Mathematical Reasoning for Elementary Teachers, Media Update, 7th edition

Published by Pearson (January 1, 2018) © 2019

  • Calvin T. Long Washington State University
  • Duane W. DeTemple Washington State University
  • Richard S. Millman Georgia Institute of Technology

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For courses in Mathematics for Teachers or Mathematics for Future Elementary Teachers. 

Fosters reasoning skills, deep conceptual understanding and a positive attitude

Mathematical Reasoning for Elementary Teachers, 7th Edition presents the mathematical content aspiring elementary or middle school teachers need for teaching within the context of the elementary classroom. The authors endeavor to answer the frequently asked question “Why are we learning this?” by going beyond skill explanations to show how these concepts are implemented in the future classroom, and what types of questions children may ask. The Common Core State Standards for Mathematics are included.

Hallmark features of this title

  • Hands On Activities begin each chapter with content-related games and puzzles that can be adapted easily for use in the elementary classroom.
  • Examples are often presented in a problem-solving framework which asks students to obtain a solution that can be compared with the solution presented in the text.
  • Problem sets end each section and include a wide variety of question types.
  • Think Clouds offer quick reminders and clarify key points in discussions.
  • The Chapter in Relation to Future Teachers is a brief concluding essay that puts the chapter into context, summarizing how the content fits into the bigger picture of teaching.
  • Cooperative Investigations are small-group activities that explore and discuss concepts, with 1 per chapter.

New and updated features of this title

  • UpdatedChapter Openers begin with an introductory activity that introduces some of the principal topics of the chapter by means of cooperative learning.
    • Key Ideas show the interconnections among the various parts of mathematics previously discussed and between mathematics and the real world.
  • Completely updated Into the Classroom features provide insights from active teachers, providing a window into their classroom via activities, projects, discussions and ideas to engage children in the mathematics being covered in that particular chapter of the text.
  • Updated Responding to Students (RTS) problems throughout the problem sets show how children try to use mathematical techniques and illustrate why future teachers will need a thorough understanding of mathematical content in order to answer students' questions.
  • New Integrating Mathematics and Pedagogy (IMAP) video references in the Annotated Instructor's Edition make it easier to incorporate the IMAP videos into the classroom at relevant point-of-use. IMAP videos allow future teachers to see elementary and middle school students working out numerical concepts.

Highlights of the DIGITAL UPDATE for MyLab Math

Instructors, contact your sales rep to ensure you have the most recent version of the course.  

  • Mathematics Education Insights videos offer an unscripted view into a real classroom in action. Students watch teachers in action and children learning lessons, interacting with classmates and asking questions. Worksheets are provided for each video plus an implementation guide for instructors.
  • Common Core in Action videos feature experienced faculty shedding light on what the CCSS really mean for the classroom and for teachers; assessment questions are also available. Common Core Assessment Analysis exercises require analysis and interpretation of sample CCSS exercises.
  • Animations let students interact with the math in a visual, tangible way. Corresponding exercises in MyLab Math make these truly assignable.

Features of MyLab Math for the 7th Edition

  • Assessment questions for lecture videos allow instructors to create assignments around lecture videos.
  • Updated Flashcards reinforce key vocabulary from the text in an interactive online format on any device.
  • Mindset material has been added to the course. This content encourages students to maintain a positive attitude about learning, value their own ability to grow, and view mistakes as learning opportunities. 

1. Thinking Critically

  • 1.1 An Introduction to Problem Solving
  • 1.2 Polya's Problem-Solving Principles and the Standards for Mathematical Practice of the Common Core State Standards for Mathematics
  • 1.3 More Problem-Solving Strategies
  • 1.4 Algebra as a 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 Algorithms for Addition and Subtraction of Whole Numbers
  • 3.3 Algorithms for Multiplication and Division of Whole Numbers
  • 3.4 Mental Arithmetic and Estimation
  • 3.5 Nondecimal Positional Systems

4. Number Theory

  • 4.1 Divisibility of Natural Numbers
  • 4.2 Tests for Divisibility
  • 4.3 Greatest Common Divisors and Least Common Multiples

5. Integers

  • 5.1 Representation 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 The Rational Number System

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, Graphing, and Connections with Geometry

  • 8.1 Variables, Algebraic Expressions, and Functions
  • 8.2 Graphing Points, Lines, and Elementary Functions
  • 8.3 Connections between Algebra and Geometry

9. Geometric Figures

  • 9.1 Figures in the Plane
  • 9.2 Curves and Polygons in the Plane
  • 9.3 Figures in Space

10. Measurement: Length, Area, and Volume

  • 10.1 The Measurement Process
  • 10.2 Area and Perimeter
  • 10.3 The Pythagorean Theorem
  • 10.4 Volume
  • 10.5 Surface Area

11. Transformations, Symmetries, and Tilings

  • 11.1 Rigid Motions and Similarity Transformations
  • 11.2 Patterns and Symmetries
  • 11.3 Tilings and Escher-like Designs

12. Congruence, Constructions, and Similarity

  • 12.1 Congruent Triangles
  • 12.2 Constructing Geometric Figures
  • 12.3 Similar Triangles

13. Statistics: The Interpretation of Data

  • 13.1 Organizing and Representing Data
  • 13.2 Measuring the Center and Variation of Data
  • 13.3 Statistical Inference

14. Probability

  • 14.1 The Basics of Probability
  • 14.2 Applications of Counting Principles to Probability
  • 14.3 Permutations and Combinations
  • 14.4 Odds, Expected Values, Geometric Probability, and Simulations

About our authors

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 more than 100 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 2 books and is the sole author of a text on number theory. In addition, he has authored over 90 articles on mathematics and mathematics education, and served as a frequent reviewer for mathematics journals including 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, Cal enjoys listening to, singing and directing classical music, reading, fly fishing, camping and backpacking.

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 was a faculty member at Washington State University, where he is now a Professor Emeritus 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 4 other books and over 100 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 teaching and research mathematics, 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 a professor of mathematics and was director of the Center for Education Integrating Science, Mathematics and Computing (CEISMC) at the Georgia Institute of Technology, which supports STEM outreach in K-12. He was formerly the Outreach Professor of Mathematics at the University of Kentucky, where he was involved in both preservice and in-service teacher training for mathematics teachers.

Dr. Millman has co-authored 4 books in mathematics, co-edited 3 others, and received 10 peer-reviewed grants. He has published over 50 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 and was a Member-at-Large of the Council of the American Mathematical Society. He was principal investigator and project director for ALGEBRA CUBED, a grant from the National Science Foundation to improve algebra education in rural Kentucky. He was the principal investigator of a Race to the Top grant from the Georgia Department of Education and another NSF grant, SLIDER, in which students use a curriculum based on engineering design in the context of building robots to learn 8th-grade physical science and math.

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.

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