5 Principles of the Modern Mathematics Classroom: Creating a Culture of Innovative Thinking

Students pursue problems they’re curious about, not problems they’re told to solve.

Creating a math classroom filled with confident problem solvers starts by introducing challenges discovered in the real world, not by presenting a sequence of prescribed problems, says Gerald Aungst. 

In this groundbreaking book, he offers a thoughtful approach for instilling a culture of learning in your classroom through five powerful, yet straightforward principles: Conjecture, Collaboration, Communication, Chaos, and Celebration.

Aungst shows you how to

  • Embrace collaboration and purposeful chaos to help students engage in productive struggle, using non-routine and unsolved problems
  • Put each chapter’s principles into practice through a variety of strategies, activities, and by incorporating technology tools
  • Introduce substantive, lasting cultural changes in your classroom through a manageable, gradual shift in processes and behaviors

Five Principles of the Modern Mathematics Classroom offers new ideas for inspiring math students by building a more engaging and collaborative learning environment.

"Bravo! This book brings a conceptual framework for K-12 mathematics to life. As a parent and as the executive director of Edutopia, I commend Aungst for sharing his 5 principles. This is a perfect blend of inspiring and practical. Highly recommended!"  
Cindy Johanson, Executive Director, Edutopia
George Lucas Educational Foundation


"Aungst ignites the magic of mathematics by reminding us what makes mathematicians so passionate about their subject matter. Grounded in research, his work takes us on a journey into classrooms so that we may take away tips to put into practice today." 
Erin Klein, Teacher, Speaker, and Author of Redesigning Learning Spaces
"1125301425"
5 Principles of the Modern Mathematics Classroom: Creating a Culture of Innovative Thinking

Students pursue problems they’re curious about, not problems they’re told to solve.

Creating a math classroom filled with confident problem solvers starts by introducing challenges discovered in the real world, not by presenting a sequence of prescribed problems, says Gerald Aungst. 

In this groundbreaking book, he offers a thoughtful approach for instilling a culture of learning in your classroom through five powerful, yet straightforward principles: Conjecture, Collaboration, Communication, Chaos, and Celebration.

Aungst shows you how to

  • Embrace collaboration and purposeful chaos to help students engage in productive struggle, using non-routine and unsolved problems
  • Put each chapter’s principles into practice through a variety of strategies, activities, and by incorporating technology tools
  • Introduce substantive, lasting cultural changes in your classroom through a manageable, gradual shift in processes and behaviors

Five Principles of the Modern Mathematics Classroom offers new ideas for inspiring math students by building a more engaging and collaborative learning environment.

"Bravo! This book brings a conceptual framework for K-12 mathematics to life. As a parent and as the executive director of Edutopia, I commend Aungst for sharing his 5 principles. This is a perfect blend of inspiring and practical. Highly recommended!"  
Cindy Johanson, Executive Director, Edutopia
George Lucas Educational Foundation


"Aungst ignites the magic of mathematics by reminding us what makes mathematicians so passionate about their subject matter. Grounded in research, his work takes us on a journey into classrooms so that we may take away tips to put into practice today." 
Erin Klein, Teacher, Speaker, and Author of Redesigning Learning Spaces
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5 Principles of the Modern Mathematics Classroom: Creating a Culture of Innovative Thinking

5 Principles of the Modern Mathematics Classroom: Creating a Culture of Innovative Thinking

by Gerald W. Aungst
5 Principles of the Modern Mathematics Classroom: Creating a Culture of Innovative Thinking

5 Principles of the Modern Mathematics Classroom: Creating a Culture of Innovative Thinking

by Gerald W. Aungst

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Overview

Students pursue problems they’re curious about, not problems they’re told to solve.

Creating a math classroom filled with confident problem solvers starts by introducing challenges discovered in the real world, not by presenting a sequence of prescribed problems, says Gerald Aungst. 

In this groundbreaking book, he offers a thoughtful approach for instilling a culture of learning in your classroom through five powerful, yet straightforward principles: Conjecture, Collaboration, Communication, Chaos, and Celebration.

Aungst shows you how to

  • Embrace collaboration and purposeful chaos to help students engage in productive struggle, using non-routine and unsolved problems
  • Put each chapter’s principles into practice through a variety of strategies, activities, and by incorporating technology tools
  • Introduce substantive, lasting cultural changes in your classroom through a manageable, gradual shift in processes and behaviors

Five Principles of the Modern Mathematics Classroom offers new ideas for inspiring math students by building a more engaging and collaborative learning environment.

