Pearson - Mathematical Reasoning for Elementary Teachers, 5/E - Calvin T. Long, Duane W. DeTemple & Richard Millman

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Description

The Fifth Edition of Mathematical Reasoning for Elementary Teachers, with new co-author Richard Millman, focuses on mathematical knowledge needed for teaching–demonstrating why future teachers are learning math content as well as when they will use it in the classroom. One of the most important aspects of teaching is being able to explain why students’ methods and ideas are either right or wrong. Imparting this skill to future teachers is the emphasis of this fantastic text.

To see available supplements that will enliven your course with activities, classroom videos, and professional development for future teachers, visit http://www.pearsonhighered.com/teachingmath.

Features

Features for Future Teachers

A teacher of mathematics should be aware of the historical development of mathematics, have some knowledge of the principal contributors to mathematics, and realize that mathematics continues to be a lively area of research. The text contains a number of features that you will find to be valuable in the classroom.

Highlights from History illustrate the contributions individuals have made to mathematics and provide a cultural, historical, and personal perspective on the development of mathematical concepts and thought.
Into the Classroom provides insights into teaching the topics of this text to elementary and middle school children. These tips often come directly from elementary or middle school teachers.
School Book Pages are taken from actual elementary or middle school textbooks and show how topics from the text are made meaningful to schoolchildren.
Did You Know? provides examples of recent advancements in mathematics, often demonstrating the important role the subject has in today’s world and in our personal lives. This feature also highlights excerpts from mathematical literature that have relevance to the classroom teacher.
Just for Fun shows the lighter side of mathematical problem solving, with engaging puzzles and teasers that have an element of surprise and humor.
Window on Technology contains explanations of special applications of graphing calculators, spreadsheets, and geometry software.
Polya Principles have been used in an increasing number of examples, with solutions written so as to highlight his four-step approach to problem solving--an approach that will be quite useful in your classes.
Hands On Activities at the beginning of each chapter serve as introductions to the material to be covered in the chapter. These offer games and puzzles that can be adapted in your class.

Chapter Elements

Except for Chapter 1, each chapter is consistently structured according to the following pattern:

Chapter opener. A class activity called “Hands On” introduces the chapter topic. We have made a number of changes in these activities in order to even more effectively introduce the material covered in the chapter. The Hands On activities are followed by “Connections” features that reveal the interconnections among the various parts of mathematics previously discussed and between mathematics and the real world.
Examples are often presented in a problem-solving mode, asking you to independently obtain a solution that can be compared with the solution presented in the text. Solutions are frequently structured in the Polya four-step format and the number of such solutions has been increased in this fifth edition.
From the NCTM Principles and Standards Extensive excerpts from The Principles and Standards help students understand the timeliness and relevance of topics.
Think clouds These notes serve as quick reminders and clarify key points in discussions.
Cooperative investigations provide activities, open-ended problems, and opportunities for cooperative learning.
Mathematical Habit of the Mind (HM): There are mathematical problems and discussions in the text (indicated by an HM) in which there is more going on than appears at first glance. This feature encourages future teachers to ask such questions as “Is there a different way to think about this problem?” or “What is there that I am not seeing?”
Problem sets are organized according to the following categories:

Understanding Concepts problems provide drill exercises and reinforce basic concepts.

Teaching Concepts problems pose questions that cause prospective teachers to carefully consider how they might go about clarifying subtle and often misunderstood points for their students in classes they may soon teach.

Thinking Critically problems offer problem-solving practice related to the section topic. Many of these problems can be used as classroom activities or with small groups.

Thinking Cooperatively problems provide cooperative problem-solving experiences specifically for small groups.

Making Connections problems apply the section concepts to solving real-life problems and to other parts of mathematics.

Communicating exercises offer opportunities to write about mathematics and to investigate mathematics as a language.

Using a Calculator problems are best solved with a calculator and are highlighted by an icon. Problems suitable for a graphing calculator have been highlighted by another icon.

Using a Computer problems give you the opportunity to use various types of software.

NEW! Responding to Students exercises give the opportunity for future teachers to see what mathematical questions and procedures children will come up with on their own and ways to respond to them.

From State Student Assessments problems provide examples of problems from the high stakes exams now in use in many states to assess student progress. These problems help make you aware of the types of knowledge that your future students will be asked to master.

For Review problems offer continual reinforcement of concepts covered earlier in the text.

