critical data for making informed decision about the direction for STEM integration in science education in K-12.
Mainstream curricula have struggled to provide American Indian students with meaningful learning experiences. This research project studied a novel approach to engaging students with science, technology, engineering, and mathematics (STEM) content through a culturally-based context. The traditional American Indian game of Snow Snakes (shushumeg in Ojibwe) presented a highly engaging context for delivering STEM content. Through the engaging context of snow snakes, the designed STEM curriculum explicitly applied mathematics (scaling and data), and science (force and motion) to an engineering prototype iteration that used available materials and tools (technology) for success. It was hypothesized that by engaging students through the carefully integrated STEM curriculum, driven by the culturally based context of snow snakes, students would exhibit an increase in science agency and achievement. The overarching research question explored for this study was: How does a culturally-based and integrated STEM curriculum impact student's science agency? Associated sub-questions were: (1) What does science agency look like for 6th grade students? (2) What key experiences are involved in the development of science agency through a culturally-based STEM curriculum context? And (3) What are the impacts on the community associated with the implementation of a culturally-based STEM curriculum? A case study research design was implemented for this research. Yin (2003) defines a case study as investigating a phenomenon (e.g. science agency) which occurs within authentic contexts (e.g. snow snakes, Adventure Learning, and Eagle Soaring School) especially when the boundaries between phenomenon and context are unclear. For this case study Eagle Soaring School acted as the bounded case with students from the 6th grade class representing the embedded units. Science agency was the theoretical framework for data analysis. Major findings were categorized as science and STEM learning, agency, and community impact. Concerning agency, students displayed science agency through: connecting snow snake experiences to outside contexts; students emerging as leaders; and students commanding a facility with science. This research lays the foundation for future inquiry into the development of science agency in students using culturally-based contexts.
|As science, technology, engineering and mathematics (STEM) education demands greater integration across all subject areas, technology teachers can showcase many of the cross-curricular projects already occurring inside their classrooms that intrigue students and build their STEM skills. Robotics, just one of those projects, has become an…
STEM is the acronym used in England for science, technology, engineering and mathematics. STEMsubjects are a central plank in developing the UK's skills base. Specialist knowledge in these subjects not only underpins many high-tech sectors--such as IT and engineering--but is also important for creativity and developing new ideas. This report…
This study aims to determine the influence of teaching Fibonacci numbers and golden ratio through history of mathematics on student achievement and the opinions of students regarding this issue. This study was carried out by case study method with 30 students who attended the 8th grade of an elementary school in Erzincan in spring term of 2009-2010 school year. Data
|The objective of this research was to identify specific factors that contribute to underrepresented minority (African American, Hispanic, Native American) undergraduate students' success in STEM disciplines at a regional university during the 2007-2010 timeframe. As more underrepresented minority (URM) students complete STEM degrees, many will…STEM education (and competitiveness) issues have received a lot of attention in recent years. Several high-profile proposals were forwarded by the academic and business communities. In February of 2006, the President released the American Competitiveness ...|This paper describes comparisons between the authors' results (from maximum-likelihood estimation techniques for cellular damage, repair, and compensatory repopulation) and published experimental data on marrow stromal cells. After biophysical consideration of the rate constants that were derived by maximizing the likelihood function (a consideration necessary to extend the model to cell populations not indicated by the model as [open quotes]critical[close quotes] for recovery), the rate constants for cellular damage to stem cells are fitted to experimental data. Rate constants for repair and proliferation of stem cells are assigned based on published data on repair/proliferation halftimes, and these assignments affect the evaluation of the rate constants for cellular damage. From the two models, that is one for [open quotes]critical[close quotes] cells (having radiosensitive and repopulation characteristics similar to stromal cells) and another for stem cells, effects on two cell populations of different radiosensitivities and repopulation rates can be demonstrated for complex schedules of protracted irradiations which could reduce either cell population below a critical need for marrow repopulation. Analysis of animal mortality data has indicated that recovery of an animal from potentially lethal irradiation is dominantly by cells with survival and repopulation characteristics similar to those of stroma cells. In contrast to the surviving fraction of hematopoietic stem cells, it appears that the probability of an animal's recovery is high if the [open quotes]critical[close quotes] population of cells is above 1% (our [open quotes]best[close quotes] maximum likelihood estimate, from mouse data, with the corresponding lower confidence bound at about 0.2%). Of course, a few stem cells-perhaps only one-must maintain a potential for repopulation of blood and marrow. 83 refs., 4 figs., 3 tabs.
There is increasing recognition that treatment failure in cancer may be associated with the failure to sterilize a small subpopulation of tumor cells that have been characterized as tumor stem cells. Defined as cells that are able to self-renew and also to replenish a phenotypically diverse tumor-cell population, such cells are also considered resistant to chemotherapy. These characteristics are optimal for targeting by using alpha-particle-emitting radionuclides. Because of their high-energy deposition density per track, alpha-particles are capable of targeting single cells or small clusters of cells with minimal normal organ toxicity. The DNA damage induced by alpha-particles is largely irreparable and, therefore, alpha-particle-induced damage is minimally susceptible to resistance mechanisms. In this work, theoretical modeling was performed to examine the potential of alpha-emitter targeting of such small clusters of cancer stem cells. Critical parameters influencing efficacy and toxicity were identified and their relationship elucidated. The results identify specific activity, antigen site density, and number of target cells as critical parameters for effective cell killing and demonstrate substantial efficacy gains by targeting a smaller number of stem cells, as opposed to the entire tumor-cell population.Diversity and the underrepresentation of women, African-Americans, Hispanics and American Indians in the nation's science, technology, engineering and mathematics (STEM) fields are the subjects of the XV: A View from the Gatekeepers--STEM Department Chairs at America's Top 200 Research Universities on Female and Underrepresented Minority…
In aerobic organisms, protection against oxidative damage involves the combined action of highly specialized antioxidant enzymes, such as copper-zinc superoxide dismutase. In this work, a cDNA clone which encodes a copper-zinc superoxide dismutase gene, named PS-CuZnSOD, has been identified from P. sibiricum Laxm. by the rapid amplification of cDNA ends method (RACE). Analysis of the nucleotide sequence reveals that the PS-CuZnSOD gene cDNA clone consists of 669 bp, containing 87 bp in the 5? untranslated region; 459 bp in the open reading frame (ORF) encoding 152 amino acids; and 123 bp in 3? untranslated region. The gene accession nucleotide sequence number in GenBank is GQ472846. Sequence analysis indicates that the protein, like most plant superoxide dismutases (SOD), includes two conserved ecCuZnSOD signatures that are from the amino acids 43 to 51, and from the amino acids 137 to 148, and it has a signal peptide extension in the front of the N-terminus (1–16 aa). Expression analysis by real-time quantitative PCR reveals that the PS-CuZnSOD gene is expressed in leaves, stems and underground stems. PS-CuZnSOD gene expression can be induced by 3% NaHCO3. The different mRNA levels' expression of PS-CuZnSOD show the gene's different expression modes in leaves, stems and underground stems under the salinity-alkalinity stress.
The purpose of this study was to investigate factors that affect the extent of international secondary students' participation in International Baccalaureate science and mathematics courses. The factors examined were gender, home region, size, percent host culture and age of the program, and coeducational and legal status of the school. Participation in math and science subjects was determined by analyzing the level and number of courses taken by students taking International Baccalaureate exams in 2010. Chi-Square and Cramer's V analysis were used to measure the effect of categorical variables on student participation and One-Way ANOVA and Bonferroni comparison of means were used to analyze the quantitative variables. All categorical variables were statistically significant (p<.01). Home region was the most important factor affecting participation in both math and science. Students from East, Southeast and South-Central Asia; and Eastern Europe have greater participation in math. The highest science participation came from students in East, Southern and Western Africa; and Southeast Asia. Top participators in science came from Australia/New Zealand, Northern Europe, East Africa and South-Central and Western Asia. State schools showed higher math and science participation. Science and math participation was also greater in all-male schools though associations were weak. Boys participated more than girls, especially in math. All quantitative variables were statistically significant. The program size had the largest effect size for both math and science with larger programs showing more participation at the higher level. A decreasing trend for age of the program and percent host culture was found for math participation. Three years of participation data were collected from an international school in Western Europe (n = 194). Variables included the influence of parent occupation, math preparedness (PSAT-Math), student achievement (GPA), and the importance of significant others in career and academic decisions. Findings indicate that performance on the PSAT- Math was the most important predictor of both science and mathematics participation. Twenty students were also interviewed. Results showed the importance of several key factors. These include the role of parents in student academic and career decisions, the importance of personal interest, and the contribution of early decisions in confidence-building.
This study investigated if a controlled water deficit during grain filling of wheat ( Triticum aestivum L.) could accelerate grain filling by facilitating the remobilization of carbon reserves in the stem through regulating the enzymes involved in fructan and sucrose metabolism. Two high lodging-resistant wheat cultivars were grown in pots and treated with either a normal (NN) or high amount
|Celebrating mathematics should be a yearlong event in which students in mathematics classes of all levels engage in mathematics activities and competitions that will encourage growth in mathematical knowledge, enthusiasm for the subject, and collaboration among students of different abilities and backgrounds. Pi Day and Pi Week festivities--a…
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included some student-level factors such as the highest level of parents'
|In many ways, the push for STEM (science, technology, engineering, and mathematics) education appears to have grown from a concern for the low number of future professionals to fill STEM jobs and careers and economic and educational competitiveness. The proponents of STEM education believe that by increasing math and science requirements in…The effect of rotational and translational acceleration on the brain was studied using two different mathematical analyses. A mathematical model of a head subjected to an angular acceleration was developed in which the brain was treated as a viscoelastic ...
|Mathematical proofs are not only the focus of every country's mathematics curriculum reforms, but also the subject of research on mathematics education. This paper is based on a survey of mathematics teachers, the goal of which was to investigate the understanding of mathematical proofs of secondary school math teachers, their levels of…
||Science, technology, engineering, and mathematics (STEM) fields, important in today's world, are underrepresented by students with disabilities. Students with visual impairments, although cognitively similar to sighted peers, face challenges as STEMsubjects are often taught using visuals. They need alternative forms of access such as enlarged or audio?converted text, tactile graphics, and involvement in hands?on science. This project focused on
Mathematics disorder is a condition in which a child's math ability is far below normal for their age, ... Children who have mathematics disorder may have trouble performing ... adding. Mathematical disorder may appear with: Developmental ...
