Awesome Math : Teaching Mathematics with Problem Based Learning

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. Cover 1 Title Page 5 Contents 9 Acknowledgments 13 About the Authors 15 Introduction 19 Section I Why Problem Solving? 23 Chapter 1 Rewards for Problem-Based Approach: Range, Rigor, and Resilience 27 Range Ignites Curiosity 27 Rigor Taps Critical Thinking 31 Resilience Is Born Through Creativity 32 Chapter 2 Maximize Learning: Relevance, Authenticity, and Usefulness 35 Student Relevance 35 Mathematical Relevance 36 Mathematical Relevance: The Math Circle Example 38 Curriculum Relevance 40 Authenticity: The Cargo Cult Science Trap 43 Authenticity in Learning 44 Usefulness 47 Chapter 3 Creating a Math Learning Environment 49 Know Yourself: Ego and Grace 49 Know Your Students 52 Know Your Approach 57 Chapter 4 What Is the Telos? 69 Autonomy to Solve Your Problems 69 Mastery Through Inquiry 70 Purpose with Competitions 72 Quadrants of Success 74 Chapter 5 Gains and Pains with a Problem-Based Curriculum 79 Teachers 80 Students 83 Parents 89 Section II Teaching Problem Solving 95 Chapter 6 Five Steps to Problem-Based Learning 97 Start with Meaningful Problems 97 Utilize Teacher Resources 101 Provide an Active Learning Environment 113 Understand the Value of Mistakes 119 Recognize That Everyone Is Good at Math 121 Chapter 7 The Three Cs: Competitions, Collaboration, Community 125 Competitions 125 Collaboration 129 Community 139 Aspire to Inspire: Stories from Awesome Educators 143 Chapter 8 Mini-Units 169 Relate/Reflect/Revise Questions 169 Roman Numeral Problems 170 Cryptarithmetic 173 Squaring Numbers: Mental Mathematics 177 The Number of Elements of a Finite Set 179 Magic Squares 181 Toothpicks Math 185 Pick’s Theorem 187 Equilateral versus Equiangular 190 Math and Chess 192 Area and Volume of a Sphere 194 Section III Full Units 197 Chapter 9 Angles and Triangles 199 Learning Objectives 199 Definitions 199 Angles and Parallel Lines 199 Summary 202 Chapter 10 Consecutive Numbers 207 Learning Objectives 207 Definitions 207 Chapter 11 Factorials! 213 Learning Objectives 213 Definitions 213 Chapter 12 Triangular Numbers 221 Learning Objectives 221 Definitions 221 Chapter 13 Polygonal Numbers 227 Learning Objectives 227 Definitions 227 Chapter 14 Pythagorean Theorem Revisited 235 Learning Objectives 235 Definitions 235 Pythagorean Theorem 236 Rectangular Boxes 236 Euler Bricks 238 Assessment Problems 241 Chapter 15 Sequences 243 Learning Objectives 243 Definitions 243 Introduce a Geometric Progression 244 Chapter 16 Pigeonhole Principle 249 Learning Objectives 249 Definitions 249 Chapter 17 Viviani’s Theorems 257 Learning Objectives 257 Definition 257 Chapter 18 Dissection Time 261 Learning Objectives 261 Definitions 261 Chapter 19 Pascal’s Triangle 267 Learning Objective 267 Summary 271 Chapter 20 Nice Numbers 277 Learning Objectives 277 Definitions 277 Index 281 EULA 290 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: (1) Move their students beyond the "calculus trap" to study the areas of mathematics most of them will need in the modern world; (2) Show students how problem solving will help them achieve their educational and career goals and form lifelong communities of support and collaboration; (3) Encourage and reinforce curiosity, critical thinking, and creativity in their students; (4) Get students into the growth mindset, coach math teams, and make math fun again; and (5) 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 "Awesome Math builds on the popular growth mindset by focusing on team-based problem solving. Applying a problem-solving approach to the education process develops the skills necessary to think critically, creatively, and collaboratively. This book will help teachers and educators form lifelong communities for their students that will expose them to the collaborators they can network with in the future. Students need to move beyond the calculus trap and study the areas of mathematics most of them will need in the modern world and problem solving is an efficient vehicle to get them where they need to go. The book will cover: curiosity; critical thinking, and creativity; getting into the mathemize mindset; coaching mathletes and thinkers; math as a team sport; developing a community through problem solving; creating lesson plans; identifying and developing resources"-- Provided by publisher