Epilogue This is a brief concluding essay that discusses the importance of the materials just covered, provides a helpful summarizing overview, or places the chapter in the context of the remainder of the book.
End-of-Chapter Material Each chapter closes with the following features: Chapter Summary; Key Concepts; Vocabulary and Notation; Chapter Review Problems; and a Chapter Test.

New To This Edition

Algebra and Problem Solving: Chapter 1, Thinking Critically, has been significantly enhanced by adding a new Section 1.4, Algebra as a Problem-Solving Strategy. The new section shows how the use of a variable can play a powerful and clarifying role in problem-solving. As algebra itself is now being introduced in the early grades, the exposure of future teachers to algebraic ideas is more important than ever.

Responding to Student Problems: Throughout the problem sets, there are many problems which give examples of the ways in which children try to use mathematical techniques. A part of every teacher’s job is to analyze what the children are doing and give them help at a conceptual level or to show them why their method works and these exercises help future teachers develop those skills.

Mathematical Habit of the Mind (HM): There are mathematical problems and discussions in the text (indicated by an HM) in which there is more going on than appears at first glance. This feature encourages future teachers to ask such questions as “Is there a different way to think about this problem?” or “What is there that I am not seeing?” Frequently, HM shows us the need to go back to how concepts are defined. In other cases, an HM highlights an approach or way of thinking that is of special importance to reason about a particular concept or procedure. Possible generalizations or dealing with the vagueness of open-ended questions are also examples of HM.

Expanded Student Statewide Assessment Problems (SSA): Many new problems of the SSA type have been added and most problem sets include several of these. Solving such problems will show you why the material of the section really is needed in elementary or middle school.

Statistics In Chapter 9: The Interpretation of Data, the view of statistics as a science has been emphasized.

Table of Contents

1. Thinking Critically

1.1 An Introduction to Problem Solving.

1.2 Pólya's Problem-Solving Principles.
1.3 More Problem-Solving Strategies.
1.4 Algebra as Problem-Solving Strategy

1.5 Additional Problem-Solving Strategies

1.6 Reasoning Mathematically

2. Sets and Whole Numbers

2.1 Sets and Operations on Sets.
2.2 Sets, Counting, and the Whole Numbers.
2.3 Addition and Subtraction of Whole Numbers.
2.4 Multiplication and Division of Whole Numbers.

3. Numeration and Computation

3.1 Numeration Systems Past and Present.
3.2 Nondecimal Positional Systems.
3.3 Algorithms for Adding and Subtracting Whole Numbers.
3.4 Algorithms for Multiplication and Division of Whole Numbers.
3.5 Mental Arithmetic and Estimation.
3.6 Getting the Most Out of Your Calculator.

4. Number Theory

4.1 Divisibility of Natural Numbers.
4.2 Tests for Divisibility.
4.3 Greatest Common Divisors and Least Common Multiples.
4.4 Codes and Credit Card Numbers: Connections to Number Theory.

5. Integers

5.1 Representations of Integers.
5.2 Addition and Subtraction of Integers.
5.3 Multiplication and Division of Integers.

6. Fractions and Rational Numbers

6.1 The Basic Concepts of Fractions and Rational Numbers.
6.2 Addition and Subtraction of Fractions
6.3 Multiplication and Division of Fractions

6.4 Properties and Applications of Rational Numbers

7. Decimals, Real Numbers, and Proportional Reasoning

7.1 Decimals and Real Numbers
7.2 Computations with Decimals.
7.3 Proportional Reasoning
7.4 Percent.

8. Algebraic Reasoning and Representation

8.1 Expressions, Functions, and Equations

8.2 Graphing Functions in the Cartesian Plane

9. Statistics: The Interpretation of Data

9.1 Graphical Representation of Data.
9.2 Measures of Central Tendency and Variability.
9.3 Statistical Inference and Sampling