This report describes a collaborative effort between a research assistant and a fourth-grade teacher to develop a classroom community for teaching and learning mathematics which fosters problem solving, reasoning, intellectual risk taking, appreciation of diversity, trust, and shared ownership. The characteristics are consistent with suggested…
Although the perceived compatibility between one's gender and science, technology, engineering, and mathematics (STEM) identities (gender-STEM compatibility) has been linked to women's success in STEM fields, no work to date has examined how the stability of identity over time contributes to subjective and objective STEM success. In the present study, 146 undergraduate female STEM majors rated their gender-STEM compatibility weekly during their freshman spring semester. STEM women higher in gender rejection sensitivity, or gender RS, a social-cognitive measure assessing the tendency to perceive social-identity threat, experienced larger fluctuations in gender-STEM compatibility across their second semester of college. Fluctuations in compatibility predicted impaired outcomes the following school year, including lower STEM engagement and lower academic performance in STEM (but not non-STEM) classes, and significantly mediated the relationship between gender RS and STEM engagement and achievement in the 2nd year of college. The week-to-week changes in gender-STEM compatibility occurred in response to negative academic (but not social) experiences. PMID:23818652
In the discipline didactics of mathematics, the didactical triangle of subject-teacher-learner is sometimes too narrowly interpreted by shortening the human side of didactics of mathematics ( fi teacher- learner) to teaching and learning in institutionalised settings, especially schools. In his working group of the ''Institute for Didactics of Mathematics'' (IDM) at Bi- elefeld University, Hans-Georg Steiner inserted good reasons and
|This study combines theories related to collective learning and theories related to mathematical creativity to investigate the notion of collective mathematical creativity in elementary school classrooms. Collective learning takes place when mathematical ideas and actions, initially stemming from an individual, are built upon and reworked,…
I argue in this article that identity as a mathematical thinker develops through self- directed learning within a supportive community of practice. The dynamic nature of identity as a mathematical thinker is illustrated by considering the experiences of primary pre-service teachers who undertook a mathematics and technology subject in their undergraduate education degree. The pre-service teachers developed their identity as
In July 2013, the diverse fields of biology, physics and mathematics converged to discuss 'The Physical Biology of Stem Cells', the subject of the third annual symposium of the Cambridge Stem Cell Institute, UK. Two clear themes resonated throughout the meeting: the new insights gained from advances in the acquisition and interpretation of quantitative data; and the importance of 'thinking outside the nucleus' to consider physical influences on cell fate. PMID:24086077 mathematics is associated with tennis. This…
There is a dire situation among American students in the public schools due to a lack of proficiency in science, technical, engineering, and mathematical (STEM) subjects. Interestingly, that lack of aptitude is now penetrating industry (research and development) and the workforce. This crisis is being addressed by many in the government and in the academic community who seek to meet
The article explores the effect of the engagement of university science, technology, engineering, and mathematics (STEM) faculty in the Math and Science Partnership program. The findings suggest that K-12 teachers benefited from the engagement in terms of improved approaches to teaching and learning, increased knowledge of subject matter content,…
A DEMONSTRATION PROGRAM WAS UNDERTAKEN FOR THE PURPOSE OF SHOWING HOW A STATE DEPARTMENT OF EDUCATION CAN UTILIZE ITS RESOURCES AND SUBJECT MATTER SPECIALISTS IN DEVELOPING OVERHEAD TRANSPARENCIES TO IMPLEMENT SECONDARY SCHOOL CURRICULUM IN THE STATE. SUBJECT SPECIALISTS (26) REPRESENTING 10 COURSE FIELDS WERE BROUGHT TOGETHER AT THE BEGINNING OF…
|The interdisciplinary approach that science, technology, engineering and mathematics (STEM) projects inspire in both teachers and students "brings to light a larger picture that promotes real-world scientific applications, which has in turn been shown to increase undergraduate persistence in STEM." The high school students have been warned…
The article gives ideas that lecturers of undergraduate Discrete Mathematics courses can use in order to make the subject more interesting for students and encourage them to undertake further studies in the subject. It is possible to teach Discrete Mathematics with little or no reference to computing. However, students are more likely to be…
The American Mathematical Society's (AMS) Books Online makes available full text of over 30 scholarly monographs published by the AMS, covering a range of subjects including algebra and algebraic geometry, analysis, applications, differential equations, geometry and topology, logic and foundations, mathematical physics, number theory, probability, and general interest. Their gateway page organizes titles by subject and author.
This paper describes some game situations used to study how subjects learn mathematical structures, in particular the structures of the cyclic groups of orders 2 and 4 and the Klein-four group. A series of experiments are reviewed and the methods used to determine whether subjects did learn the structures are discussed. Differences in strategies,…
A broad collection of mathematical bibliographies and links to pages explaining important concepts. One highlighted feature is a link to Euclid's 'Elements', which contains all 13 books and illustrated figures. Another interesting attribute is a link to the famous 1900 speech of David Hilbert, a leading twentieth century mathematician, in which he addressed the International Congress of Mathematicians in Paris and described 23 important mathematical problems. A history of mathematics by region gives bibliographies, and sometimes maps and chronologies for Babylonia, Egypt, China, Greece, India, the Arab sphere, Japan, and Europe. Bibliographies and some web links are provided for the subjects of numerals and counting, algebra, geometry, arithmetic and number theory, mathematical analysis, and probability and statistics. Lists of books and other non-internet resources, such as organizations devoted to the history of mathematics, journals, and catalogs are also listed.
Contemporary debates on effective pedagogies for K-12 mathematics have called for shifts in the way teachers and teacher educators conceptualise mathematics as a subject and how it should be taught. This is reflected by changes in the curriculum including the inclusion of a strand called Working Mathematically within K-12 mathematics curriculum…
This article is a report on a longitudinal case study that investigated the problem of lowered engagement with mathematics and students' perspectives of the factors that influenced their engagement during the middle years of schooling. The article provides a synthesis of the entire study and a summary of its findings. In order to address the research question a group of 20 students from within the same school cohort participated in the study spanning three school years from their final year of primary school, to their second year of secondary school. Data was collected through interviews, focus group discussions, and classroom observations. A major finding of this study was that positive pedagogical relationships between teachers and their students must be developed as a foundation for sustained engagement.As science, technology, engineering, and mathematics (STEM) education becomes increasingly important, U.S. students are lagging behind other nations on international assessments, according to a recent Trends in International Mathematics and Science study. A 22 June report from the U.S. National Research Council (NRC) calls for increasing the focus on STEM education in the United States. "To make progress in improving STEM education for all students, policy makers at the national, state, and local levels should elevate science to the same level of importance as reading and mathematics," states the report, "Successful K-12 STEM Education: Identifying Effective Approaches in Science, Technology, Engineering, and Mathematics." It outlines several goals: expand the number of students who pursue advanced degrees and careers in STEM fields; expand the STEM-capable workforce, while also broadening the participation of women and minorities; and increase STEM literacy for all students, whether or not they pursue STEM-related careers or additional study in those areas.
Maple is a mathematics software package, which contains graphic, computation, and programming tools. Maple animation is a powerful tool that can help in comprehending many fundamental concepts in mathematics and other sciences. This paper deals with the use of maple animation to demonstrate many fundamental concepts in mathematics that are difficult to explain verbally or through static figures. We show Maple animations effectively convey different concepts. We present problems taken from the literature to exemplify and explain Maple animation procedures. Using Maple in teaching mathematics facilitates the students with a tool to experiment and visualize complicated mathematical concepts and thus, strengthen their grasp of the subject.
|This paper explores the current Science, Technology, Engineering and Mathematics (STEM) education research base through an analysis of articles from eight journals focused on the STEM disciplines. Analyzed are both practitioner and research publications to determine the current scope of STEM education research, where current STEM education introductory toThe main purpose of this study was to determine if validity coefficients for ACT scores, both composite scores and subject area test scores, and high school grade point average (HSGPA) decayed or held stable over eight semesters of undergraduate study in science, technology, engineering, and mathematics (STEM) fields at civilian four-year institutions, and whether the decay patterns differed from those found in non-STEM fields at the same institutions. Data from 62,212 students at 26 four-year institutions were analyzed in a hierarchical meta-analysis in which student major category (SMC), gender, and admission selectivity levels were considered potential moderators. Four sets of analyses were run. The first was by the three SMCs: STEM-Quantitative majors, STEM-Biological majors, and non-STEM majors. The second was SMC by gender. The third was SMC by admission selectivity level. The fourth was SMC by gender by admission selectivity level. The results across all four analyses indicated that ACT score validity coefficients for STEM-Quantitative and STEM-Biological majors decayed less over eight semesters than the validity coefficients for non-STEM majors did. This was true for the uncorrected and corrected validity coefficients. For the HSGPA validity coefficients, this was true for the corrected validity coefficients. Non-STEM majors had very similar validity decay patterns regardless of the level of analysis. However, four of the eight STEM subgroups in the final set of analyses had minimal amounts of decay, and in some instances small amounts of validity growth.Mathematics is often thought of as the coldest expression of pure reason. But few subjects provoke hotter emotions--and inspire more love and hatred--than mathematics. And although math is frequently idealized as floating above the messiness of human life, its story is nothing if not human; often, it is all too human. "Loving and HatingFor the last several years, concern has been brewing about America's underinvestment and underperformance in science, technology, engineering and mathematics--the fields collectively known as STEM. STEM can be described as an initiative for securing America's leadership in science, technology, engineering and mathematics fields and identifying…
S.O.S. MATHematics is a collection of review materials for math subjects. The material includes important results, techniques and formulas in college and pre-college mathematics. Self-testing units are presented in worksheet format and require active participation.The UK national STEM Ambassadors programme provides inspiring role models for school students in science, technology, engineering, mathematics (STEM) subjects. STEMNET, the national body responsible for STEM Ambassa- dors aims to provide more than 27,000 STEM Ambassadors nationwide by the end of 2011. This paper reports on a project at Kingston University to embed STEM Ambassador training and activity in Year 2 of the undergraduate Aerospace Engineering, Astronautics and Space Technology degree. The project, known as KUSPACE (Kingston University Students Providing Amazing Classroom Experiences), was conceived to develop students' communication, planning and presentation skills and build links between different cohort years, while providing a valuable contribution to local primary schools' STEM programmes and simultaneously raising the public engagement profile of the university. This paper describes the pedagogical conception of the KUSPACE, its implementation in the curriculum, the delivery of it in the university and schools and its effect on the undergraduate students, as well as identifying good practice and drawing attention to lessons learned.STEMNET ( is the UK's Science, Technol- ogy, Engineering and Mathematics Network. Working with a broad range of UK partners and funded by the UK govern- ment's Department for Business Innovation and Skills, STEMNET plays a significant role in ensuring that five to nineteen year olds and their teachers can experience a wide range of activities and schemes which enhance and enrich the school curriculum [1]. Covering all aspects of Science, Tech- nology, Engineering and Maths (STEM), these activities and schemes are designed both to increase STEM awareness and literacy in the young people and also to encourage more of them to undertake post-16 STEM qualifications and associated careers [2]. STEMNET operates through forty-five local con- tract holders around the UK which help the network deliver its programmes to schools and organisations in their particular areas, mainly through the STEM Ambassador Programme (see below) and the Schools STEM Advisory Network.In support of its vision - `To increase young people's choice and chances through science, technology, engineering, and mathematics ' - STEMNET seeks to be a recognised leader in enabling all young people to achieve their potential in STEM by:In this paper, the investigative approach to mathematics teaching and learning as a mathematical inquiry that stems from the constructivist belief is examined. The implications on the nature of mathematical knowledge and activities that the approach requires are also considered and are followed by suggestions on how teachers might use schemes or textbooks to help children gain experiences in investigating.
