Awesome Math: Teaching Mathematics with Problem Based Learning

✍ Scribed by Titu Andreescu, Kathy Cordeiro, Alina Andreescu

• Publisher: Jossey-Bass
• Year: 2019
• Tongue: English
• Leaves: 290
• Category: Library

✦ Synopsis

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

Cover
Title Page
Contents
Acknowledgments
About the Authors
Introduction
Section I Why Problem Solving?
Chapter 1 Rewards for Problem-Based Approach: Range, Rigor, and Resilience
Range Ignites Curiosity
Rigor Taps Critical Thinking
Resilience Is Born Through Creativity
Chapter 2 Maximize Learning: Relevance, Authenticity, and Usefulness
Student Relevance
Mathematical Relevance
Mathematical Relevance: The Math Circle Example
Curriculum Relevance
Authenticity: The Cargo Cult Science Trap
Authenticity in Learning
Usefulness
Chapter 3 Creating a Math Learning Environment
Know Yourself: Ego and Grace
Know Your Students
Know Your Approach
Chapter 4 What Is the Telos?
Autonomy to Solve Your Problems
Mastery Through Inquiry
Purpose with Competitions
Quadrants of Success
Chapter 5 Gains and Pains with a Problem-Based Curriculum
Teachers
Students
Parents
Section II Teaching Problem Solving
Chapter 6 Five Steps to Problem-Based Learning
Start with Meaningful Problems
Utilize Teacher Resources
Provide an Active Learning Environment
Understand the Value of Mistakes
Recognize That Everyone Is Good at Math
Chapter 7 The Three Cs: Competitions, Collaboration, Community
Competitions
Collaboration
Community
Aspire to Inspire: Stories from Awesome Educators
Chapter 8 Mini-Units
Relate/Reflect/Revise Questions
Roman Numeral Problems
Cryptarithmetic
Squaring Numbers: Mental Mathematics
The Number of Elements of a Finite Set
Magic Squares
Toothpicks Math
Pick’s Theorem
Equilateral versus Equiangular
Math and Chess
Area and Volume of a Sphere
Section III Full Units
Chapter 9 Angles and Triangles
Learning Objectives
Definitions
Angles and Parallel Lines
Summary
Chapter 10 Consecutive Numbers
Learning Objectives
Definitions
Chapter 11 Factorials!
Learning Objectives
Definitions
Chapter 12 Triangular Numbers
Learning Objectives
Definitions
Chapter 13 Polygonal Numbers
Learning Objectives
Definitions
Chapter 14 Pythagorean Theorem Revisited
Learning Objectives
Definitions
Pythagorean Theorem
Rectangular Boxes
Euler Bricks
Assessment Problems
Chapter 15 Sequences
Learning Objectives
Definitions
Introduce a Geometric Progression
Chapter 16 Pigeonhole Principle
Learning Objectives
Definitions
Chapter 17 Viviani’s Theorems
Learning Objectives
Definition
Chapter 18 Dissection Time
Learning Objectives
Definitions
Chapter 19 Pascal’s Triangle
Learning Objective
Summary
Chapter 20 Nice Numbers
Learning Objectives
Definitions
Index
EULA