10. Probability

10.1 Empirical Probability.
10.2 Principles of Counting.
10.3 Permutations and Combinations

10.4 Theoretical Probability

11. Geometric Figures

11.1 Figures in the Plane.
11.2 Curves and Polygons in the Plane.
11.3 Figures in Space.
11.4 Networks.

12. Measurement: Length, Area, and Volume

12.1 The Measurement Process.
12.2 Area and Perimeter.
12.3 The Pythagorean Theorem.
12.4 Surface Area and Volume.

13. Transformations, Symmetries, and Tilings

13.1 Rigid Motions and Similarity Transformations.
13.2 Patterns and Symmetries.
13.3 Tilings and Escher-like Design.

14. Congruence, Constructions, and Similarity

14.1 Congruent Triangles.
14.2 Constructing Geometric Figures.
14.3 Similar Triangles.

Appendix A Manipulatives in the Mathematics Classroom

Appendix B Spreadsheets

Appendix C Graphing Calculators

Appendix D A Brief Guide to the Geometer’s Sketchpad

Appendix E Resources

Courses

Math for Future Elementary Teachers (Mathematics)

Previous Edition(s)

Mathematical Reasoning for Elementary Teachers, 4/E
Long & DeTemple
©2006 | Pearson | Cloth; 1080 pp | Out of Print
ISBN-10: 0321286960 | ISBN-13: 9780321286963
Brief Description |
The fourth edition of Mathematical Reasoning has an increased focus on professional development and connecting the material from this class to the elementary and middle school classroom. The authors have provided more meaningful content and pedagogy to arm students with all the tools that they will need to become excellent elementary or middle school teachers.
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Next Edition(s)

Mathematical Reasoning for Elementary School Teachers, 6/E
Long, DeTemple & Millman
©2012 | Pearson | Cloth; 944 pp | Instock
ISBN-10: 0321693124 | ISBN-13: 9780321693129
Net price: $115.00 (What's this?)Brief Description |
Mathematical Reasoning for Elementary Teachers presents the mathematical knowledge needed for teaching, with an emphasis on why future teachers are learning the content as well as when and how they will use it in the classroom.

The Sixth Edition has been streamlined throughout to make it easier to focus on the important concepts. The authors continue to make the course relevant for future teachers by adding new features such as questions connected to School Book Pages; enhancing hallmark features such as Responding to Students exercises; and making the text a better study tool through the redesigned Chapter Summaries. For this edition, MyMathLab has been expanded to include new exercises, the integration of IMAP videos, and additional resources to make it easier to assign homework and provide resources to students.

To see available supplements that will enliven your course with activities, classroom videos, and professional development for future teachers, visit www.pearsonhighered.com/teachingmath
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In this section:

Author Bios

Author Bios

Calvin Long received his B.S. in Mathematics from the University of Idaho. Following M.S. and Ph.D. degrees in Mathematics from the University of Oregon he worked briefly as an analyst for the National Security Agency and then joined the faculty at Washington State University. His teaching ran the gamut from elementary algebra through graduate courses and included frequently teaching the content courses for prospective elementary school teachers.

His other professional activities include serving on numerous committees of the National Council of Teachers of Mathematics and the Mathematical Association of America, and holding various leadership positions in those organizations. Professor Long has also been heavily engaged in directing and instructing in-service workshops and institutes for teachers at all levels, has given over one hundred presentations at national and regional meetings of NCTM and its affiliated groups, and has presented invited lectures on mathematics education abroad.

Professor Long has co-authored two books and is the sole author of a text in number theory. In addition, he has authored over ninety articles on mathematics and mathematics education, and also served as a frequent reviewer for both The Arithmetic Teacher and The Mathematics Teacher. In 1986, he received the Faculty Excellence Award in Teaching from Washington State University and, in 1991, he received a Certificate for Meritorious Service to the Mathematical Association of America.

Aside from his professional activities, Dr. Long enjoys listening to, singing, and directing classical music, reading, fly fishing, camping, and back packing.

-------------------------

Duane DeTemple received his B.S. with majors in Applied Science and Mathematics from Portland State College. Following his Ph.D. in Mathematics from Stanford University, he joined the faculty at Washington State University, where he is now Professor of Mathematics. He has been extensively involved with teacher preparation and professional development at both the elementary and secondary levels. Professor DeTemple has been a frequent consultant to projects sponsored by the Washington State Office of the Superintendent of Public Instruction, the Higher Education Coordinating Board, and other boards and agencies.

Dr. DeTemple has co-authored three other books and over 80 articles on mathematics or mathematics materials for the classroom. He is a member of the Washington State University President’s Teaching Academy, and in 2007 was the recipient of the WSU Sahlin Faculty Excellence Award for Instruction and the Distinguished Teaching Award of the Pacific Northwest Section of the Mathematical Association of America.

In addition to mathematics teaching and research, Duane enjoys reading, listening to and playing music, hiking, biking, canoeing, traveling, and playing tennis.