There is broad acceptance that mathematics teachers' beliefs about the nature of mathematics influence the ways in which they\\u000a teach the subject. It is also recognised that mathematics as practised in typical school classrooms is different from the\\u000a mathematical activity of mathematicians. This paper presents case studies of two secondary mathematics teachers, one experienced\\u000a and the other relatively new to|"Liberal arts mathematics" differs from traditional mathematics courses in that it consists of a disparate collection of topics, rather than being organized around a single mathematicalsubject. As a result, the educational rationale for and purpose of the course may be vague both to instructors and students. The purpose of this study is to…
|This article extends the notion of "knowledge at the mathematical horizon" or "horizon knowledge" introduced by Ball and colleagues as a part of teachers' subject matter knowledge. Our focus is on teachers' mathematical knowledge beyond the school curriculum, that is, on mathematics learnt during undergraduate college or university studies. We…
Developed from Noddings's (2002) care theory, von Glasersfeld's (1995) constructivism, and Ryan and Frederick's (1997) notion of subjective vitality, a mathematical caring relation (MCR) is a quality of interaction between a student and a mathematics teacher that conjoins affective and cognitive realms in the process of aiming for mathematical…
Mathematics performance in 32 children with spina bifida was investigated at 3.8 through 8.8 years and two years later. About half showed mathematics difficulties. At the time of the second data collection, 28% of the subjects were identified with mathematics and other learning disabilities and with language impairments. Visual perception…
|This article describes a framework for how to provide more accessible, relevant, and effective instruction in science, technology, engineering, and mathematics (STEM) education to all students. The STEM for All initiative asserts that all students, including those with disabilities and other diverse learning needs, should be included in…
|We are in the STEM generation whose comprehensive purpose is to resolve (1) societal needs for new technological and scientific advances; (2) economic needs for national security; and (3) personal needs to become a fulfilled, productive, knowledgeable citizen. STEM specifically refers to science, technology, engineering, and mathematics, but now…
|This article presents a list of the top Science, Technology, Engineering, and Mathematics (STEM) degree producers in the U.S. This list is broken down into seven categories: (1) Total Minority Research/Scholarship and Other Doctoral: Mathematics and Statistics; (2) Total Minority Bachelors: Biological and Biomedical Sciences; (3) Total Minority…
A series of activities were undertaken to understand the underrepresentation of people with disabilities in science, technology, engineering, and mathematics (STEM) careers and increase their participation in these fields. "AccessSTEM" collaborated with key stakeholders to conduct a "Capacity-Building Institute" ("CBI") in April 2009; share…
|Elementary pre-service teachers report high levels of mathematics anxiety (MA), but the construct less widely addressed is their mathematics teaching anxiety (MTA). This study investigated the frequency with which MA stemming from prior experiences leads to MTA. Fifty-three elementary pre-service teachers' written reflections were analyzed, using…
The Mathematics Genealogy Project is maintained by the Department of Mathematics at North Dakota State University. The goal of this project is "to compile information about ALL the mathematicians of the world." It is soliciting information from anyone who participates in the development of research level mathematics or has information on mathematicians to include in the database. The site notes some of the challenges to this project such as imperfect data sources and the ways in which the model the project is using may be anachronistic for the earlier periods. Nonetheless, as of May 15, 2005, the project has amassed 86,827 records. The database can be searched by a variety of criteria, such as individual name, name of school, year of degree, country, math subject, or key word from a thesis.
Quality Science, Technology, Engineering, and Mathematics (STEM) education is vital for the future success of students. Integrated STEM education is one way to make learning more connected and relevant for students. There is a need for further research and discussion on the knowledge, experiences, and background that teachers need to effectively teach integrated STEM education. A support, teaching, efficacy, and
|STEM (an acronym for science, technology, engineering and mathematics) had its origins in the 1990s at the National Science Foundation (NSF) and has been used as a generic label for any event, policy, program, or practice that involves one or several of the STEM disciplines. However, a recent survey on the "perception of STEM" found that most…
|Educational reformation has proceeded slowly despite the many calls to improve science and mathematics for our students. The acronym STEM (science, technology, engineering, and mathematics) has been adopted by numerous programs as an important focus for renewed global competitiveness for the United States, but conceptions of what STEM entails
||STEM--the catchy shorthand for "science, technology, engineering and mathematics"--has been part of the school improvement discussion for more than a decade, as educational leaders and policy makers have underscored the importance of these areas in preparing students for an internationally competitive, 21st-century economy. But while the acronym…
|STEM--shorthand for "science, technology, engineering, and mathematics"--has been part of the school improvement discussion for more than a decade, as educational leaders and policy makers have underscored the importance of these areas in an internationally competitive, 21st-century economy. But building and implementing programs that emphasize…
There are many unsolved problems in discrete mathematics and mathematical cybernetics. Writing a comprehensive survey of such problems involves great difficulties. First, such problems are rather numerous and varied. Second, they greatly differ from each other in degree of completeness of their solution. Therefore, even a comprehensive survey should not attempt to cover the whole variety of such problems; only the most important and significant problems should be reviewed. An impersonal choice of problems to include is quite hard. This paper includes 13 unsolved problems related to combinatorial mathematics and computational complexity theory. The problems selected give an indication of the author's studies for 50 years; for this reason, the choice of the problems reviewed here is, to some extent, subjective. At the same time, these problems are very difficult and quite important for discrete mathematics and mathematical cybernetics. Bibliography: 74 items.
|This work addresses the subject of mathematics education at secondary schools from a current and stimulating point of view intimately related to computational science. Cryptology is a captivating way of introducing into the classroom different mathematicalsubjects such as functions, matrices, modular arithmetic, combinatorics, equations,…
|In too many schools, science and mathematics are taught separately with little or no attention to technology and engineering. Also, science and mathematics tend to function in isolation from other core subjects. In California, Linked Learning: Pathways to College and Career Success connects core academics to challenging professional and technical…
In too many schools, science and mathematics are taught separately with little or no attention to technology and engineering. Also, science and mathematics tend to function in isolation from other core subjects. In California, Linked Learning: Pathways to College and Career Success connects core academics to challenging professional and technical…
The guide is one of a series developed in a pilot project to integrate career education concepts with subject matter in secondary grades. The units are designed to reveal career orientation aspects of traditional topics within five major subject areas: English, social studies, mathematics, science, and health and physical education. The lesson…This study explores the causal links between mathematics achievement, career aspirations, and perceived importance of mathematics for senior high students. Findings suggest that causal directionality is a function of gender and grade level. Mathematics is the one subject that most high school students identify as their \\
Mathematics educators often fail to see that their subject has social and ethical dimensions. If anything, mathematics is seen as a neutral tool that has a social dimension only because it can be used to solve social problems. This study critically examines this idea by arguing that, although school mathematics is indeed a technology, technology…
an…
Mathematics can be perceived as being a difficult subject to learn due to the conceptual leaps required to understand particular mathematical topics. In some areas of mathematics, part of the difficulty may be associated with applying sufficient imagination to visualize a particular mathematical concept, and applying sufficient visio-spatial…
|… debate, reproductive cloning has been banned in Australia and only embryos considered to be excess to assisted reproductive technologies in existence on the 5th of April 2002 are currently valid research material. This paper argues that underpinning both pieces of legislation is a profound belief in the disruptive potential of all types of human cloning for the very nature and integrity of human species being. A belief, moreover, that is based on a presumption that it is apparently possible to conceptualise what being human even means for all Australians. PMID:16552928
ABSTRACT The state of science, technology, engineering and math (STEM) education in the United States has seen some unfavorable assessments over the past decade. In early February, 2010 the House of Representatives heard testimony on undergraduate and graduate education. The message from the panel, which included experts from academia, STEM-based industries, and the National Science Foundation (NSF) was dire and required an urgent response. The experts along with the committee���¢��������s chairperson, U. S. Representative Daniel Lipinski (D-IL) cited that the complexity of Science, Technology, Engineering, and Mathematics applications and coursework and the methodology utilized to teach these subjects are forcing students out of these disciplines. As the National Academies described in its 2007 report Rising Above the Gathering Storm, successful STEM education is not just an academic pursuit���¢��������it���¢��������s a necessity for competing in the knowledge-based economy that the United States had a key role in creating. The potential for action is being made available again as the America COMPETES Act of 2007 is up for reauthorization. Its initial focus was on STEM education at the K-12 levels, but efforts at the undergraduate and graduate levels are needed to retain students to fill the jobs left vacant as baby boomers retire. The Educational Advancement Alliance, Inc. (EAA) has for two decades created programs that have not only addressed the issues of ensuring that students are aptly prepared for college but have focused its efforts over the past decade on increasing the number of students who pursue degrees in STEM disciplines. For the EAA, the introduction of the wonders of science begins at the elementary and middle school level via the Learning Lab, a state-of-the-art mobile science laboratory that visits students in grades 4-6 at the various schools throughout Philadelphia and The Math/Tech Academy which meets on Saturdays for students in grades 5-7. For the past two years the EAA has assisted college graduates in their quest to attain advanced degrees in STEM by providing fellowships. The EAA continued this effort by recruiting and providing fellowships to students who aspired to continue their education at the graduate level. The fellowships provided funding for tuition, fees, books, technology, and stipends to assist with room, board, and living expenses during the academic year and salary, transportation, and living expenses to those students who secured internships with the Department of Energy. Additionally the EAA designed and implemented needed support systems to ensure successful completion of the Masters degree programs, including but not limited to membership in professional associations, attendance at industry and academic conferences, and professional development workshops, and tutorial assistance if needed. This program assisted over 80 students directly and society-at-large by helping to educate and develop future physicists, engineers, biostatisticians, and researchers who will have the necessary skillsets to fill the increasing numbers of positions that require such expertise.
Evidence has accumulated that cancer develops from a population of quiescent tissue committed\\/pluripotent stem cells (TCSC\\/PSC) or cells developmentally closely related to them that are distributed in various organs. To support this notio n, stem cells (SC) are long lived cells and thus may become the subject of accumulating mutations that are crucial for initiation\\/progression of cancer. More important, they
The University of Illinois at Urbana-Champaign has developed a multi-pronged approach to remedying the lack of academic emphasis on the STEMsubjects, from preschool through college, as well as the lack of interest in STEMsubjects on the part of youth in the United States. Visitors can read about the University's four goals under the "Goals" tab at the top of any page. The "STEM Ed Projects" tab contains a directory of externally funded projects divided into four categories, and which are then further divided into subcategories. Visitors will find such projects as "Improving Supply and Demand Data for the Preparation of Secondary Science and Math Teachers" and "Clean Energy Education Workshop", under the category that aims to shape policy and advocate for STEM education. The "Resources" tab contains half a dozen categories under which visitors will find Outreach Resources, Teacher Development and Resources, and Policy and Advocacy for STEM Ed. G-CSF, expressed as early hyperleukocytosis necessitating significant dose reduction, and suboptimal CD34+ cells yields. One-month HU-pretreatment prevented hyperleukocytosis and allowed successful CD34+ cell collections when an optimal washout period was maintained, but it significantly prolonged the mobilization procedure. Plerixafor resulted in rapid and effective mobilization in both SPL and non-SPL patients and was well-tolerated. For gene therapy of thalassemia, G-CSF or Plerixafor could be used as mobilization agents in non-SPL patients whereas Plerixafor appears to be the mobilization agent of choice in SPL adult thalassemics in terms of safety and efficacy.
The phrase STEM education is shorthand for an enterprise that is as complicated as it is important. What students learn about the science disciplines, technology, engineering, and mathematics during their K-12 schooling shapes their intellectual developme...