"Bravo! This book brings a conceptual framework for K-12 mathematics to life. As a parent and as the executive director of Edutopia, I commend Aungst for sharing his 5 principles. This is a perfect blend of inspiring and practical. Highly recommended!"  
Cindy Johanson, Executive Director, Edutopia
George Lucas Educational Foundation


"Aungst ignites the magic of mathematics by reminding us what makes mathematicians so passionate about their subject matter. Grounded in research, his work takes us on a journey into classrooms so that we may take away tips to put into practice today." 
Erin Klein, Teacher, Speaker, and Author of Redesigning Learning Spaces

Product Details

ISBN-13: 9781506322995
Publisher: SAGE Publications
Publication date: 10/09/2015
Series: Corwin Mathematics Series
Sold by: Barnes & Noble
Format: eBook
Pages: 200
File size: 2 MB

About the Author

Gerald Aungst has nearly 30 years experience as a professional educator, specializing in design thinking, computer science, mathematics, gifted education, and digital technology. In his various roles as a classroom teacher, gifted support specialist, administrator, curriculum designer, and professional developer, he has worked to create a rich and vibrant learning culture. Gerald is a founder of AllAboutExplorers.com and GamifyED.net.

Since 2016, Gerald has served as the gifted support and STEM teacher at Cheltenham Elementary School in the Cheltenham School District, Pennsylvania. He led the development and launch of the school’s makerspace, and worked on the team developing the district’s K-12 computer science curriculum. Gerald is also an adjunct faculty member at Holy Family University in Philadelphia and the University of Iowa.

An experienced speaker, Mr. Aungst gave the keynote address at the 2016 EIRC Gifted and Talented Learning Fair. He was also a member of the keynote panel and a featured presenter at Digital Learning Day 2013. He has presented on a wide range of topics including curiosity, makerspaces, and gamification at many regional and national conferences, including ISTE, Educon, NAGC, PCTM, PETE&C, ITEC, FETC, and Carnegie-Mellon University.

Gerald holds a bachelor’s degree from Penn State University and a master of education degree from Widener University. You can find him on Twitter at @geraldaungst and on the web at www.geraldaungst.com.

 

Table of Contents

Foreword by Mark Barnes
Preface
Acknowledgements
About the Author
Chapter 1. Math for the 21st Century and Beyond
Mathematics as Literacy
Mathematics as an Innovation Incubator
Goals of This Book
What Else to Expect
For PLC and Study Groups
Chapter 2. Classroom Environment: A Medium for Change
Why Classroom Culture?
Depth and Rigor
A Focus on the Practices
The 5 Principles of the Modern Mathematics Classroom
For PLC and Study Groups
Chapter 3. Conjecture
The Power of Mysteries
The Curious Brain
Problem Solving Is a Cycle, Not a Recipe
Grades K–3
Grades 2–5
Grades 4–7
Grades 6–9
Grades 8–12
Technology Integration for Conjecture: Case Studies
For PLC and Study Groups
Chapter 4. Communication
The Mysterious Mathemagical Mind Trick
First and Foremost, Communicate
Six Levels of Mastery
Grades K–3
Grades 2–5
Grades 4–7
Grades 6–9
Grades 8–12
Technology Integration for Communication: Case Study
For PLC and Study Groups
Chapter 5. Collaboration
But, Isn’t That Cheating?
Recognizing, Defining, and Representing Problems
Grades K–3
Grades 2–5
Grades 4–7
Grades 8–12
Grades 6–9
Technology Integration for Collaboration: Case Study
For PLC and Study Groups
Chapter 6. Chaos
Features of Effective Math Instruction
Disorganized Chaos
Productive Struggle
Grades K–3
Grades 2–5
Grades 4–7
Grades 6–9
Grades 8–12
Technology Integration for Chaos: Case Studies
For PLC and Study Groups
Chapter 7. Celebration
Today, We Celebrate
Cautions About Celebration
Grades K–3
Grades 2–5
Grades 4–7
Grades 6–9
Grades 8–12
Digital Tools and Resources for Celebration
Technology Integration for Celebration: Case Study
For PLC and Study Groups
Chapter 8. Becoming a Problem-Solving Classroom
Transformation Is Possible
Self-Assessment
Goal-Setting and Planning
Maintaining Your Momentum
Appendix: Digital Tools
References
Index
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