## Description

Each chapter section contains insights and examples of how children come to understand mathematics. Many of the descriptions of how children learn are based on research, but some are based on the authors’ personal experiences with helping children learn mathematics. As appropriate, the authors also include information on the “why” behind certain mathematical topics, how to incorporate manipulatives into the classroom, and some activities to try. Each section also has “Questions for Discussion” to encourage reflection while learning. At the end of each section are “Problems and Exercises” that are specifically designed to help show how children learn mathematics. The material is presented by topic, following the standard topics covered in a traditional mathematics for future elementary or middle school teacher's course.

**CourseSmart textbooks do not include any media or print supplements that come packaged with the bound book.**

## Table of Contents

**Introduction**

**Chapter 1 Problem Solving **

1.1 An Introduction to Problem Solving

1.2 Patterns

1.3 Mathematical Reasoning

**Chapter 2 Sets**

2.1 Set Theory

2.2 Venn Diagrams

**Chapter 3 Whole Numbers**

3.1 Numeration Systems

3.2 Addition and Subtraction

3.3 Multiplication and Division

3.4 Properties of Whole Number Operations

3.5 Algorithms

3.6 Mental Math & Estimation

**Chapter 4 Number Theory **

4.1 Factors and Multiples

4.2 Divisibility Tests

4.3 Prime and Composite Numbers

4.4 Greatest Common Factor & Least Common Multiple

**Chapter 5 Integers **

5.1 Children’s Understanding of Negative Numbers

5.2 Addition and Subtraction of Integers

5.3 Multiplication and Division of Integers

**Chapter 6 Rational Numbers - Fractions **

6.1 Fractions

6.2 Addition and Subtraction of Fractions

6.3 Multiplication and Division of Fractions

6.4 Properties of Rational Numbers

**Chapter 7 Decimals, Percents, and Real Numbers **

7.1 Place Value

7.2 Decimals

7.3 Decimal Computation

7.4 Ratio and Proportion

7.5 Percents

7.6 Rational, Irrational, and Real Numbers

**Chapter 8 Geometry **

8.1 Basic Geometric Concepts

8.2 Basic Shapes

8.3 Angles

8.4 Proof/Mathematical Reasoning/Justification/Argumentation

8.5 Three-Dimensional Geometry

**Chapter 9 More Geometry **

9.1 Transformations or Rigid Motions

9.2 Constructions

9.3 Symmetry

9.4 Similarity

**Chapter 10 Measurement**

10.1 The Concept of Measurement

10.2 Linear Measurement

10.3 Area and Perimeter

10.4 Volume and Surface Area

10.5 Time

**Chapter 11 Statistics/Data Analysis **

11.1 Data Analysis and Statistical Graphs

11.2 Statistical Deceptions and Examining Statistics Critically

11.3 Mean, Mode, and Median

11.4 Variation or Spread

11.5 Statistical Samples

**Chapter 12 Probability**

12.1 Basic Notions of Probability

12.2 More Sophisticated Concepts of Probability

**Chapter 13 Algebraic Reasoning**

13.1 The Concept of Variable

13.2 Algebraic Reasoning: Generalizing

13.3 Generalizing with Two Variables — Functions

13.4 Graphing: Coordinate Geometry

13.5 The Concept of Equality

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Connecting Math for Elementary Teachers: How Children Learn Mathematics, CourseSmart eTextbook

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$14.99 | ISBN-13: 978-0-321-54673-9