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

Published by Pearson (September 26, 2014) © 2015

  • Calvin T. Long Washington State University
  • Duane W. DeTemple Washington State University
  • Richard S. Millman Georgia Institute of Technology
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Mathematical Reasoning for Elementary Teachers, 7th Edition helps you develop the reasoning skills, deep conceptual understanding and positive attitude that future elementary or middle school teachers need. It presents the mathematical content for teaching within the context of the elementary classroom. The authors aim to answer “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 8 Standards for Mathematical Practice from the Common Core State Standards are integrated throughout. Hands On Activities begin each chapter with content-related games and puzzles that can be adapted easily for use in the future classroom. 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, and much more.

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

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