Teaching Secondary and Middle School Mathematics

Contents

Preface

Acknowledgements

Meet the Author

UniT 1 What Does It Mean to "Do," "Teach," and "Learn" Mathematics?

Chapter 1 Mathematics as a Process

National and International Assessment Data　　　　

How Would You React?

The Need for Reform　　　

"Doing" Mathematics　　　

Problem Solving　　　　

Mathematical Reasoning　

Spotlight on Technology

Communication　　　

Connections　and Structure

Representation　

Classroom Dialogues

Conclusion

Glossary

Discussion Questions and Activities

Chapter 2 Principles of Mathematics Education

The Six Principles　　

Teaching and Learning

How Would You React?

Access and Equity

Curriculum

Tools and Technology

Spotlight on Technology

Assessment　　　　

Professionalism

Classroom Dialogues

Connecting the Principles　　

Conclusion

Glossary

Discussion Questions and Activities

Chapter 3 Learning Theories and Psychology in Mathematics Education

Research in Mathematics Education　　

Quantitative and Qualitative Methods　　

How Would You React?

Experimental and Descriptive Research　　

Learning Theories in Mathematics　

Development of Learning Theory　

Bruner’s Stages of Representation　　

The van Hiele Model　

The Inquiry Approach and Constructivist Model　　　

Spotlight on Technology

Inductive versus Deductive Teaching　　

Classroom Dialogues

Motivation

Conclusion

Glossary　　

Discussion Questions and Activities

Unit 2 Mathematics Curriculum AND PLanning

Chapter 4 Standards, Objectives, and Resources

Developing Curriculum Standards – Historical Perspective

How Would You React?

The Common Core State Standards for Mathematics

The Core Curriculum

Traditional versus Integrated Sequences　　

Spotlight on Technology

Goals and Objectives in the Mathematics Classroom

Classifying Objectives

Affective Objectives

Cognitive Objectives

Selection and Organization of Resources

Print Resources

Classroom Dialogues

The Internet

Organizing a Resource File

Conclusion

Glossary