Awesome Math: Teaching Mathematics with Problem Based Learning

ISBN-13: 9781119575733 / Angielski / Miękka / 2019 / 288 str.

Alina Andreescu

Spis treści

Acknowledgments xiAbout the Authors xiiiIntroduction xviiI. Why Problem Solving?Chapter 1: Rewards for Problem-Based Approach: Range, Rigor, and Resilience 5Range Ignites Curiosity 5Rigor Taps Critical Thinking 9Resilience is Born Through Creativity 10Chapter 2: Maximize Learning: Relevance, Authenticity, and Usefulness 13Student Relevance 13Mathematical Relevance 14Mathematical Relevance: The Math Circle Example 16Curriculum Relevance 18Authenticity: The Cargo Cult Science Trap 21Authenticity in Learning 22Usefulness 25Chapter 3: Creating a Math Learning Environment 27Know Yourself: Ego and Grace 27Know Your Students 30Know Your Approach 35Chapter 4: What is the Telos? 47Autonomy to Solve Your Problems 47Mastery Through Inquiry 48Purpose with Competitions 50Quadrants of Success 52Chapter 5: Gains and Pains with a Problem-Based Curriculum 57Teachers 58Students 61Parents 67II. Teaching Problem SolvingChapter 6: Five Steps to Problem-Based Learning 75Start with Meaningful Problems 75Utilize Teacher Resources 79Provide an Active Learning Environment 91Understand the Value of Mistakes 97Recognize That Everyone is Good at Math 99Chapter 7: The Three Cs: Competitions, Collaboration, Community 103Competitions 103Collaboration 107Community 117Aspire to Inspire: Stories from Awesome Educators 121Chapter 8: Mini-Units 147Relate/Reflect/Revise Questions 147Roman Numeral Problems 148Cryptarithmetic 151Squaring Numbers: Mental Mathematics 155The Number of Elements of a Finite Set 157Magic Squares 159Toothpicks Math 163Pick's Theorem 165Equilateral versus Equiangular 168Math and Chess 170Area and Volume of a Sphere 172III. Full UnitsChapter 9: Angles and Triangles 177Learning Objectives 177Definitions 177Angles and Parallel Lines 177Summary 180Chapter 10: Consecutive Numbers 185Learning Objectives 185Definitions 185Chapter 11: Factorials! 191Learning Objectives 191Definitions 191Chapter 12: Triangular Numbers 199Learning Objectives 199Definitions 199Chapter 13: Polygonal Numbers 205Learning Objectives 205Definitions 205Chapter 14: Pythagorean Theorem Revisited 213Learning Objectives 213Definitions 213Pythagorean Theorem 214Rectangular Boxes 214Euler Bricks 216Assessment Problems 219Chapter 15: Sequences 221Learning Objectives 221Definitions 221Introduce a Geometric Progression 222Chapter 16: Pigeonhole Principle 227Learning Objectives 227Definitions 227Chapter 17: Viviani's Theorems 235Learning Objectives 235Definition 235Chapter 18: Dissection Time 239Learning Objectives 239Definitions 239Chapter 19: Pascal's Triangle 245Learning Objective 245Summary 249Chapter 20: Nice Numbers 255Learning Objectives 255Definitions 255Index 259

O autorze

Dr. Titu Andreescu is an Associate Professor at the University of Texas at Dallas in the Science and Mathematics Education department. As a mathematics educator and leader, he has developed math camps, competitions, and curricula that have received international attention. Titu was a long-time head coach of Team USA participating in the International Math Olympiad. He is cofounder of AwesomeMath, a premiere mathematics camp held across the United States.Kathy Cordeiro, MBA, is a leading developer of education initiatives for business and academia. She founded Eudaimonia Academy, where she coached mathematics teams and worked with highly and profoundly gifted students. Other roles include facilitator for the Metroplex Math Circle as well as Director of Marketing and Communications for AwesomeMath, where she was able to work with the finest mathematical minds from across the globe. She continues to speak about maximizing mathematics education for parents, schools, and gifted organizations.Alina Andreescu, MA, is the co-founder and Operations Director of AwesomeMath and founder of XYZ Press. She fosters an international community of staff, students, and instructors that values critical thinking, creativity, passionate problem solving, and lifetime mathematical learning.