________________

Richard Millman received a B.S. from the Massachusetts Institute of Technology and a Ph.D. from Cornell University in Mathematics. He is the Outreach Professor of Mathematics at the University of Kentucky, which supports pre-service and in-service teacher training for PreK-12 mathematics teachers. He is Principal Investigator and Project Director for ALGEBRA CUBED, a grant from the National Science Foundation to improve algebra education in rural Kentucky.

Dr. Millman has co-authored three books in mathematics, co-edited two others, and received nine peer reviewed grants. He has published over 40 articles about mathematics or mathematics education and has taught a wide variety of mathematics and mathematics education courses throughout the undergraduate and graduate curriculum, including those for preservice teachers. He received, with a former student, an Excel Prize for Expository Writing for an article in The Mathematics Teacher.

Rich enjoys traveling, writing about mathematics, losing golf balls, listening to music, and going to plays and movies. He also loves and is enormously proud of his grandchildren with whom he enjoys discussing the conceptual basis of mathematics, among other topics.

Websites and Online Courses

In this section:

Websites and Online Courses

MyMathLab with eBook -- Instant Access -- for Mathematical Reasoning for Elementary Teachers, 5/E
Long, DeTemple & Millman
©2009 | On-line Supplement; 1120 pp | Access Code Required | Live
ISBN-10: 0321528530 | ISBN-13: 9780321528537
Online purchase price: $82.00 | Students, buy access Take a Tour | More Info

MyMathLabPlus for Mathematical Reasoning for Elementary Teachers, 5/E
Long
©2011 | Pearson | Website | Live
ISBN-10: 0558840302 | ISBN-13: 9780558840303
Online purchase price: $92.00More Info

In this section:

Instructor Resources

Downloadable Instructor Resources
Other Instructor Resources

Student Resources

Websites and online courses
Other student resources

eLearning & Assessment

Websites and Online Courses

Course & Discipline Resources

For the Mathematics Discipline

Active Learning Questions (Download only) for Mathematical Reasoning for Elementary Teachers, 5/E
Long, DeTemple & Millman
©2009 | Pearson | On-line Supplement | Live
ISBN-10: 0321538099 | ISBN-13: 9780321538093

Instructor's Guide (Download only) for Activities for Mathematical Reasoning for Elementary Teachers, 5/E
Dolan, Williamson & Muri
©2009 | Pearson | On-line Supplement | Live
ISBN-10: 0321529197 | ISBN-13: 9780321529190

Instructor's Testing Manual for Mathematical Reasoning for Elementary Teachers, 5/E
Long, DeTemple & Millman
©2009 | Pearson | Paper; 338 pp | Out of Stock
ISBN-10: 0321528522 | ISBN-13: 9780321528520

PowerPoint Slides for Mathematical Reasoning for Elementary Teachers - Download only, 5/E
Long, DeTemple & Millman
©2009 | Pearson | On-line Supplement | Live
ISBN-10: 0321535987 | ISBN-13: 9780321535986

TestGen® Computerized Test Bank for Mathematical Reasoning for Elementary Teachers, 5/E
Long, DeTemple & Millman
©2009 | Pearson | On-line Supplement | Live
ISBN-10: 0321528514 | ISBN-13: 9780321528513

Websites and online courses

IMAP CD-ROM: Integrating Mathematics and Pedagogy to Illustrate Children's Reasoning
San Diego State University Foundation
©2005 | Pearson | CD-ROM Only | Instock
ISBN-10: 0321588304 | ISBN-13: 9780321588302
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MathXL -- Instant Access -- for Mathematical Reasoning for Elementary Teachers, 5/E
Long, DeTemple & Millman
©2009 | Pearson | On-line Supplement | Live
ISBN-10: 0321528565 | ISBN-13: 9780321528568
More Info

MyMathLabPlus for Mathematical Reasoning for Elementary Teachers, 5/E
Long
©2011 | Pearson | Website | Live
ISBN-10: 0558840302 | ISBN-13: 9780558840303
Online purchase price: $92.00More Info

MyMathLabPlus for Mathematical Reasoning for Elementary Teachers, 5/E
Long
©2011 | Pearson | Website | Live
ISBN-10: 0558840302 | ISBN-13: 9780558840303
Online purchase price: $92.00More Info

