Awesome Math: Teaching Mathematics with Problem Based Learning (Paperback)

Acknowledgments

About the Authors

Introduction

Section I: Why Problem Solving?

Chapter 1: Rewards for Problem-Based Approach: Range, Rigor, and Resilience

Range Ignites Curiosity

Rigor Taps Critical Thinking

Resilience is Born through Creativity

Chapter 2: Maximize Learning: Relevance, Authenticity, and Usefulness

Student Relevance

Mathematical Relevance

Mathematical Relevance: The Math Circle Example

Curriculum Relevance

Authenticity: The Cargo Cult Science Trap

Authenticity in Learning

Usefulness

Chapter 3: Creating a Math Learning Environment

Know Yourself: Ego and Grace

Know Your Students

Know Your Approach

Chapter 4: What is the Telos?

Autonomy to Solve your Problems

Mastery through Inquiry

Purpose with Competitions

Quadrants of Success

Chapter 5: Gains and Pains with a Problem-Based Curriculum

Teachers

Students

Parents

Section II: Teaching Problem Solving

Chapter 6: Five Steps to Problem-Based Learning

Start with Meaningful Problems

Teacher Resources

Active Learning Environment

The Value of Mistakes

Everyone is Good at Math

Chapter 7: The Three C’s: Competitions, Collaboration, Community

Competitions

Collaboration

Community

Chapter 8: Mini-Units

Relate/Reflect/Revise Questions

Roman Numeral Problems

Cryptarithmetic

Squaring Numbers: Mental Mathematics

The Number of Elements of a Finite Set

Magic Squares

Toothpicks Math

Pick's Theorem

Equilateral vs Equiangular

Math and Chess

Area and Volume of a Sphere

Section III: Full Units

Angles and Triangles

Consecutive Numbers

Factorials!

Triangular Numbers

Polygonal Numbers

Pythagorean Theorem Revisited

Sequences

Pigeonhole Principle

Viviani's Theorems

Dissection Time

Rectangular Boxes and Euler Bricks

Important Facts about Pascal's Triangle

Nice Numbers