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