Other student resources

Connecting Math for Elementary Teachers: How Children Learn Mathematics
Feikes, Schwingendorf & Gregg
©2009 | Pearson | Paper; 336 pp | Instock
ISBN-10: 0321542665 | ISBN-13: 9780321542663
Net price: $27.50 (What's this?)More Info

E-Manipulatives CD for Future Elementary School Teachers, Version 2.1, 10/E
Pearson
©2010 | Pearson | CD-ROM Only | Instock
ISBN-10: 0321640802 | ISBN-13: 9780321640802
Net price: $25.00 (What's this?)More Info

IMAP CD-ROM: Integrating Mathematics and Pedagogy to Illustrate Children's Reasoning
San Diego State University Foundation & Philipp
©2005 | Pearson | CD-ROM Only; 1 pp | Instock
ISBN-10: 0131198548 | ISBN-13: 9780131198548
Net price: $19.50 (What's this?)More Info

For the Mathematics Discipline

Allied Health Study Card, 2/E
Forshier
©2006 | Pearson | Study Card | Instock
ISBN-10: 0321394747 | ISBN-13: 9780321394743
Net price: $3.00 (What's this?)More Info

Basic Math Review Card, 2/E
Addison-Wesley
©2006 | Pearson | Study Card; 6 pp | Instock
ISBN-10: 0321394763 | ISBN-13: 9780321394767
Net price: $3.00 (What's this?)More Info

Center for Excellence Sticker
Addison Wesley Higher Education Group
©2000 | Pearson | Unknown / Other | Instock
ISBN-10: 0201716275 | ISBN-13: 9780201716276
Suggested retail price: $0.00Net price: $0.00 (What's this?)More Info

Concept Videos: Algebra
Addison-Wesley
©2008 | Pearson | Multiple Media Package | Instock
ISBN-10: 0321517199 | ISBN-13: 9780321517197
Suggested retail price: $36.67Net price: $27.50 (What's this?)More Info

Concept Videos: Basic Math & Prealgebra
Addison-Wesley
©2008 | Pearson | Multiple Media Package | Instock
ISBN-10: 032151758X | ISBN-13: 9780321517586
Suggested retail price: $36.67Net price: $27.50 (What's this?)More Info

Discovering Algebra: Examples with Keystrokes on the TI-83/TI-82 and TI-85/TI-86, A Laboratory Approach
Pirich & Bigliani
©1997 | Pearson | Paper; 195 pp | Instock
ISBN-10: 0136492037 | ISBN-13: 9780136492030
Net price: $35.85 (What's this?)More Info

Graphing Calculator Tutorial CD
Addison-Wesley
©2006 | Pearson | CD-ROM Only | Instock
ISBN-10: 0321357744 | ISBN-13: 9780321357748
Net price: $10.00 (What's this?)More Info

Overcoming Math Anxiety, 2/E
Davidson & Levitov
©2000 | Pearson | Paper | Instock
ISBN-10: 0321069188 | ISBN-13: 9780321069184
Net price: $27.50 (What's this?)More Info

Prealgebra Review Workbook
Wheel
©2006 | Pearson | Paper; 300 pp | Instock
ISBN-10: 0321473329 | ISBN-13: 9780321473325
Net price: $27.50 (What's this?)More Info

Review of Algebra, A
Howard
©2002 | Pearson | Paper; 224 pp | Instock
ISBN-10: 0201773473 | ISBN-13: 9780201773477
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Spanish Basic Math Study Card
Leonarte
©2007 | Pearson | Study Card | Instock
ISBN-10: 0321438582 | ISBN-13: 9780321438584
Net price: $3.00 (What's this?)More Info

TestGen All-in-One 2005 Package
Addison-Wesley
©2005 | Pearson | CD-ROM Only | Instock
ISBN-10: 0321334469 | ISBN-13: 9780321334466
Suggested retail price: $0.00Net price: $0.00 (What's this?)More Info

Websites and Online Courses

MyMathLabPlus for Mathematical Reasoning for Elementary Teachers, 5/E
Long
©2011 | Pearson | Website | Live
ISBN-10: 0558840302 | ISBN-13: 9780558840303
Online purchase price: $92.00More Info

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Mathematical Reasoning for Elementary Teachers, CourseSmart eTextbook, 5/E
Long, DeTemple & Millman
©2009 | Pearson | Electronic Book; 1120 pp | Available
ISBN-10: 0321546830 | ISBN-13: 9780321546838
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