Twelve experienced mathematics teachers in Hong Kong were invited to face-to-face semi-structured interviews to express their views about mathematics, about mathematics learning and about the teacher and teaching. Mathematics was generally regarded as a subject that is practical, logical, useful and involves thinking. In view of the abstract nature of the subject, the teachers took abstract thinking as the goal
|There is considerable national interest in STEM initiatives, but yet there is little discussion concerning what STEM means in terms of a curriculum concept to be applied to school programming. This article focuses on STEM as a curriculum concept. First, STEM programming is discussed in terms of separate subjects, correlated and broad fields…
Understanding survival/antiapoptosis of murine embryonic stem (ES) cells may enhance their clinical potential. We hypothesized that Oct-4 might be involved in survival of undifferentiated ES cells under stress. The Oct-4 tetracycline conditional knockout cell line ZHBtc4 was used to test this possibility, and apoptosis was induced by either etoposide, heat shock, or UV exposure. Apoptosis in Oct-4 knocked-down ES cells was significantly increased in response to all stress situations compared with parental cells. Oct-4 knockdown was not associated with changes in morphology or expression of Nanog, SSEA-1, KLF-4, or Sox2 within the time frame and culture conditions used, suggesting that enhanced sensitivity of these cells to apoptosis was not due to an overtly differentiated state of the cells. To address potential intracellular mediators, we focused on the inhibitor of apoptosis proteins family member Survivin, an antiapoptosis protein. The Survivin promoter was transfected into ES cells after knockdown of Oct-4. Survivin promoter activity was dramatically decreased in the Oct-4 knock Leukemia inhibitory factor-induced signal transducer and activator of transcription-3 (STAT3) is responsible for ES cell survival, and STAT3 regulates Survivin expression in breast cancer cells. Western blot analysis showed that downregulated Oct-4 was associated with decreased phosphorylation of STAT3. Our results suggest that Oct-4 is essential for antiapoptosis of ES cells in response to stress, effects that may be mediated through the STAT3/Survivin pathway. PMID:17932422
Understanding survival/anti-apoptosis of murine embryonic stem (ES) cells may enhance their clinical potential. We hypothesized that Oct-4 might be involved in survival of undifferentiated ES cells under stress. Oct-4 tetracycline conditional knockout cell line ZHBtc4 was used to test this possibility and apoptosis was induced by either etoposide, heat shock or UV exposure. Apoptosis in Oct-4 knocked-down ES cells was significantly increased in response to all stress situations compared to parental cells. Oct-4 knockdown was not associated with changes in morphology, or expression of nanog, SSEA-1, KLF-4, or Sox2 within the time-frame and culture conditions used, suggesting that enhanced sensitivity of these cells to apoptosis was not due to an overtly differentiated state of the cells. To address potential intracellular mediators, we focused on IAP family member Survivin, an anti-apoptosis protein. The Survivin promoter was transfected into ES cells after knock-down of Oct-4. Survivin promoter activity was dramatically decreased in the Oct-4 knock- LIF-induced STAT3 is responsible for ES cell survival, and STAT3 regulates Survivin expression in breast cancer cells. Western Blot analysis showed that down regulated Oct-4 was associated with decreased phosphorylation of STAT3. Our results suggest that Oct-4 is essential for anti-apoptosis of ES cells in response to stress, effects that may be mediated through the STAT3/Survivin pathway.
I discuss the Pythagorean law of small numbers and its use in interpretations of our sensory discriminations of consonance vs. dissonance. It seems that the fact of non-western musical traditions contradicts the law and forces us to interpret the discriminations as acquired and subjective. I would like to show that this is a wrong interpretation, because it is based on the irrelevant empirical evidence. It does not take into account the correct mathematical and physical explanation of the law, provided by Helmholtz's theory in 1877 and corroborated by Plomp-Levelt experiment in 1965.
|Over the past three years, the authors have conducted research in middle and high school classrooms in an effort to improve the effectiveness of robotics to teach science, technology, engineering, and mathematics (STEM) education--their focus has been on math. The authors have found that subtle changes in the design and setup of the lesson make a… project. As students move from understandings that range from local to global in perspective on issues of energy and environment, there is a significant increase in the need for mathematical and statistical conceptual understanding. These understandings must be accessible to the students within the scientific context, requiring the special understandings that are endemic within quantitative reasoning. The QR STEM project brings together interdisciplinary teams of higher education faculty and middle/high school teachers to explore complex problems in energy and environment. The disciplines include life sciences, physics, chemistry, earth science, statistics, and mathematics. These interdisciplinary teams develop open ended performance tasks to implement in the classroom, based on scientific concepts that underpin energy and environment. Quantitative reasoning is broken down into three components: Quantitative Literacy, Quantitative Interpretation, and Quantitative Modeling. Quantitative Literacy is composed of arithmetic concepts such as proportional reasoning, numeracy, and descriptive statistics. Quantitative Interpretation includes algebraic and geometric concepts that underlie the ability to interpret a model of natural phenomena which is provided for the student. This model may be a table, graph, or equation from which the student is to make predictions or identify trends, or from which they would use statistics to explore correlations or patterns in data. Quantitative modeling is the ability to develop the model from data, including the ability to test hypothesis using statistical procedures. We use the term model very broadly, so it includes visual models such as box models, as well as best fit equation models and hypothesis testing. One of the powerful outcomes of the project is the conversation which takes place between science teachers and mathematics teachers. First they realize that though they are teaching concepts that cross their disciplines, the barrier of scientific language within their subjects restricts students from applying the concepts across subjects. Second the mathematics teachers discover the context of science as a means of providing real world situations that engage students in the utility of mathematics as a tool for solving problems. Third the science teachers discover the barrier to understanding science that is presented by poor quantitative reasoning ability. Finally the students are engaged in exploring energy and environment in a manner which exposes the importance of seeing a problem from multiple interdisciplinary perspectives. The outcome is a democratic citizen capable of making informed decisions, and perhaps a future scientist.||This article presents a mathematical solution to a motorway problem. The motorway problem is an excellent application in optimisation. As it integrates the concepts of trigonometric functions and differentiation, the motorway problem can be used quite effectively as the basis for an assessment tool in senior secondary mathematicssubjects.…
This monograph is aimed at helping the reader understand the built-in logic of various calculator operating systems. It is an outgrowth of workshop contacts with in-service and pre-service teachers of mathematics and is in response to their request for a book on the subject of calculator logic systems and calculator algorithms. The mathematical…
This study reports the effects of an integrated instructional program (the Keystone Method) on the students' performance in mathematics and reading, and tracks students' persistence and retention. The subject of the study was a large group of students in remedial mathematics classes at the college, willing to learn but lacking basic educationalWe report the results of 2 experiments and a verbal protocol study examining the component processes of solving mathematical word problems by analogy. College students first studied a problem and its solution, which provided a potential source for analogical transfer. Then they attempted to solve several analogous problems. For some problems, subjects received one of a variety of hints designed
In underscoring the affective elements of mathematics experience, we work with contemporary readings of the work of Spinoza on the politics of affect, to understand what is included in the cognitive repertoire of the Subject. We draw on those resources to tell a pedagogical tale about the relation between cognition and affect in settings of…
Subject: Proof theory and logical foundations of computer science. Castagna, Ghelli and Longo (1) provide a theoretical foundation for object-oriented programming via -calculi with overloading. However, their full calculus exposes a new form of impredicativity for which no denotational semantics was available. In this talk we introduce the system OTN of explicit mathematics based on elementary separation, product, join and
Science education scholars emphasize the significance of an integrative, interdisciplinary STEM (Science, Technology, Engineering, and Mathematics) education that encourages students to learn about the natural world through exploration, inquiry, and problem-solving experiences. This article reports on a professional development program aimed at improving a group of secondary science and mathematics teachers' competence in using a problem-based approach in the teaching
Probabilistic safety analyses (PSAs) often depend on significant subjectivity. The recent successes of fuzzy logic and fuzzy and hybrid mathematics in portraying subjectivity is a reminder that a selection made from the most applicable mathematical tools is more important than forced adaptation of conventional tools. We consider new approaches that enhance conventional and fuzzy PSA by improved handling of subjectivity.To gain a better understanding of teachers' beliefs about, perceptions of, and classroom practices using STEM integration, a multi-casecase study was conducted with three middle school teachers. These teachers were purposefully selected from a pool of teachers involvedin a year-long professional development module on STEM integration to represent science, mathematics and engineering teachers. Thisstudy addresses the following research questions: (1)
|One of the most critical labor shortages facing the U.S. involves the number of young adults entering careers in what's now commonly referred to as STEM (science, technology, engineering, and mathematics). Equally troubling is that the participation of blacks and Hispanics in STEM careers continues to lag that of whites and Asians. High school is…
This page describes five ways to assess mathematical thinking skills. The assessment tool is one of a series of Classroom Assessment Techniques (CATs) provided by the Field-tested Learning Assessment Guide (FLAG) website. The CATs of FLAG were constructed as a resource for science, technology, engineering and mathematics (STEM) instructors to emphasize deeper levels of learning and to give instructors valuable feedback during a course. The Mathematical Thinking Classroom Assessment Techniques (Math CATs) are designed to promote and assess thinking skills in mathematics by checking results and correcting mistakes, making plausible estimates of quantities which are not known, modeling and defining new concepts, judging statements and creating proofs, and organizing unsorted data and drawing conclusions. An overview of this assessment instrument includes information about why Math CATs are beneficial to use and how to use them. This site is also linked to a set of discipline-specific "tools" that can be downloaded for immediate use, as well as supplementary links and sources to further explore this assessment tool.
Swan, Malcolm; Ridgway, Jim; The National Institute for Science Education; College Level One TeamSponsored by NASA and the National Science Foundation, the Pathways to Science Project was created by the Institute for Broadening Participation to support "pathways to the STEM fields: science, technology, engineering, and mathematics." The project works on connecting underrepresented groups with STEM programs, funding, mentoring, and resources. The "Students" area features a sign-in area where students can sign up to receive targeted emails that will inform them of new STEM-focused scholarship and mentoring opportunities. The "Programs" area features a database of over 1500 programs designed for K-8 students, college educators, and undergraduate students. Additionally, the site also includes a "News" area where users can learn about recent success stories from universities around the United States, along with the particulars of upcoming conferences and seminars.
|This is a case study of the implementation of state STEM (science, technology, engineering, and mathematics) policy over the period of the first 18 months of building a regional STEM partnership. Fullan's change theory is the framework used to determine progress and associated challenges with building a regional STEM educational partnership and…
Alexander Bogomolny, a software developer and former mathematics professor, operates this educational and interesting Web site. His intention in creating the site is to help people "learn, if not math itself, then, at least, ways to appreciate its beauty." Although beauty is something most of us generally do not associate with the subject, the material manages to spark creative thinking by providing a fun, original way of looking at math. There are Java games and puzzles representing many different topics. A monthly interactive column called Cut The Knot! describes various abstract mathematical problems and concepts. Some of the topics discussed on the site are quite advanced, but others are relatively simple.
