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Mathematical Reasoning for Elementary School Teachers, 6th Edition

By Calvin T. Long, Duane W. DeTemple, Richard S. Millman

Published by Pearson

Published Date: Jan 3, 2011

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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 to make it easier to focus on the most important concepts. The authors continue to make the course relevant for future teachers, including the new features like Examining School Book Pages, as well as the hallmark features like Into the Classroom discussions and Responding to Students questions. Activities, classroom videos, and resources for professional development for future teachers are also available at

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 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 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


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 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 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 and Connections with Geometry

8.1 Algebraic Expressions, Functions, and Equations

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

9.4 Networks


10. Measurement: Length, Area, and Volume

10.1 The Measurement Process

10.2 Area and Perimeter

10.3 The Pythagorean Theorem

10.4 Surface Area and Volume


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 Experimental Probability

14.2 Principles of Counting

14.3 Permutations and Combinations

14.4 Theoretical Probability



A. Manipulatives in the Mathematics Classroom

B. Getting the Most out of Your Calculator

C. A Brief Guide to the Geometer's Sketchpad

D. Resources

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