Succeeding at teaching mathematics, K-6

Acknowledgments

About the Authors

Introduction

How the Book Is Organized

1. A Glimpse at Mathematics Instruction

Two Illustrations

Vignette 1. Second Grade-Subtraction With Regrouping

Discussion

Vignette 2. Fourth Grade-Developing the Concept of Fractions

Discussion

Success in Teaching Mathematics

Summary

2. Standards-Based Teaching

Why Do We Need Standards for Teaching Mathematics?

The National Council of Teachers of Mathematics Principles and Standards

Principles

Content and Process Standards

The Five Content Standards

The Five Process Standards

State and District Standards for Teaching Mathematics

The Relationship Between Standards and Standards-Based Mathematics Textbooks

NCTM Curriculum Focal Points

Examples of Standards-Based Activities Involving Algebraic Thinking

Overview of Lessons

Kindergarten: Day and Night

First and Second Grades: Bigger and Bigger Blocks

Third Through Sixth Grades: Time for a Party

NCTM Standards Addressed

Content Standards

Process Standards

Summary

3. Engaging Students in Learning Mathematics

What Is Engagement?

Engaging Learners in the Affective Domain

Vignette 1. Third Grade Multiplication-Around the World

Vignette 2. Fifth Grade-Math Jeopardy

A Description of Glasser's Five Basic Needs

Vignette 3. Increasing a Student's Confidence in Mathematics

A Fresh Look at Around the World and Math Jeopardy

Affective Issues Related to Teaching and Learning Mathematics

Attitudes Toward Learning Mathematics

Getting to Know Your Students

Students Engaged in Learning Probability

Vignette 4. Fifth Grade Probability-Socializing by Spinners

Revisiting the Affective Domain

Engaging Learners in the Behavioral Domain

Engaging Learners in the Cognitive Domain

Multiple Representations

Problem Solving

The Mangoes Problem

Summary

4. Engagement Strategies for Special Populations

The Special Needs Learner

Know Your Learner

Create a Positive Classroom Culture

Increase Opportunities for Communication and Participation

Differentiate Instructional Strategies

The Gifted Learner

Know Your Learner

Create a Positive Classroom Culture

Increase Opportunities for Communication and Participation

Differentiate Instructional Strategies

Possible Pitfalls

The English Language Learner

Know Your Learner

Create a Positive Classroom Culture

Increase Opportunities for Communication and Participation

Differentiate Instructional Strategies

Example of Engaging Learners in a Mathematics Classroom

Tessellations and Geometry

Discussion

Summary

5. Assessment

Developing Assessments: The Use of Backward Design

Stages of Backward Design

Stage 1. Identify Desired Results

Stage 2. Determine Acceptable Evidence

Stage 3. Plan Learning Experiences

Types of Assessment

Unit Tests and Quizzes

Open-Middled and Open-Ended Questions

Projects

Portfolios

Journals

Observation and Questioning

Rubrics

Grading and Assessment Schemes

Practical Ways of Assessing Throughout the Instructional Process

Tailoring Assessments for Special Populations

Data-Driven Instructional Practices

A Word About Standardized Tests

Summary

6. Putting It All Together

The Year at a Glance: Designing Your Curriculum

Making Connections Within Mathematics

The Perfect Party Place

Making Connections Across the Curriculum

Mathematics in Language Arts

Vignette 1. Second Grade-Multiplication

Mathematics Within Science

Mathematics Within Art

Mathematics Within the Social Sciences

Creating Thematic Lessons

Mathematical Connections Across Grades

Vignette 2. Fourth and Fifth Grade Collaboration

Succeeding at Teaching Mathematics-and Loving It!

Appendix A. Communicating With Families

Appendix B. Mathematics and Literature Connections

Appendix C. Growing as a Professional

References

Index