Visible Thinking in the K-8 Mathematics Classroom

by Ted H. Hull

• ISBN13: 9781412992053
• ISBN10: 1412992052
• Format: Paperback
• Copyright: 2011-01-21
• Publisher: Corwin Pr

Summary

The key to students' success in math lies in a way of teaching that provides clear evidence of how students are thinking about problems and builds on that thinking to take them to a deeper level of understanding. Seasoned math educators Ted Hull, Don Balka, and Ruth Harbin Miles offer teachers a sequential and developmental plan for integrating visual thinking into current classroom practices, and gradually, but steadily, initiating successful instructional changes in mathematics. Their new book provides teachers with numerous sample problems and classroom scenarios, showing successful teacher interventions at work, and offers guidance on how teachers can adapt traditional problems to promote visible thinking in their own classrooms.

Table of Contents

Preface

Acknowledgments

About the Authors

Preparing the Foundation

What Is Visible Thinking?

Understanding Mathematical Concepts

Thinking as a Mathematical Premise

Visible Thinking in Classrooms

Area and Perimeter

Summary

How Do Students Learn Mathematics?

What Is Thinking?

What Does Brain Research Indicate about Thinking and Learning?

What is Mathematical Learning?

What Are Thinking and Learning Themes from Research?

Example Problems Revisited

Addition of Fractions

Summary

What Is Happening to Thinking in Mathematics Classrooms?

Improvement Initiatives and Visible Thinking

Subtraction with Regrouping

Summary

Promoting Visible Thinking with an Alternative Instructional Model

How Do Effective Classrooms Depend on Visible Thinking?

What Are Strategies, Conditions, and Actions?

Practice into Action

Technology as Visible Thinking

Division

Summary

How Are Long-Term Changes Made?

Broad Goals of Enhancing Student Learning

Teaching Approaches

Mixed Numerals

Place Value

Summary

How Are Short-Term Changes Made?

Pitfalls and Traps

Strategy Sequence

The Relationship Among the Strategy Sequence, Conditions, and Goals

Basic Addition and Subtraction Facts

Exponents

Summary

How Are Lessons Designed to Achieve Short-Term and Long-Term Changes?

The Current Approach to Teaching Mathematics

Elements of an Alternative Instructional Model

Types of Problems

Summary

Implementing the Alternative Model at Different Grade Levels

How Is Thinking Made Visible in Grades K - 2 Mathematics?

Brainteaser Problem Example

Group-worthy Problem Example

Transforming Problem Example

Summary

How Is Thinking Made Visible Grades 3 - 5 Mathematics?

Brainteaser Problem Example

Group-worthy Problem Example

Transforming Problem Example

Summary

How Is Thinking Made Visible in Grades 6 - 8 Mathematics?

Brainteaser Problem Example

Group-worthy Problem Example

Transforming Problem Example

Summary

Continuing the Work

How Do Teachers, Leaders, and Administrators Coordinate Their Efforts to Improve Mathematics Teaching and Learning?

Working with Administrators

Embedding Lessons into the Curriculum

Providing Professional Development

Co-planning and Co-teaching

Summary

Appendix

References

Index

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