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

This book provides general descriptions of children’s learning and is intended to help show how children approach mathematics differently than adults. By connecting children’s thinking to our own learning, we hope that this book will improve understanding of both mathematics and children’s thinking, thereby enhancing the teaching of mathematics to children. The more you understand mathematics and how children think about mathematics, the better teacher you will be!
 
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.

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