The copperplate Melencolia I engraved by Dürer in 1514 illustrates various interdependencies between mathematics and melancholy. Dürer's engraving is one of the best known works of art in our western history. Up to our own times it has been interpreted repeatedly. The significance of Dürer's Melencolia I for our cultural history is subject of this essay. On the one hand the various changes of the conception of melancholy from antiquity up to Dürer' s times will be called in mind. In addition to it some examples will assert that during the last five centuries the correlation between mathematics and melancholy has been contemplated and shaped as well. PMID:15202454
|Many men and women who are talented in science, technology, engineering, and\\ success, such as the role that
|Secondary school educators are told to teach more mathematics and science to their students to help them become more proficient in the two subjects. Coordination of mathematics and science teaching is recognized as another means of improving proficiency. The National Science Foundation has funded the "Mathematics, Science and Technology…
For many students, mathematical testing proves to be a challenge. Some students struggle to understand mathematical concepts. Some of these feel that they can grasp other subjects in a firmer way. However, performing mathematical equations while listening to music may playa critical role in student performance. Different types of music are known for their calming effect and enhancement of focusing
|In what unique ways can mathematics tasks contribute to pre-service teachers' understanding of subject matter and pedagogy? And what school mathematics tasks can usefully be included in a pre-service program? To contribute to answering these questions, we report on the selection and choice criteria for mathematics tasks that we use in an…
In this paper the priorities that second year education students hold for primary mathematics content and student learning are presented. Data were collected from students who participated in a tutorial task that was used to engage students in discussion about primary mathematics curriculum. The data were collected annually for four years. Reflections about the mathematicssubjects in the course are
Discusses the priorities that second-year education students hold for primary mathematics content and student learning. Reflects upon the mathematicssubjects within the context of current research and mathematics curriculum policy and inferences about education students' beliefs. (Author/KHR)
education and a long?lasting under?representation of women. However, despite similarities concerning policy
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|For almost 50 years, ACT has played a pivotal role in promoting student access into and success in science, technology, engineering, and mathematics (STEM) careers. Through academic and career assessments, career development tools, and extensive research, they have helped inform students, parents, teachers, career counselors, employers, and… differences among learning modes preferred by female and male students, their…
Federal policymakers have a longstanding interest in science, technology, engineering, and mathematics (STEM) education that dates to at least the 1st Congress. In its contemporary construct, this interest largely focuses on the connection between STEM ed... Teachers|The United States' economy depends greatly on a citizenry that possesses scientific and technical skills within the fields of science, technology, engineering, and mathematics (STEM) for economic growth. In the past few decades, technological advancement has created a demand for a highly skilled workforce possessing scientific and mathematical…
We report the construction and validation of a self-report 'Mathematics self-efficacy (MSE)' instrument, designed to measure this construct as a learning outcome of students following post-compulsory mathematics programmes. The sample ranged across two programmes: a traditional preparation for university study in mathematicalsubjects (Advanced level) and an innovative 'modelling'-based programme intended to widen participation in mathematics through use of technology
Within the Caribbean, there has been a perception that students are underachieving in mathematics. This assessment has seemingly been based amongst other things upon the proportion of students who are successful in mathematics compared to other subjects in external examinations. This notion was investigated in a case study of secondary schools in…
Studies have been conducted in the broad area of la nguage in mathematics teaching, but the research in this paper investigated the language us ed by a teacher in her physics and mathematics courses. Several commonalities and differences of this teacher's talk when teaching the two subjects were identified and are p resented here. The style of her talk varied
High school mathematics (beginning with algebra) is widely regarded as the "gatekeeper" to college. It is also the subject students in U.S. public schools fail most often. As the standards movement gains momentum, students who are members of subordinated populations continue to perform worse on standardized measures of mathematical skill than do…
Women continue to be underrepresented in science, technology, engineering, and mathematics (STEM) fields and in STEM leadership positions. According to the most recent data available from the National Science Foundation, in academia only 31% of full-time STEM faculty and 27% of STEM deans and department heads are women. By comparison at Stevenson…
|A collaborative of STEM (science, technology, engineering, and mathematics) and education faculty developed a STEM certificate aimed at elementary education majors. A four-phase process model was used to create and evaluate courses. The certificate is comprised of three interdisciplinary, team-taught, lab-based courses: Environmental Biology,…
|The Business-Higher Education Forum's (BHEF's) Securing America's Leadership in STEM Initiative has broken new ground in addressing one of the nation's most critical challenges--increasing the number of students who are interested in and pursue careers in science, technology, engineering or mathematics, the so-called "STEM" fields. The…
This ATE professional development project is a collaboration between STEM faculty teams from Butler County Community College (Butler, PA), Purdue University (West Lafayette, IN), Sinclair Community College (Dayton, OH), Ventura College (Ventura, CA), College of the Redwoods (Eureka, Ca.), as well as high school STEM faculty in each of the states involved. Faculty teams at the respective locations are working together to design, build, and analyze solid body electric guitars as a means of learning applied concepts of science, technology, engineering, mathematics, and as a means of understanding product lifecycle management. This experience is providing teachers and students an accurate simulation of the collaborative design and rapid manufacturing processes routinely used in business and industry. Over 150 STEM faculty members from high schools and community colleges are participating in an intense five-day Summer Professional Development Program and are having extensive academic year follow-up activities. The teacher participants are using these processes and simulations in their classrooms to enhance the STEM laboratory learning experience. Nearly 5000 students are learning about cross-disciplinary STEM problem solving that is becoming increasingly important for new design technicians to experience.On the site, visitors can find curriculum materials including classroom tools and information on guitar fabrication. There are also details of upcoming workshops and professional development opportunities. In the Storefront section, visitors can learn about how to purchase a guitar kit.
|For nearly 50 years, leaders in American industry, military, education, and politics have focused considerable attention on STEM (science, technology, engineering, and mathematics) education. Given the increased societal demand for STEM careers, the relationships among classroom climate, self-efficacy, and achievement in undergraduate mathematicsCell lines and genetically modified single cell organisms have been considered patentable subjects for the last two decades. However, despite the technical patentability of genes and stem cell lines, social and legal controversy concerning their 'ownership' has surrounded stem cell research in recent years. Some granted patents on stem cells with extremely broad claims are casting a shadow over theMany students find mathematics a difficult subject. In the context of Caribbean countries, the failure rate in mathematics has been very high. This paper discusses the creation of a personalized game-based mobile learning application to assist secondary school students in improving their mathematical skills. The aim of this application is to motivate and encourage students to practise mathematics. The personalizationThe purpose of the study is to identify problems related to mathematics and science learning faced by students as perceived by the Form two At-Risk students, and as perceived by the mathematics and science teachers when teaching the subjects, to examine student's mathematics and science learning climate, to identify teaching strategies frequently used by the mathematics and science teachers, andLocated at the University of Wales, the Centre for the Popularisation of Mathematics brings a more artistic side to the often plainly presented subject. Several online exhibits and galleries illustrate sculptures and knots that have a basis in math. One of the most interesting and famous mathematical sculptures is the Mobius Band. The centre gives a description of the Mobius Band and its significance, as well as instructions on how to create one and interesting experiments to try. Many other sculptures are presented in the same way, touching on topics of fractals and mathematics. The Knots Exhibition briefly introduces knot theory and shows many different knot configurations. application of knowledge and reflect…
The potential of stem cells to replace damaged cells and organs is the subject of public discourse and political debate. Stem\\u000a cell biology is in an explosive phase of growth, but has not yet yielded a fundamental understanding of the molecular control\\u000a of stem cell fate. Surprisingly the role of the gaseous environment in the control of stem cell biology
COMETS is an information dissemination project funded by the National Science Foundation, implemented to address the urgent need for well-grounded information about "best practices" in teaching and curriculum development for deaf students in science, technology, engineering, and mathematics (STEM) courses. The primary focus of COMETS is K-16 STEM educators. One of the goals of COMETS is to develop a network for systemic reform through information dissemination in mathematics. The resource contains documentation, called "workshops," designed to help teachers more effectively teach science and math to deaf and hard-of-hearing students knowledge. To tackle the mathematics problem, a remedial mathematics…
There have been recent advances in metabolic flux analysis. In particular, the marriage of traditional flux balancing with NMR isotopomer distribution analysis holds great promise for the detailed quantification of physiology. Nevertheless, flux analysis yields only static snap-shots of metabolism. To robustly predict the time evolution of metabolic networks, dynamic mathematical models, especially those that contain a description of both gene expression as well as enzyme activity, must be utilized. When mechanistic control and regulatory information is not available, heuristic-based methods, such as the cybernetic framework, can be employed to describe the action of these control mechanisms. In the 'high-information' future, as more biological information becomes available, such heuristic-based approaches can be replaced by mechanistic mass-action representations of physiology that stem directly from genetic sequence. PMID:10209144
This online publication provides resources for teaching mathematics by using the history of the science. The website features a library of articles on the history of mathematics that is searchable by keyword or term and browseable by subject, format, or type. Advanced searching allows users to select subject, format, resource type, author. keywords, and a publishing date range. Other materials at the website include literature reviews, a portrait gallery of famous mathematicians, historic math problems, an "On This Day" feature, a quote of the day, and links to news items and featured articles.
This article rehearses the argument that being a critical mathematics educator is associated with a particular epistemological stance, one which views the truths of mathematics as historically located, influenced by the knower and mutable. Case study data, collected in England, is offered which exemplifies this connection between epistemology and openness to equity issues in the thinking of some beginning secondary mathematics teachers. Teachers' responses are analysed around four themes: their beliefs about the nature of mathematics, how those beliefs affect their pedagogy, how they explain student failure, and their views on initial teacher education. These are linked to their commitment to social justice in and through mathematics. The links between subject studies in teacher education and equity issues in the classroom are discussed.
|Over the coming decade, America will need one million more science, technology, engineering, and mathematics (STEM) professionals than was originally projected. This is the conclusion of a February 2012 report, "Engage to Excel: Producing One Million Additional College Graduates with Degrees in Science, Technology, Engineering, and Mathematics".…
The 1996 Advisory Committee report to the National Science Foundation, "Shaping the Future: New Expectations for Undergraduate Education in Science, Mathematics, Engineering, and Technology," called for many changes in STEM (science, technology, engineering, and mathematics) education. The committee's overriding recommendation was that "all…The Mathematical Association of America (MAA) Journal Writing Awards honor the best mathematical writing from their various journals, and they also serve as a repository of great instructional resources for mathematics educators. The awards here include The Carl B. Allendoerfer Awards, the Trevor Evans Awards, and The Lester R. Ford Awards. Visitors can browse through all of the past winners, or they may also view the winning pieces by name. Most visitors may wish to use the subject listing as well, and topics like "Discrete mathematics" and "Analysis" are featured prominently. The archive is easy to use, and visitors will want to tell others working in this field about this resource, as it is one that can be used in a number of different settings and skill levels.
It is well known that student have difficulties with concepts in physics and space science as well as other STEM fields. Some of these difficulties may be rooted in student conceptual errors, whereas other difficulties may arise from issues with visual cognition and spatial intelligence. It has also been suggested that some aspects of high attrition rates from STEM fields can be attributed to students' visual spatial abilities. We will be presenting data collected from introductory courses in the College of Engineering, Department of Physics, Department of Chemistry, and the Department of Mathematics at the University of Texas at Arlington. These data examine the relationship between students' visual spatial abilities and comprehension in the subject matter. Where correlations are found to exist, visual spatial interventions can be implemented to reduce the attrition rates.Current and possible future shortages of science, technology, engineering and mathematics (STEM) professionals in the US are again becoming hot topics of discussion amongst policy makers and educators alike. In an innovative approach to addressing these concerns, Tai et al. (2006) analyzed a large set of longitudinal study data to gain a deeper understanding of the impact of early STEM
In previous decades, researchers have identified a gender gap in the careers and academic achievement of men and women in science, technology, engineering, and mathematics (STEM). Recently, it has been suggested that some of these gender gaps no longer exist; however, the picture is more nuanced, for women are represented well in some STEM fields…
Expanded learning opportunities, such as afterschool and summer programs, are particularly well positioned to help address science, technology, engineering, and mathematics (STEM) education crisis. A large percentage of youth participating in afterschool programs are members of groups traditionally underrepresented in STEM fields. Additionally,…
|Graduate students and post-doctoral scholars at research universities will shape the future of undergraduate education in the natural and social sciences, technology, engineering, and mathematics (the STEM disciplines) in the United States. In 2009 alone, more than 41,000 doctorates were awarded in STEM fields, and if employment trends hold,…
This study examined how mathematical experiences influence Dutch pupils' course enrollment in mathematics. Are gender differences in extracurricular, mathematics-related activities related to achievements in or attitudes towards mathematics, and consequently to differences between girls and boys in the selection of mathematics for their final examination curriculum? In total, 213 Dutch secondary education pupils (i.e., 139 females and 74 males) between
||This study addressed the mentoring of historically underrepresented groups (HUGs) in science, technology, engineering, and mathematics (STEM) disciplines by focusing on the Presidential Awards for Excellence in Science, Mathematics, Engineering Mentoring (PAESMEM). The primary research question that guided this study was \\
This Carsey brief reveals that students in rural areas and small towns have less access to higher-level mathematics courses than students in urban settings, which results in serious educational consequences, including lower scores on assessment tests and fewer qualified students entering science, technology, engineering, and mathematics (STEM) job pipelines.
