## Table of Contents

Preface

Acknowledgments

About the Author

Quick Reference Guide

**UNIT 1 What Does It Mean to “Do,” “Teach,” and “Learn” Mathematics?**

**■ CHAPTER 1** Mathematics as a Process

National and International Assessment Data

Trends in Mathematics and Science Study (TIMSS)

Program for International Student Assessment (PISA)

National Assessment of Educational Progress (NAEP)

**How Would You React?**

The Need for Reform

21^{st} Century Skills

“Doing” Mathematics

Problem Solving

Mathematical Reasoning

**Spotlight on Technology**

Communication

Connections and Structure

Representation

**Classroom Dialogues**

Conclusion

Glossary

Discussion Questions and Activities

**Links and Resources**

**■ 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

**Links and Resources**

**■ 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

Behaviorist Theory

Zone of Proximal Development

Communities of Practice

Multiple Intelligences

Mindsets

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

Ego Versus Mastery Goals

Emotions – Interest and Curiosity

Self-Confidence (Self-Efficacy)

Disposition and Math Anxiety

Conclusion

Glossary

Discussion Questions and Activities

**Links and Resources**

**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

Tracking

Reasons Why Schools Choose (or Reject) an Integrated Curriculum

**Spotlight on Technology**

Goals and Objectives in the Mathematics Classroom

Classifying Objectives

Affective Objectives

Cognitive Objectives

Knowledge and Skill

Concept

Application

Selection and Organization of Resources

Textbooks

Print Resources

**Classroom Dialogues**

Organizing a Resource File

Conclusion

Glossary

Discussion Questions and Activities

**Links and Resources**

**■ CHAPTER 5 **Planning for Instruction

Unit Planning

**How Would You React?**

Lesson Planning

General Information

Standards and Objectives

Materials and Resources

Motivation

Lesson Procedure

Closure

Extension

Assessment

**Spotlight on Technology**

Sample Lesson Plans

Analysis of Sample Lesson Plan 1

Analysis of Sample Lesson Plan 2

**Classroom Dialogues**

Lesson Imaging versus Lesson Planning

Reflecting on a Lesson

Conclusion

Glossary

Discussion Questions and Activities

**Links and Resources**

**UNIT 3 Assessment in Mathematics**

**■ CHAPTER 6** Assessment: Purposes and Strategies

What Is Assessment?

Purposes for Assessment

Test Construction

Preparing Items

Ensuring Validity and Reliability

Scoring Student Work

**How Would You React?**

Including Review Items

Limitations to Written Tests

Alternate Strategies for Assessing Student Progress

Journals

Open-Ended Questions and Rubrics

**Spotlight on Technology**

Individual and Team Projects

Observations and Checklists

Interviews

Self-Assessment

**Classroom Dialogues**

Portfolios

Conclusion

Glossary

Discussion Questions and Activities

**Links and Resources**

**■ CHAPTER 7 **Assessment: Standards, Homework, and Grading

NCTM Recommendations on Assessment

The Assessment Standards

**How Would You React?**

The Assessment Principle

Equity and Assessment

Homework Assignments

Homework Amount and Frequency

Checking Homework Assignments

**Spotlight on Technology**

Using Homework Assignments in Assessment

Data-Driven Decision Making

**Classroom Dialogues**

Evaluation: Maintaining and Determining Final Grades

Conclusion

Glossary

Discussion Questions and Activities

**Links and Resources**

**UNIT 4 Mathematics Teaching**

**■ CHAPTER 8 **Teaching and Learning: Tasks, Learning

Environment, and Discourse

Teaching Standards and Related Principles

The NCTM Standards for Teaching and Learning Mathematics

Knowledge Standards

The Teaching and Learning Principle

Selecting Activities and Problems

**How Would You React?**

Learning Environment

**Spotlight on Technology**

Classroom Discourse

The Role of Discourse

Questioning Skills

Reading and Literacy

**Classroom Dialogues**

Cooperative Learning

Structures of Cooperative Learning

Reflective Practices

Conclusion

Glossary

Discussion Questions and Activities

**Links and Resources**

**■ CHAPTER 9** Teaching and Learning: Tools and Technology

**How Would You React?**

Classroom Tools

Hands-on Manipulative Materials

**Spotlight on Technology**

Diagrams, Graphs, and Other Discussion Starters

Classroom Technology

Calculators

CAS Technology

Interactive Whiteboards

Mobile Devices

**Classroom Dialogues**

Dynamic Geometry Software

Document Cameras

Blended Classes and Flipped Classrooms

Conclusion

Glossary

Discussion Questions and Activities

**Links and Resources**

**■ CHAPTER 10 **Teaching Number Sense and Algebra

Reasoning and Sense Making

**How Would You React?**

The Teaching of Number Sense

Sample Lesson Plan: Number Sense

Number Sense—Activities Sampler

**Spotlight on Technology**

The Teaching of Algebra

Sample Lesson Plan: Algebra

**Classroom Dialogues**

Algebra—Activities Sampler

Conclusion

Glossary

Discussion Questions and Activities

**Links and Resources**

**■** **CHAPTER 11 **Teaching Geometry, Statistics/Probability,

and Discrete Mathematics

The Teaching of Geometry

Sample Lesson Plan: Geometry

**How Would You React?**

Geometry—Activities Sampler

**Spotlight on Technology**

The Teaching of Statistics and Probability

Sample Lesson Plan: Statistics and Probability

Statistics and Probability—Activities Sampler

The Teaching of Discrete Mathematics

Sample Lesson Plan: Discrete Mathematics

**Classroom Dialogues**

Discrete Mathematics—Activities Sampler

A Word on Pre-Calculus and Calculus

Conclusion

Glossary

Discussion Questions and Activities

**Links and Resources**

**UNIT 5 Meeting Individual Student and Teacher Needs**

**■ CHAPTER 12** Managing a Mathematics Classroom

Defining and Achieving Equity

Students with Special Needs

**How Would You React?**

Gender

**Spotlight on Technology**

Ethnic and Cultural Issues

English Language Learners

**Classroom Dialogues**

Ideas for Meeting Diverse Student Needs

Differentiated Instruction

General Suggestions for Differentiating in the Classroom

Classroom Management Tips

Conclusion

Glossary

Discussion Questions and Activities

**Links and Resources**

**■ CHAPTER 13** The Teacher of Mathematics in the School Community

Working with Parents

**Hints for Helping Your Child in Mathematics**

**How Would You React?**

The Supervision and Evaluation of Teachers

**Spotlight on Technology**

Functioning in a Department

Ongoing Professional Development

Making the Case for Long-Term Development

**Classroom Dialogues**

Opportunities for Professional Development

The Professional Development Plan

Conclusion

Discussion Questions and Activities

**Links and Resources**

Bibliography

Index