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# Reconceptualizing Mathematics

## Second EditionJudith Sowder; Larry Sowder; Susan Nickerson

©2013
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## Table of Contents

**PART I Reasoning About Numbers and Quantities**

1. Reasoning About Quantities

2. Numeration Systems

3. Understanding Whole Number Operations

4. Some Conventional Ways of Computing

5. Using Numbers in Sensible Ways

6. Meanings for Fractions

7. Computing with Fractions

8. Multiplicative Comparisons and Multiplicative Reasoning

9. Ratios, Rates, Proportions, and Percents

10. Integers and Other Number Systems

11. Number Theory

**PART II Reasoning About Algebra and Change**

12. What is Algebra?

13. A Quantitative Approach to Algebra and Graphing

14. Understanding Change: Relationships Among Time, Distance, and Rate

15. Further Topics in Algebra and Change

**PART III Reasoning About Shapes and Measurement**

16. Polygons

17. Polyhedra

18. Symmetry

19. Tessellations

20. Similarity

21. Curves, Constructions, and Curved Surfaces

22. Transformation Geometry

23. Measurement Basics

24. Area, Surface Area, and Volume

25. Counting Units Fast: Measurement Formulas

26. Special Topics in Measurement

**PART IV Reasoning About Chance and Data**

27. Quantifying Uncertainty

28. Determining More Complicated Probabilities

29. Introduction to Statistics and Sampling

30. Representing and Interpreting Data with One Variable

31. Dealing with Multiple Data Sets or with Multiple Variables

32. Variability in Shapes

33. Special Topics in Probability