This article presents a lesson for studying minority and women's contributions to the field of mathematics in the middle school classroom. This lesson may be able to stem the tide of the shrinking number of students entering the field of mathematics by helping them become interested in its history. Nonetheless, this project encourages students to…
|This study presents problem solving strategies and processes of thinking of mathematically gifted elementary children with respect to non-routine word problems. The data stem from a university-based course, especially designed to foster gifted children, ages 6-10 years, through the enrichment of the elementary mathematics curriculum. Videotapes…
Stem cells maintain homeostasis in adult tissues via self-renewal and generation of terminally differentiated cells. Alterations in this intricate balance can result in disease. It has become increasingly evident that cancer can be initiated at the level of stem cells. Therefore, understanding what causes stem cells to become cancerous may lead to new therapeutic approaches. Multiple signaling pathways ultimately affect stem cell survival and proliferation, thus maintaining homeostasis in the gut. Changes in these pathways could perturb normal stem cell behavior, leading to cancerous stem cells. In addition, cancerous stem cells show resistance to current therapies and may lead to a dangerous selection process resulting in recurrence and metastasis. Genomic instability, the driving force of mutation and resistance, may give cancerous stem cells an adaptive advantage, especially when subjected to cancer therapies. Targeting the unique characteristics of cancerous stem cells to promote either terminal differentiation or destruction would effectively eradicate cancer and improve patient care and survival.
|Today, there are more program options in science, technology, engineering, and mathematics (STEM) than ever before. Because people are living in an age of increasing globalization, advocates of gifted children must understand that involvement in STEM fields is paramount for the children to be competitive in the job market and for the nation to…
|Literacy and other content-specific demands presented within science, technology, engineering, and mathematics (STEM) coursework can overwhelm all students and especially students with learning challenges. Although STEM content is often complex in itself (e.g., numerous multisyllabic words, lengthy expository texts, abstract concepts), some…
There has been much research attention on ability level, motivation, and self-efficacy of students at schools of science, technology, engineering and mathematics (STEM). However, there is scant research on vocational choice, career development and aspirations of these students. The current study addresses this gap in the literature by asking…
||There has been much research attention on ability level, motivation, and self-efficacy of students at schools of science, technology, engineering and mathematics (STEM). However, there is scant research on vocational choice, career development and aspirations of these students. The current study addresses this gap in the literature by askingThis peer-reviewed, web-only publication explores innovations and emerging topics in undergraduate teaching and learning in science, mathematics, engineering, and technology (STEM). It emphasizes real-world case studies that are relevant and important to STEM practitioners. Case studies often cover nontechnical issues such as finance, cost, management, risk, and safety. Case studies are typically framed around problems and issues facing a decision maker in an organization. The journal aims to develop student thinking and problem solving and understands recent developments that impact STEM education in areas of policy and industry needs.|Science, technology, engineering and mathematics (STEM) workers drive the nation's innovation and competitiveness by generating new ideas, new companies and new industries. However, U.S. businesses frequently voice concerns over the supply and availability of STEM workers. Over the past 10 years, growth in STEM jobs was three times as fast as…
|In the United States, less than half of the students who enter into science, technology, engineering, and mathematics (STEM) undergraduate curricula as freshmen will actually graduate with a STEM degree. There is even greater disparity in the national STEM graduation rates of students from underrepresented groups with approximately three-fourths…
|Despite an increased national focus on science, technology, engineering, and mathematics (STEM) instruction, students with high incidence disabilities continue to struggle with STEM content at both the K-12 and postsecondary levels. As a result, very few students with disabilities pursue STEM careers. This article provides K-12 special education…
Individuals with disabilities are underrepresented in postsecondary education; in science, technology, engineering, and mathematics (STEM) majors; in graduate and post-doctoral work; and in faculty positions, particularly in STEM. Despite these lags behind their non-disabled counterparts, few organizations recruit persons with disabilities into…
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Questions of gender equity and the underrepresentation of women in the science, technology, engineering, and mathematics (STEM) professoriate in U.S. institutions of higher education have become central issues in debates on the role and makeup of the STEM workforce in today's innovation-driven economy. In response, policy makers, advocacy groups, academics, and other stakeholders have called for the dedicated enforcement of
|Americans with disabilities are underemployed in science, technology, engineering and mathematics (STEM) at higher rates than their nondisabled peers. This article provides an overview of the National science Foundation's Research in Disabilities Education (RDE) program, of technology use by students with disabilities (SWD) in STEM, and of…
|This synthesis paper explores current leadership training in science, technology, engineering and mathematics (STEM) education in Bulgaria. The analysis begins with discussion of global factors influencing the implementation of leadership training in STEM education in general and then presents information about the current status of leadership…
The objectives of the study were to (1) develop an instrument for measuring the mathematical thinking of high school students and (2) determine the effects of the class level and student's gender on the mathematical thinking of high school students in Nebraska. The subjects of the study were 239 high school students (grades 9?12) selected from 18 Central Nebraska high
The article discusses an empirical study on the use of history (as a goal) in mathematics education. A historical module was designed and implemented in a Danish upper secondary class to study how students' discussions of metaperspective issues of the historical development of mathematics may be anchored in the taught and learned subject matter of…
Few studies have examined the student learning effects of integrating science with mathematics and technology. We compared a school that integrated mathematics, science and technology in grade 9 to a school in the same district that taught the three courses separately. The distinguishing feature of the integrating school was the reorganization of instruction in the three subjects to prepare students
|Until recently, few valid and reliable assessments were available to measure young children's mathematics and science learning in a "comprehensive" way. Now, a number of mathematics assessments have been developed and subjected to testing (Klein, Starkey, & Wakeley, 2000; Ginsburg, 2008; Clements & Sarama, 2008), and progress has been made in…
|Relatively low participation in the hard sciences (mathematics, science, engineering and technology) has become a concern with respect to the capacity of Australia to meet critical infrastructure projects. This problem has its roots in poor student attitudes towards and perceptions about the study of prerequisite subjects including mathematics…
|The present demand for quantitative proficiency makes low mathematics achievement not only a formidable obstacle in occupational aspirations but also in the academic arena. To modify the current understanding of the problem of mathematics anxiety and to develop an effective treatment program, college students (12 subjects per group; 8 females, 4…
Women and mathematics have been thought of as two totally separate subjects for decades. In July, 1994 a group of mathematicians from around the country gathered in Berkeley, CA for three days to discuss ways to increase the representation of women in Ph.D. programs in the mathematical sciences. The primary goal of this conference was to broaden…
|Biology and mathematics are inextricably linked. In this article, we show a few of the many areas in which this linkage might be made explicit. By doing so, teachers can deepen students' understanding and appreciation of both subjects. In this article, we explore some of these areas, providing brief explanations of the mathematics and some of the…
|In this article, I make a case for the inputs that Martin Heidegger's theoretical perspective offers to current concerns about the nature of mathematics, its teaching and learning, and the problem of subjectivity. In particular, I consider Heidegger's notion of positive science and discuss both its applicability to mathematics and its importance…
|Mathematics learning and achievement is one area of research that has gained momentum in recent years because of its importance as a subject in the school curriculum and its usefulness as a prerequisite for developing the quantitative and analytical skills. However, studies on factors affecting mathematics achievement in Malaysia are limited both…
|The Secondary Literacy Inservice Package for High School Science and Mathematics was developed to assist teachers of science and mathematics in helping their students become more literate in these two subject areas. This article examines the meaning of literacy and its relationship to language and learning, and describes the outcomes from trying…
''The Age of Newton'' is an intensive course in mathematics (calculus), mechanics, optics, and astronomy directed mainly toward nonscientists. Although it introduces the subjects in a consciously historical context, it is a course in-not merely about-science and mathematics. The course is divided into a central lecture series, at which guest lecturers may participate, a series of topical tutorial lectures, and
|The National Assessment of Educational Progress (NAEP) is the nation's only ongoing representative sample survey of student achievement in core subject areas. In 2000, NAEP conducted a national mathematics assessment of fourth-, eighth-, and twelfth-grade students. State-level results were also collected at the fourth and eighth grades within…
A mathematical model of a memory trace and forgetfulness is proposed here based on an improved version of our previous work (Harth et al., 1970; Anninos et al., 1970). Thus it was shown that the trace of a stimulus pattern presented to a subject decays with time due to the interference theory which assumes that competition among different associations leads
`Mathematical physics' is an extremely broad subject, and the days when one person could be conversant with all its aspects have long since passed. Hence a conference as sweeping as this one is apt have something for everyone, but not enough for anyone. Overviews can be valuable, though, and while this book is not the place to learn anything in
|Some authors have begun to appeal directly to studies of argumentation in their analyses of mathematical practice. These include\\u000a researchers from an impressively diverse range of disciplines: not only philosophy of mathematics and argumentation theory,\\u000a but also psychology, education, and computer science. This introduction provides some background to their work.
|This article proposes four strategies for posing mathematics problems that raise the cognitive demands of the tasks given to students. Each strategy is illustrated with three common middle school mathematics examples: finding the greatest common factor, finding area or perimeter, and finding the equation of a line. Posing these types of problems…
This three lesson unit from Illuminations focuses on connections between mathematics and football with the common theme of the Super Bowl. Students are asked to look at the Super Bowl not just as "the big game" but as an opportunity to apply mathematics to some interesting problems. The activities involve number sense, measurement, statistics, estimations, and problem solving.
Computer science and software engineering are young, maturing disciplines. As with other mathematically based disciplines, such as the natural sciences, economics, and engineering, it takes time for the mathematical roots to grow and flourish. For computer science and software engineering, others have planted these seeds over many years, and it is our duty to nurture them. This working group is
|Although mathematics is visual language of symbols and numbers it is also expressed and explained through written and spoken words. For students to excel in mathematics, they must recognize, comprehend and apply the requisite vocabulary. Thus, vocabulary instruction is as critical in content areas as it is in language arts. It is especially…
This article addresses some important issues in mathematics instruction at the middle and secondary levels, including the structuring of a district's mathematics program; the choice of textbooks and use of calculators in the classroom; the need for more rigorous lesson planning practices; and the dangers of teaching to standardized tests rather…
Results Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre--kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society.
