CONTENTS

ACKNOWLEDGEMENTS XII

PREFACE XIII

Part I

Chapter 1 Teaching and Learning Math at the

Elementary School Level:

The First Equation 1

Why Math Is Important 1

Teaching and Learning 6

The First Equation 9

Chapter 2 Six Personality Components to

Effective Teaching 13

Caring 13

Passion 15

Patience 16

Alertness 17

Analysis 17

Teaching Procedure 18

Research 19

Chapter 3 Fostering Your Child’s Interest 25

Fostering Interest 25

Fostering Responsibility 27

Responsibility Is the Resource that

Keeps Interest 28

Responsibility Is the Seed of Growing

Enjoyment 29

Fostering Self-Learning Ability 29

Fostering Problem-Solving Ability 31

Chapter 4 Encouraging with the Six Character Traits 35

Encouragement versus Reproach 35

Care and Passion Are the Foundation of

Encouragement 37

Encouragement with Patience 38

Encouragement should be Given at All

Times and in All Circumstances 39

Alertness, Thinking and Research Yield

More Effective Encouragement 41

Chapter 5 The Best Teaching Method: Eliciting

with the Six Character Traits 47

Eliciting versus Repetition

(Inculcation) 48

The Eliciting Method Fosters

Responsibility 52

The Eliciting Method Improves Self-

Learning Abilities 54

Chapter 6 Relationship Links between Teachers,

Parents and Students 61

Support, Understanding and Attention:

three bonds that connect teachers with

students or parents with children 61

Three Dimensions of Education at the

Elementary School Level 61

Understanding and Attention Back

Support To Help Find and Solve

Problems 63

Support, Understanding and Attention

Create a Strong and Close Connection 63

Knowing Your Children 66

Four Academic Bonds that Connect

Teachers and Parents with Children 67

The Problem: Identifying Functions 72

Chapter 7 Three Learning Levels and Another

Equation for Implementing Learning

Processes 75

Perceptual Level 75

Conscious Level 77

The Rational Level 80

The Second Equation 82

Chapter 8 Five Determinants with Five Learning

Steps in the Second Equation 87

Five Determinants 87

Practice 88

Evaluation 89

Example 90

Five Learning Steps in the Second

Equation 91

Chapter 9 Building Positive Attitudes by Fostering

Interest and Responsibility 99

Punishment: The Negative Approach 99

Encouragement: The Positive Approach 101

Punishment versus Reward 103

A Story of Fostering Interest and Encouragement 104

Giving Up versus Persistence 106

Time is the Measure and Treasure of Our Lives 106

The Excuses 107

Options for Those Who Say “I Am Too Busy” 108

Plan for Consistent Educational Time

with Your Children 109

Discipline: A Prerequisite to Persistence 109

Personal Responsibility versus Other’s

Responsibility 111

Discovering Why will Help to Solve the

Problem 112

Healthy Bodies, Good Morals and

Academics 114

Chapter 10 Children’s Learning Process Verses

Adult’s Learning Process 121

Memory and Understanding Differences

between Adults and Children 121

The Different Sequences of General

Learning Steps between Children and Adults 128

The Different Perspectives of Problems

between Adults and Children 134

The Differences in Logical Thinking
between Adults and Children 136

Knowledge Base and Skills 138

Part II

Chapter 11 What’s Missing When Parents Teach Math? 143

Problem 143

Diagnostics 143

Solution 145

Chapter 12 How to Put Fun into Abstract Geometry 153

Problem 153

Diagnostics 155

Solution 158

Chapter 13 Finding the Missing Links in the

Problem Solving Procedure 167

Problem 167

Diagnostics 168

Solution 179

Chapter 14 Finding the Child-learning Methods

that Lead Students to Understand

Problem Solving Strategies 173

Problem 173

Diagnostics 174

Solution 176

Chapter 15 Finding the Child-learning Methods

that Lead Students toward Critical

Thinking 179

Problem 179

Diagnostics 180

Solution 181

Questions to Ask Ourselves 185

Chapter 16 Missing Necessary Practices in

Teaching Multiplication 187

Problem 187

Diagnostics 188

Solution 191

Chapter 17 Teaching with Fun Word Problems 195

Word Problems Help Students

Understand Basic Math concepts 195

Constructing Fun Word Problems 196

Comparing Word Problems, Using

Cartoons and Money 199

The Different Interests of Adults and Children 201

Chapter 18 Essential Calculation Practice For

Lower Grades 203

Practice Makes the Difference 203

Two Stories about How My Daughters

Practice Math 204

Proficiency Generates Skills and

Identifies Short Cuts 209

Proficiency in Calculation Helps

Students Solve Word Problems with Ease 212

Chapter 19 What Should We Do After “Guess

and Check?” 217

“Guess and Check” and Other Methods 217

Example: Listing All the Different Ways

to Add Two Numbers to 10 and Up 219

Three Critical Thinking Problems 221

Chapter 20 The Transition of Math Concepts from

the Primary to Secondary Level 223

Example 1: Finding Consecutive

Numbers 223

Example 2: Counting Tigers 225

Example 3: Traveling Upstream and

Downstream 228

Example 4: How Many Sums Are

There? 231

Example 5: Comparing the Distributive

Properties 233

Example 6: Comparing Common

Factors 234

Example 7: Comparing How to Balance

the Seesaw and Solve the

Equations Using Addition 235

Problems High School Students Face

When Starting Algebra I 235

APPENDIX I Turn Your Child’s Addition and

Subtraction Skills around Quickly

Using a Specially Designed Child-

Sized Abacus I - I

APPENDIX I Introducing Explore the Secrets of Math II -I