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Table of Contents

1. Thinking Critically.

Some Surprising Tidbits.

An Introduction to Problem Solving.

Pólya's Problem-Solving Principles.

More Problem-Solving Strategies.

Additional Problem-Solving Strategies.

2. Sets and Whole Numbers.

Sets and Operations on Sets.

Sets, Counting, and the Whole Numbers.

Addition and Subtraction of Whole Numbers.

Multiplication and Division of Whole Numbers.

3. Numeration and Computation.

Numeration Systems Past and Present.

Nondecimal Positional Systems.

Algorithms for Adding and Subtracting Whole Numbers.

Algorithms for Multiplication and Division of Whole Numbers.

Mental Arithmetic and Estimation.

Getting the Most Out of Your Calculator.

4. Number Theory.

Divisibility of Natural Numbers.

Tests for Divisibility.

Greatest Common Divisors and Least Common Multiples.

Codes and Credit Card Numbers: Connections to Number Theory.

5. Integers.

Representation of Integers.

Addition and Subtraction of Integers.

Multiplication and Division of Integers.

Clock Arithmetic.

6. Fractions and Rational Numbers.

The Basic Concepts of Fractions and Rational Numbers.

The Arithmetic of Rational Numbers.

The Rational Number System.

7. Decimals and Real Numbers.

Decimals.

Computations with Decimals.

Ratio and Proportion.

Percent.

8. Algebraic Reasoning and Representation.

Algebraic Expressions and Equations.

Functions.

Graphing Functions in the Cartesian Plane.

9. Statistics: The Interpretation of Data.

The Graphical Representation of Data.

Measures of Central Tendency and Variability.

Statistical Inference.

10. Probability.

Empirical Probability.

Principles of Counting.

Theoretical Probability.

11. Geometric Figures.

Figures in the Plane.

Curves and Polygons in the Plane.

Figures in Space.

Networks.

12. Measurement.

The Measurement Process.

Area and Perimeter.

The Pythagorean Theorem.

Surface Area and Volume.

13. Transformations, Symmetries, and Tilings.

Rigid Motions and Similarity Transformations.

Patterns and Symmetries.

Tilings and Escher-like Designs.

14. Congruence, Constructions, and Similarities.

Congruent Triangles.

Constructing Geometric Figures.

Similar Triangles.

Appendices.

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.

Answers to Selected Problems.


Acknowledgments.


Mathematical Lexicon.


Index and Pronunciation Guide.

Get Mathematical Reasoning for Elementary Teachers, 3rd Edition by Calvin T. Long, Washington State University Duane W. DeTemple, Washington State University

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