Details

Awesome Math

Teaching Mathematics with Problem Based Learning
1. Aufl.

von: Titu Andreescu, Kathy Cordeiro, Alina Andreescu
16,99 €
Verlag:	Wiley
Format:	PDF
Veröffentl.:	13.11.2019
ISBN/EAN:	9781119575719
Sprache:	englisch
Anzahl Seiten:	288

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Beschreibungen

Titelbeschreibung

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: <ul> <li>Move their students beyond the calculus trap to study the areas of mathematics most of them will need in the modern world</li> <li>Show students how problem solving will help them achieve their educational and career goals and form lifelong communities of support and collaboration</li> <li>Encourage and reinforce curiosity, critical thinking, and creativity in their students</li> <li>Get students into the growth mindset, coach math teams, and make math fun again</li> <li>Create lesson plans built on problem based learning and identify and develop educational resources in their schools</li> </ul> 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.

Inhaltsverzeichnis

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

Autorenportrait

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.

Back cover copy

INSPIRE AND GUIDE STUDENTS TOWARD TRUE MATH MASTERY FOR TODAY'S WORLD "This book is a brilliant road map that delights in its own theorem of authenticity and relevance. Full of the philosophical groundwork, expert insights, and plenty of practice problems, Awesome Math: Teaching Mathematics with Problem Based Learning is a must read for any Math or STEM educator concerned with the relevance and joy of a beautiful and expansive discipline." —Ben Koch, Co-founder and CEO, Numinds Enrichment "Awesome Math makes a strong case for ditching rote memorization and turning to collaborative problem-solving and mastery-based learning instead. This book is a must-read for parents and educators in all subject areas who wish to develop their students' creative and critical thinking skills." —Jaime Smith, Founder and CEO of OnlineG3.com "Awesome Math emphasizes the importance of collaborative problem solving in a classroom setting, featuring interesting and carefully chosen concepts and problems that can be used in a regular classroom and enrichment academic mathematics programs such as math circles or summer camps." —Zvezdelina Stankova, Teaching Professor of Mathematics at the University of California, Berkeley "This inclusive book speaks in voices of the many. It has the irresistible flow of a well-curated social feed. There are shiny treasures to repost, 'today-I-learned' surprises to ponder, wise checklists to save, heartfelt polemics to debate — and so many kind math friends to meet!" —Dr. Maria Droujkova, Founding Director of Natural Math