This relationship is omnipresent to those who appreciate the shared attributes of these two areas of creativity. The dynamic nature of media, and further study, enable mathematicians and artists to present new and exciting manifestations of the "mathematics in art", and the "art in mathematics". The illustrative images of the relationship--that…
|The mathematics learning center at Tacoma Community College aims to provide an effective method of reaching a diversity of student needs using three programs: independent-tutorial study, student tutorial, and a basic arithmetic skills laboratory. More than 30 mathematics courses are offered; each has an option of individualized instruction or…
This document reports on the Radio Mathematics Project (RMP) over a five-year period. In 1973, the United States Agency for International Development (AID) asked the Institute for Mathematical Studies in the Social Sciences (IMSSS) at Stanford University to develop an instructional program with radio as the medium of delivery. IMSSS was to devise…
|Analyzes the relationship between cognitive psychology as a broad theoretical framework, and the psychology of mathematics education. Argues that mathematics education should not simply borrow from cognitive psychology; rather, it should provide its own psychological research problems, adapted investigation strategies, and adequate original…
|Developing deep knowledge and understanding of mathematics is a lifelong process, and building the foundation for teachers' development must begin in preservice preparation and continue throughout one's professional life. While teaching mathematics content courses and methods courses, the authors have found that preservice elementary school…
||Designed to accompany a series of videotapes, this textbook provides information, examples, problems, and solutions relating to mathematics and its applications in technical fields. Chapter I deals with basic arithmetic, providing information on fractions, decimals, ratios, proportions, percentages, and order of operations. Chapter II focuses on…
Direct-to-consumer (DTC) advertising of suspect goods and services has burgeoned because of the Internet. Despite very limited approval for use, DTC stem cell-marketed "treatments" have emerged for an array of conditions, creating global public health and safety risks. However, it remains unclear whether such use of stem cells is subject to drugs or biologics regulations. To address this gap, regulatory agencies should be given clear authority, and the international community should create a framework for appropriate stem cell use. In addition, consumer protection laws should be used to scrutinize providers. PMID:22972840
Learning with understanding has increasingly received attention from educators and psychologists, and has progressively been elevated to one of the most important goals for all students in all subjects. However, the realization of this goal has been problematic, especially in the domain of mathematics. To this might have contributed the fact that, although the vision of students learning mathematics with
Integration of the Science, Technology, Engineering and Mathematics (STEM) disciplines in K-12 education have been promoted through national education standards and a variety of curricular initiatives. This research examines the adoption of these standards through analysis of book purchasing pattern information available through amazon.com. A directed network was developed starting with four "root" books chosen to represent either key education
The STEM (science, technology, engineering, and mathematics) community is implementing several new observation systems that rely on sensor technology. With this revolution, the need to educate more science and engineering technicians to work (design, assemble, deploy, troubleshoot and communicate) with sensor networks and meet workforce demands will rise quickly in the near future. The incorporation of technology-enabled systems, tools and
|Lego robotics is engaging, hands-on, and encompasses every one of the NETS for Students. It also inspires a love of science, technology, engineering, and mathematics (STEM) and provides the experience students need to use digital age skills in the real world. In this article, the author discusses how schools get involved with Lego Robotics and…
|We examined perfectionistic personality characteristics and their association with science self-efficacy beliefs and academic performance among college students in science, technology, engineering, and mathematics (STEM). We were especially interested in gender differences in effects given that women remain significantly underrepresented in…
|STEM--science, technology, engineering, and mathematics--has become a fixture of the education debate, and much effort already has been put toward improving student performance. Yet troubling statistics persist: On the latest round of testing for the National Assessment of Educational Progress (NAEP), only 40 percent of fourth graders nationwide…
The number of women earning advanced degrees in science, technology, engineering, and mathematics (STEM) has increased, yet women remain underrepresented at all ranks of the academic hierarchy in these fields. To help explain this pattern, we explored mechanisms in the recruitment and hiring process at the level of the department that hinder or promote the hiring of women into tenure-track
|Proposes the use of children's literature as a method to connect language and mathematics. Presents examples of children's books by mathematical topic and methods by which they can be employed in mathematics instruction. (31 references) (MDH)|
Several general aspects are discussed. These include the role of mathematics in scientific and technical progress, some deficiencies in training, the role of mathematics in engineering faculties, and methods of improving mathematical training. (MP)Colorectal cancer is one of the most common types of cancer. To better understand about the kinetics of cancer growth, mathematical models are used to provide insight into the progression of this natural process which enables physicians and oncologists to determine optimal radiation and chemotherapy schedules and develop a prognosis, both of which are indispensable for treating cancer. This thesis investigates the stability of colorectal cancer mathematical models. We found that continuous saturating feedback is the best available model of colorectal cancer growth. We also performed stability analysis. The result shows that cancer progress in sequence of genetic mutations or epigenetic which lead to a very large number of cells population until become unbounded. The cell population growth initiate and its saturating feedback is overcome when mutation changes causing the net per-capita growth rate of stem or transit cells exceed critical threshold.
This paper reports on interviews held with voluntee r students in the first cohort of year 12 Mathematical Methods (CAS) in Victoria, Australia. The subject MM(CAS) was established by the Victorian Curriculum and Assessment Authority (VCAA, n.d.) in conjunction with the CAS-CAT research project (CAS-CAT, n.d). It was the first mathematicssubject where students were allowed to use CAS in
This research explored nursing students' mathematics anxiety, beliefs about mathematics, and mathematics self-efficacy in relation to performance on a medication mathematics test. Results revealed that the participants experienced some mathematics anxiety and had positive beliefs about mathematics and mathematics self-efficacy. Qualitative responses indicated that participants worried about the consequences of failing the medication mathematics test and that practice helped reduce this anxiety. In addition, participants acknowledged the importance of correct dosage calculations for nursing practice. Implications for nursing education are discussed. PMID:18770952
The Society for Mathematical Biology (SMB) is an international society devoted to increasing communication between the mathematical and biological communities through holding conferences and publishing journals.
This website provides a syllabus for a course that uses "writing to reinforce the learning and understanding of mathematical concepts, while also using mathematics and statistics as a topic for the essays." Students gain experience in both English and Math skills as well as developing critical thinking, written and oral communication, quantitative skills, and group interaction skills. Instructors can use the syllabus, assignments, and other activities as inspiration in their own lectures or course designs. In addition, students of all levels will find the provided instructive material helpful as they attempt to write about mathematical concepts at the college levelDuring the last several decades, educational researchers have focused significant attention on the improvement of Science, Technology, Engineering and Mathematics (STEM) subjects. These researchers have identified many shortcomings of "traditional" lecture-based instruction and have developed and demonstrated the efficacy of alternative models of instruction. Yet, many STEM faculty continue to teach traditionally. To better understand this situation we have conducted an interdisciplinary literature review related to change strategies employed in the improvement of undergraduate STEM instruction. Results suggest that there are at least three important groups working towards such change and that approaches to change differ significantly by group. In this session, we will present an overview of the literature review. Participants will engage in discussions about how to combine the strengths of these different approaches towards promoting change as well as how to work towards an interdisciplinary agenda that can lead to improved communication and practice related to promoting change in undergraduate STEM instruction. Collaborators: Andrea Beach, Western Michigan University Noah Finkelstein, University of Colorado, Boulder
The electronic issues of the Pacific Journal of Mathematics is available as of October, 2000. Articles on Stekloff eigenvalues, Cantor systems, and Bertini Theorems are among those featured. Articles may be viewed in .pdf, hyperdvi, dvi, or .ps format.
The document consists of a series of thirteen articles appearing in Chemical Engineering in 1968-9. It covers many approaches to the development of mathematical models of engineering systems. Techniques covered include frequency response, pulse testing, c...
Benjamin Banneker, a self-taught African American mathematician, kept a journal containing a number of mathematical puzzles. Explores four of these puzzles, 200 years later, with the aid of 21st century technology. (Author/NB)
By the term of mathematical models of epidemics are understood the equations or systems of equations whose parameters reflect quantitative relationships of basic factors and motive forces of epidemics. The solution of these equations reproduces a certain ...
|Benjamin Banneker, a self-taught African American mathematician, kept a journal containing a number of mathematical puzzles. Explores four of these puzzles, 200 years later, with the aid of 21st century technology. (Author/NB)| "…. how to study mathematics, how to approach problem-solving…. and when and how to get help."A description and review of a comprehensive book on theoretical geodesy is presented. Geodesy is placed on a firm mathematical and physical foundation. The aim of this book is to liberate geodesy from its traditional bifuration into horizontal and vertica... how to study mathematics, how to approach problem solving, and when and how to get help.Investigations about attitudes toward mathematics carried out in the past decade were revised. The instruments used to measure attitudes toward mathematics were analysed as well as the attitudes toward different aspects of mathematics, their relation with other school subjects and their stability through time. Opinions about the influence of…
Music improves the development of our brains and helps to improve our abilities in other subjects such as reading and mathematics. From simple sums to complex functions, mathematical concepts form part of the world of music. Because of this connection, it is possible to establish a positive correlation between participation\\/performance in music and cognitive development in mathematics. Gardner's theory of
|Mathematics and science achievements have been assessed in the Third International Mathematics and Science Study (TIMSS) and its repetition (TIMSS-R). The released TIMSS and TIMSS-R reports are largely divided into subject domains. To merge the research outcomes, this study focused on an examination of the relationship between mathematics and…
|Investigations about attitudes toward mathematics carried out in the past decade were revised. The instruments used to measure attitudes toward mathematics were analysed as well as the attitudes toward different aspects of mathematics, their relation with other school subjects and their stability through time. Opinions about the influence of…
This paper explores the nature and source of mathematics homework and teachers' and students' perspectives about the role of mathematics homework. The subjects of the study are three grade 8 mathematics teachers and 115 of their students. Data from field notes, teacher interviews and student questionnaire are analysed using qualitative methods.…
|Mathematics is not a race-neutral subject. Access and opportunity in mathematics for students of color in the United States continue to be limited. While a great deal of attention has been given to increasing the number of underrepresented minority students in the mathematics pipeline, there is little consideration of who they are as learners or…
|Investigated stresses confronted by Portuguese secondary mathematics teachers during the first semester in a master's course, Perspectives on Mathematics Education, noting how they negatively affected teachers' self-confidence and morale and discussing fundamental issues teachers addressed in bridging the academic mathematics and mathematics…Investigated gender pattern differences in spatial- or mathematics-related activities in 213 junior high school students in the Netherlands to determine whether these activities are related to mathematical achievement or to attitudes toward mathematics and whether these differences influence student choice of mathematical study. Results suggest… and their tertiary academic success. Longitudinal data based on student feedback and…
Mathlanding offers high-quality digital mathematics content and contextualized resources, enabling educators to easily incorporate them into effective instructional practice. This NSDL Pathway is provided by Maryland Public Television (MPT), Math Forum at Drexel University, and the International Society for Technology in Education (ISTE) to foster excellence in elementary mathematics education, and is targeted to support elementary classroom teachers and specialists, coaches, supervisors, educators involved in teacher preparation, and parents.
The ATETV project delivers web-based videos to connect students to careers in advanced technology. In this episode of ATETV, students will see how important a strong foundation in mathematics is for those entering technical fields. This video would be particularly useful for students who struggle to see the importance of learning mathematics- they will get a glimpse at some of the real world applications of what they are learning. Running time for the episode is 2:55.
ThisIn this three-lesson unit, students participate in activities in which they focus on connections between mathematics and childrenâs literature. Three pieces of literature are used to teach geometry and measurement topics in the mathematics curriculum, i.e. using and describing geometric figures, estimating the volume of an irregular solid, and exploring the need for a standard unit of length. Activity worksheets and ideas for extension are included.
The power of mathematics is discussed as a way of expressing reasoning, aesthetics and insight in symbolic non-verbal communication. The human culture of discovering mathematical ways of thinking in the enterprise of exploring the understanding of the nature and the evolution of our world through hypotheses, theories and experimental affirmation of the scientific notion of algorithmic and non-algorithmic [`]computation', is examined and commended upon.
In the first volume of the treatise "Éléments de Mathématique," N. Bourbaki has given one of the possible rigorous definitions\\u000a of a mathematical structure. However, it turned out that this definition leads to considerable conceptual difficulties in\\u000a defining a general notion of a mathematical system, because structures in Bourbaki's sense possess a bracket division, which\\u000a means a definite order ofA mathematical modeling approach is applied for deriving subject-specific stabilometric parameters associated with center-of-pressure sway measurements for assessing balancing ability of subjects in quiet standing on a force platform. Based on the inverted pendulum model, a new combined stabilometric parameter including anthropometric characteristics (body height and mass) is obtained which represents a measure of postural instability. A physical meaning of the subject-specific parameter is related to the effective stiffness of the inverted pendulum model. PMID:22795475
In the United States, less than half of the students who enter into science, technology, engineering, and mathematics (STEM)\\u000a undergraduate curricula as freshmen will actually graduate with a STEM degree. There is even greater disparity in the national\\u000a STEM graduation rates of students from underrepresented groups with approximately three-fourths of minority students leaving\\u000a STEM disciplines at the undergraduate level. A
Science, technology, engineering, and mathematics (STEM) education programs help to enhance the nations global competitiveness. Many federal agencies have been involved in administering these programs. Concerns have been raised about the overall effective...
