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The Mathematics Pre-Service Teachers Need to Know
Contents
Preface vii
Chapter 1. Introduction 1
1. Why is math important? 3
2. The critical role of mathematics in modern society 5
3. Common misconceptions by pre-service teachers about
mathematics 7
4. The mathematics K - 8 teachers need to know 9
5. Mathematical problem solving 10
6. Chapter 2 - the mathematics students need to know 12
7. Chapter 3 - the core material central to all school mathematics 13
8. The detailed course discussions, chapters 4 - 8 15
9. Chapter 9, experiences teaching pre- and in-service teachers 20
10. The first appendix 20
11. The book The Mathematical Education of Teachers 21
Chapter 2. The Basic Topics in K - 8 Mathematics 23
1. Introduction 23
2. Place Value and Basic Number Skills 24
3. Fractions 27
4. Ratios, Rates and Percents 32
5. The Core Processes of Mathematics 36
6. Functions and Equations 44
7. Real Measurement and Measurement in Geometry 49
8. Course Outline for the First Course 55
9. Course Outline for the Fractions Course 68
Chapter 3. Topics Needing Special Attention Attention in all Four
Courses 71
1. Introduction 71
2. Making Sense of Mathematics for Students 72
3. Abstraction 76
4. Definitions 78
5. Problem Solving: Overview 85
6. Well-Posed and Ill-Posed Problems in K-8 Mathematics 89
7. Problems with Hidden Assumptions 93
8. Problems where Psychology Affects the Outcome 94
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Contents
Preface vii
Chapter 1. Introduction 1
1. Why is math important? 3
2. The critical role of mathematics in modern society 5
3. Common misconceptions by pre-service teachers about
mathematics 7
4. The mathematics K - 8 teachers need to know 9
5. Mathematical problem solving 10
6. Chapter 2 - the mathematics students need to know 12
7. Chapter 3 - the core material central to all school mathematics 13
8. The detailed course discussions, chapters 4 - 8 15
9. Chapter 9, experiences teaching pre- and in-service teachers 20
10. The first appendix 20
11. The book The Mathematical Education of Teachers 21
Chapter 2. The Basic Topics in K - 8 Mathematics 23
1. Introduction 23
2. Place Value and Basic Number Skills 24
3. Fractions 27
4. Ratios, Rates and Percents 32
5. The Core Processes of Mathematics 36
6. Functions and Equations 44
7. Real Measurement and Measurement in Geometry 49
8. Course Outline for the First Course 55
9. Course Outline for the Fractions Course 68
Chapter 3. Topics Needing Special Attention Attention in all Four
Courses 71
1. Introduction 71
2. Making Sense of Mathematics for Students 72
3. Abstraction 76
4. Definitions 78
5. Problem Solving: Overview 85
6. Well-Posed and Ill-Posed Problems in K-8 Mathematics 89
7. Problems with Hidden Assumptions 93
8. Problems where Psychology Affects the Outcome 94
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