Help your students to think critically and creatively through team-based problem solving instead of focusing on testing and outcomes.
Professionals throughout the education system are recognizing that standardized testing is holding students back. Schools tend to view children as outcomes rather than as individuals who require guidance on thinking critically and creatively. Awesome Math focuses on team-based problem solving to teach discrete mathematics, a subject essential for success in the STEM careers of the future. Built on the increasingly popular growth mindset, this timely book emphasizes a problem-solving approach for developing the skills necessary to think critically, creatively, and collaboratively.
In its current form, math education is a series of exercises: straightforward problems with easily-obtained answers. Problem solving, however, involves multiple creative approaches to solving meaningful and interesting problems. The authors, co-founders of the multi-layered educational organization AwesomeMath, have developed an innovative approach to teaching mathematics that will enable educators to:
- Move their students beyond the calculus trap to study the areas of mathematics most of them will need in the modern world
- Show students how problem solving will help them achieve their educational and career goals and form lifelong communities of support and collaboration
- Encourage and reinforce curiosity, critical thinking, and creativity in their students
- Get students into the growth mindset, coach math teams, and make math fun again
- Create lesson plans built on problem based learning and identify and develop educational resources in their schools
Awesome Math: Teaching Mathematics with Problem Based Learning is a must-have resource for general education teachers and math specialists in grades 6 to 12, and resource specialists, special education teachers, elementary educators, and other primary education professionals.
Table of Contents
Acknowledgments xi
About the Authors xiii
Introduction xvii
I. Why Problem Solving?
Chapter 1: Rewards for Problem-Based Approach: Range, Rigor, and Resilience 5
Range Ignites Curiosity 5
Rigor Taps Critical Thinking 9
Resilience is Born Through Creativity 10
Chapter 2: Maximize Learning: Relevance, Authenticity, and Usefulness 13
Student Relevance 13
Mathematical Relevance 14
Mathematical Relevance: The Math Circle Example 16
Curriculum Relevance 18
Authenticity: The Cargo Cult Science Trap 21
Authenticity in Learning 22
Usefulness 25
Chapter 3: Creating a Math Learning Environment 27
Know Yourself: Ego and Grace 27
Know Your Students 30
Know Your Approach 35
Chapter 4: What is the Telos? 47
Autonomy to Solve Your Problems 47
Mastery Through Inquiry 48
Purpose with Competitions 50
Quadrants of Success 52
Chapter 5: Gains and Pains with a Problem-Based Curriculum 57
Teachers 58
Students 61
Parents 67
II. Teaching Problem Solving
Chapter 6: Five Steps to Problem-Based Learning 75
Start with Meaningful Problems 75
Utilize Teacher Resources 79
Provide an Active Learning Environment 91
Understand the Value of Mistakes 97
Recognize That Everyone is Good at Math 99
Chapter 7: The Three Cs: Competitions, Collaboration, Community 103
Competitions 103
Collaboration 107
Community 117
Aspire to Inspire: Stories from Awesome Educators 121
Chapter 8: Mini-Units 147
Relate/Reflect/Revise Questions 147
Roman Numeral Problems 148
Cryptarithmetic 151
Squaring Numbers: Mental Mathematics 155
The Number of Elements of a Finite Set 157
Magic Squares 159
Toothpicks Math 163
Pick’s Theorem 165
Equilateral versus Equiangular 168
Math and Chess 170
Area and Volume of a Sphere 172
III. Full Units
Chapter 9: Angles and Triangles 177
Learning Objectives 177
Definitions 177
Angles and Parallel Lines 177
Summary 180
Chapter 10: Consecutive Numbers 185
Learning Objectives 185
Definitions 185
Chapter 11: Factorials! 191
Learning Objectives 191
Definitions 191
Chapter 12: Triangular Numbers 199
Learning Objectives 199
Definitions 199
Chapter 13: Polygonal Numbers 205
Learning Objectives 205
Definitions 205
Chapter 14: Pythagorean Theorem Revisited 213
Learning Objectives 213
Definitions 213
Pythagorean Theorem 214
Rectangular Boxes 214
Euler Bricks 216
Assessment Problems 219
Chapter 15: Sequences 221
Learning Objectives 221
Definitions 221
Introduce a Geometric Progression 222
Chapter 16: Pigeonhole Principle 227
Learning Objectives 227
Definitions 227
Chapter 17: Viviani’s Theorems 235
Learning Objectives 235
Definition 235
Chapter 18: Dissection Time 239
Learning Objectives 239
Definitions 239
Chapter 19: Pascal’s Triangle 245
Learning Objective 245
Summary 249
Chapter 20: Nice Numbers 255
Learning Objectives 255
Definitions 255
Index 259