Although the National Science Board (Board) has long been concerned with quality P-20 education in Science, Technology, Engineering, and Mathematics (STEM) fields, this action plan has its genesis during the development of the 2006 Science and Engineering...
|The National Council of Teachers of Mathematics'"Curriculum and Evaluation Standards for School Mathematics" and "Professional Standards for Teaching Mathematics" reflect the belief that all students can learn a significant core of high-quality mathematics. Recognizing the magnitude of the task of reaching all students, this book was put together…
The course described in this article, "Multicultural Mathematics," aims to strengthen and expand students' understanding of fundamental mathematics--number systems, arithmetic, geometry, elementary number theory, and mathematical reasoning--through study of the mathematics of world cultures. In addition, the course is designed to explore the…
The view discussed is that mathematics teachers are becoming a rare, if not endangered, species, and the public image of mathematics needs to be changed. The mathematics teacher is termed the crucial variable, and a need is seen for changes in mathematics teacher education. The approach described is based on the following assumptions: (1)…
Issues in mathematics education figure prominently in efforts to improve American education. During the past decade, rather than studying the outcomes of mathematics learning in experimentation with specific teaching strategies, cognitive psychology has been advancing understanding of the fundamental nature of mathematics learning. Nesher demonstrates the promise of cognitive theories for instruction via several illustrative studies on elementary mathematics. This
Attitudes towards mathematics of college students in mathematics, psychology, and other fields were measured. Items describing mathematics as a good mental exercise and valuable mental training were selected by more than 55 percent of the students sampled. Overall similarity in attitudes among the three samples was high. Mathematics was highly…
The importance of afterschool programs have been linked to improved reading and math grades and a steady decline in drug, cigarette, and alcohol use by those who participate in such programs. The Afterschool Alliance was established in 2000 with funding provided by the Charles Stewart Mott Foundation. The website for the Alliance has a section on afterschool programs and the role they can play in learning and encouraging interest in STEMsubjects. At the top right hand side of the "Afterschool & STEM" section, visitors can learn about the "curriculum," "allies," "funding," "research," "policy," and "resources" for STEM afterschool programs. There are almost a dozen resources for high quality activities, curricula, and programs, in the curriculum link, including "Thinkfinity" (free), "Design Squad" (free) and "FIRST Robotics." The "funding" link provides 11 sources of afterschool STEM funds from such companies as Honda, Intel and Motorola, as well as from a multitude of federal government agencies.
|Addressing the under-representation of women, minorities, and persons with disabilities in science, technology, engineering, and mathematics (STEM) fields has been an initiative of the U.S. Congress for the past 30 years, but the challenge still remains unresolved. The National Science Foundation (NSF) and the Congressional Committee on Equal…
Advocating for advanced learning or talent development in science, technology, engineering, and mathematics (STEM) is both timely and very important. It is very important to speak out on behalf of talent development as the future of society depends on providing opportunities for developing talent to optimum levels. Some basic questions can set an…
|Efforts by federal and state governments to increase the STEM (science, technology, engineering and mathematics) workforce in support of innovation and competitiveness are frustrated by a shortage of adequately prepared and interested students. Less than half of 12th graders meet the math proficiency benchmark that indicates college readiness.…
For the purpose of our research we define Advanced Mathematical Knowledge|This document features an activity for estimating the distance from the earth to the moon during a solar eclipse based on calculations performed by the ancient Greek astronomer Hipparchus. Historical, mathematical, and scientific details about the calculation are provided. Internet resources for teachers to obtain more information on the subject…
|Medicine will be faced with a major challenge in coming years, namely how to treat for tissue dysfunction due to disease and aging There are two basic options: drug therapy and cell therapy. Stem cells have been the subject of intense speculation and controversy for several years, as they open up radically new therapeutic possibilities. Classical drugs can only smoothen consequences of tissue dysfunction, whereas cell therapy has the potential to restore tissue function by providing fresh cells. Cell therapy is totally different from organ transplantation, which can only benefit a limited number of patients. The use of the generic term "stem cells" to designate a whole variety of cell types that are present throughout life, is a source of confusion and ambiguity. It will take years of cognitive research to unravel the molecular mechanisms that govern a stem cell's multi- or totipotent status before we can fully exploit this therapeutic tool to the full. The younger a stem cell the greater its potential and, probably, the more durable its benefits, but the use of embryonic stem cells raises ethical issues. The redundancy or equivalence of diferent categories of cells is another source of controversy, yet researchers must be able to study stem cells in all their diversity, as complementary rather than competitive alternatives, in an acceptable ethical and regulatory environment. We briefly describe the three types of stem cells: pluripotent embryonic stem cells, fetal and adult stem cells, and pluripotent reprogrammed adult somatic cells. Only the former two categories have physiological functions: the first gives rise to tissues and organs while the second maintains tissue function during adulthood PMID:19883007
Tourism in Antarctica has increased dramatically with tens of thousands of tourists visiting the White Continent each year. Tourism cruises to Antarctica offer a unique educational experience for lay people through informal science-technology-engineering-mathematics (STEM) education. Passengers attend numerous scientific lectures that cover topics such as the geology of Antarctica, plate tectonics, glaciology, and climate change. Furthermore, tourists experience the geology and glaciology first hand during shore excursions. Currently, the grand challenges facing our global society are closely connected to the Earth sciences. Issues such as energy, climate change, water security, and natural hazards, are consistently on the legislative docket of policymakers around the world. However, the majority of the world's population is uninformed about the role Earth sciences play in their everyday lives. Tourism in Antarctica provides opportunities for informal STEM learning and, as a result, tourists leave with a better understanding and greater appreciation for both Antarctica and Earth sciences.
The Mathematical Physics Electronic Journal is a refereed periodical that publishes papers in mathematical physics and related areas. Articles are presented in the form of a single postscript file. Cover pages, tables of contents, abstracts, and articles dating back to 1995; about the journal and the publisher; home and mirror sites; editorial board; procedures and copyright policies; submitting an article; sample paper and abstract; subscribing to the journal or the abstracts; about e-mail correspondence with MPEJ; getting articles, abstracts, and other information by e-mail.
The Java Mathematical Expression Parser (JEP) is a handy tool "for parsing and evaluating mathematical expressions." It is a no-frills package that incorporates several important features, including user-definable functions and implicit multiplication for easy use. JEP can be downloaded as a complete application, or a couple of its features can be used online as applets. There is a separate page of documentation and installation instructions. Also available on this Web site is the AutoAbacus, which allows users to input a system of equations and obtain the solutions instantaneously.
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The last decade has seen an enormous development in infinite-valued\\u000asystems and in particular in such systems which have become known as\\u000amathematical fuzzy logics.\\u000a¶\\u000aThe paper discusses the mathematical background for the interest in\\u000asuch systems of mathematical fuzzy logics, as well as the most\\u000aimportant ones of them. It concentrates on the propositional cases,\\u000aand mentions the
Subjects in an Introductory Physical Science (IPS) program who received a pretest of mathematical skills and were exposed to a mathematics overview were found to obtain significantly higher achievement scores on an IPA achievement test than those subjects not receiving the treatment. (CP)
Staffing American schools with well-qualified teachers has long been a prominent issue in elementary and secondary education. Mathematics and science teachers are of particular interest because mathematics and science are core subjects in both elementary and secondary public schools. These subjects continue to attract attention as the need for…
\\u000a The recognition of beauty arises from various mental operations, spontaneous or induced, passively accepted or pressingly\\u000a imposed. The perception of beauty under the subjective aesthetical sensibility can be analyzed, and at least partially justified,\\u000a with different approaches: neuro-psychological or evolutionary, socio-cultural and mathematical formalizing. These approaches\\u000a individualize many factors in the determinations of the concept of beautiful, consequential to ancestral
For 23 years I have been teaching physics and other subjects in science and math in Chicago public high schools. In the 1970s, an integration consent decree issued in federal court mandated that, except for impaired learners, all students in the high school where I was teaching must take four years of science and mathematics. The students at Robeson High were poor African-American students, most of whom had weak reading and math backgrounds.
|Mechanics has never been the most popular subject in A-level mathematics, the UK's public examination for 16-18-year olds, either with students, teachers or educators. The attempts to popularize mechanics have failed and it is conceivable that the subject will be dropped from the A-level syllabus in the foreseeable future. This article argues the…
Science Technology Engineering and Mathematics UPRM K-12 Partnership Circles (STEM Circles) is a proposal for an after school program developed by the University of Puerto Rico Mayagüez Campus (UPRM) and submitted to the National Science Foundation. The purpose of the STEM Circles is to create collaboration between the UPRM and the Puerto Rico Department of Education (DE) to develop an
|These tables provide state-level information on the conferring of Science, Technology, Engineering, and Mathematics (STEM) awards (degrees and certificates) from academic years 2000-01 and 2008-09, both overall and by field. Specifically, the tables provide information on: (1) the number of awards conferred in STEM fields, overall (table 1) and…
Many physicists wonder at the usefulness of mathematics in physics. According Madrid to Einstein mathematics is admirably appropriate to the objects of reality. Wigner asserts that mathematics plays an unreasonable important role in physics. James Jeans affirms that God is a mathematician, and that the first aim of physics is to discover the laws of nature, which are written in mathematical language. Dirac suggests that God may have used very advanced mathematics in constructing the universe. And Barrow adheres himself to Wigner's claim about the unreasonable effectiveness of mathematics for the workings of the physical world.
Following a 2011 report by the National Research Council (NRC) on successful K-12 education in science, technology, engineering, and mathematics (STEM), Congress asked the National Science Foundation to identify methods for tracking progress toward the re...This resource guide from the Middle School Portal 2 project, written specifically for teachers, provides links to exemplary resources including background information, lessons, career information, and related national mathematics education standards. This publication offers online resources that connect mathematics to three subject areas: social studies, art, and science. Each section contains lesson plans, problems to solve, and examples of mathematics at work within contexts not usually associated with school mathematics. What is the point of integrating these disciplines? NCTM has reached this conclusion: If all the middle-grades teachers in a school do their best to connect content areas, mathematics and other disciplines will be seen as permeating life and not as just existing in isolation.
The effective mathematics education of Latinos and Latinas is the focus of the Center for the Mathematics Education of Latinos/as (CEMELA), and their website gives a more in-depth explanation of the importance of their work, in "About the Center". Their research has found that "given the unique language, social, and political issues associated with Latino/a students and communities, a multidisciplinary approach [can] be used to adequately and appropriately address their needs." Visitors can read research studies, working papers, and publications as well as view presentations that fortify CEMELA's findings on how to teach Latinos/as mathematics, and why. The "Research Studies" are divided up into the subjects of "Research on Teacher Education", "Research with Parents", and "Research on Student Learning". Visitors will find that the two studies on Research with Parents look at the use of Latino parents' use of mathematics in everyday contexts, and parents' perceptions of teaching and learning mathematics.This is the first of five pages of word problems (41 altogether) which develop logical and mathematical reasoning. They involve a range of difficulty levels and invite a variety of solution strategies. Most provide the opportunity for solvers to practice computational skills. Each problem includes a link to a solution. Red asterisks indicate more challenging problems.
We propose a simple cognitive model where qualitative and quantitative com- parisons enable animals to identify objects, associate them with their properties held in memory and make naive inference. Simple notions like equivalence re- lations, order relations are used. We then show that such processes are at the root of human mathematical reasoning by showing that the elements of totally|This book looks at how practitioners have focused on the fully educational application of intellect to the problem of developing mathematical thinking among one's pupils. Each chapter demonstrates reflective minds at work, relying on close observation, willingness to understand the student's thinking processes and patient commitment to students…Mathematics teachers are both more difficult to attract and more difficult to retain than social sciences teachers. This fact is not unique to the United States; it is reported as being a problem in Europe as well (Howson, 2002). In the United States, however, the problem is particularly preoccupying. Because of the chronic teacher shortages and…
|The Nobel prize winning physicist Richard Feynman (2007) famously enthused about "the pleasure of finding things out". In day-to-day classroom life, however, it is easy to lose and undervalue this pleasure in the process, as opposed to products, of mathematics. Finding things out involves a journey and is often where the learning takes place.…
A new approach to Preisach's hysteresis model, which emphasizes its phenomenological nature and mathematical generality, is briefly described. Then the theorem which gives the necessary and sufficient conditions for the representation of actual hysteresis nonlinearities by Preisach's model is proven. The significance of this theorem is that it establishes the limits of applicability of this model.
In order to fully appreciate and understand the complexity of cellular signaling, biologists are turning to mathematical models and computational approaches. Yaffe provides insight into his strategies for dividing and conquering papers that use complex math to make new predictions about biological systems. |
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