Elementary Mathematics for Teachers

​​Elementary Mathematics for Teachers is designed for the first semester of a university mathematics course for prospective elementary teachers. It is also appropriate for practicing teachers. This book focuses exclusively on K-8 mathematics. The text uses five Primary Mathematics Textbooks as a source of problems and to repeatedly illustrate several themes, including: (a) How the nature of a mathematics topic suggests an order for developing it in the classroom. (b) How topics are developed through "teaching sequences" which begin with easy problems and incrementally progress until the topic is mastered. (c) How the mathematics builds on itself through the grades.

Elementary Geometry for Teachers is the sequel to Elementary Mathematics for Teachers.

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Sample Pages

Elementary Mathematics for Teachers

Preface

About the Textbook

1. Place Value and Models for Arithmetic

1.1 Counting
1.2 Place Value
1.3 Addition
1.4 Subtraction
1.5 Multiplication
1.6 Division
1.7 Addendum on Classroom Practice

2. Mental Math and Word Problems

2.1 Mental Math
2.2 Word Problems
2.3 The Art of Word Problems

3. Algorithms

3.1 The Addition Algorithm
3.2 The Subtraction Algorithm
3.3 The Multiplication Algorithm
3.4 Long Division by 1-digit Numbers
3.5 Estimation
3.6 Completing the Long Division Algorithm

4. Prealgebra

4.1 Letters and Expressions
4.2 Identities, Properties, Rules
4.3 Exponents

5. Factors, Primes, and Proofs

5.1 Definitions, Explanations and Proofs
5.2 Divisibility Tests
5.3 Primes and the Fundamental Theorem of Arithmetic
5.4 More On Primes
5.5 Greatest Common Factors and Least Common Multiples

6. Fractions

6.1 Fraction Basics
6.2 More Fraction Basics
6.3 Multiplication of Fractions and a Review of Division
6.4 Division of Fractions
6.5 More Division Word Problems
6.6 Fractions as a Step Toward Algebra

7. Ratios, Percentages, and Rates

7.1 Ratios and Proportions
7.2 Changing Ratios and Percentages
7.3 Solving Percent Problems by the Unitary Method
7.4 Rates, Speed, and Dimensional Analysis

8. Negative, Numbers and Integers

8.1 Negative Numbers
8.2 Arithmetic with Integers
8.3 Integers as a Step Towards Algebra

9. Decimals, Rational and Real Numbers

9.1 Decimals
9.2 Rational Numbers and Decimals
9.3 Real Numbers and Decimals
9.4 Newton’s Method and √2

Bibliography

Index