Table of Contents


Foreword
 by Steven Leinwand

Introduction

Chapter 1 Algebraic Habits of Mind

What are Mathematical Habits of Mind?

Algebraic Habits of Mind

Conclusion

Chapter 2 Mental Mathematics Is More Than Mental Arithmetic

Slow Learners and Struggling Students

Arithmetic, Mathematics, and Executive Functions

Why Use These Exercises in High School?

Designing and Using Mental Mathematics Exercises

Conclusion

Chapter 3 Solving and Building Puzzles

What Makes a Puzzle a Puzzle?

Why Do People Invent Puzzles, Do Them, and Like Them?

Who Am I? Puzzles

Mobiles and Mystery Number Puzzles

Latin Square-Based Puzzles

Teaching with Puzzles

Conclusion

Chapter 4 Extended Investigations for Students

Experience Before Formality: Try It Yourself

Principles: What Makes a Good Investigation?

Aspects of Investigation: Entering, Shaping, and Extending Investigations

Teaching Through Investigation

Conclusion

Chapter 5 A Geometric Look at Algebra

The Number Line: Numbers as Locations and Distances

Area as a Model for Multiplication, Division, and Factoring

Conclusion

Chapter 6 Thinking Out Loud

Benefits of Discussion in the Classroom

Teaching Students How to Discuss

When Discussions Falter

Models of Mathematical Discussions

Conclusion

References