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.

Table des matières

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

A propos de l'auteur

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.

Résumé

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.

Détails du produit

• Auteurs: Alina Andreescu, Tit Andreescu, Titu Andreescu, Titu Cordeiro Andreescu, Kath Cordeiro, Kathy Cordeiro
• Edition: Wiley, John and Sons Ltd
• Langues: Anglais
• Format d'édition: Livre de poche
• Sortie: 31.12.2019
• EAN: 9781119575733
• ISBN: 978-1-119-57573-3
• Pages: 288
• Catégories: Ecole et pédagogie > Autres; Sciences humaines, art, musique > Pédagogie > Pédagogie, didactique, méthode; Sciences naturelles, médecine, informatique, technique > Mathématiques; Mathematikunterricht, Mathematik, K-12 School, General K-12 School, Mathematics & Statistics/K-12