5 Principles of the Modern Mathematics Classroom

Creating a Culture of Innovative Thinking
Gerald W. Aungst - School District of Cheltenham Township; Elkins Park, PA
5 Principles of the Modern Mathematics Classroom
October 2015 | 200 pages | Corwin
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ISBN: 9781506301624
Available from January 0001
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ISBN: 9781483391427
Available from January 0001

Description

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

Take a look at Gerald describe why you need this book!

Contents

Foreword by Mark Barnes

Foreword by Mark Barnes

Preface

Preface

Acknowledgements

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

Appendix: Digital Tools

References

References

Index

Index

Additional materials

Description

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

Take a look at Gerald describe why you need this book!

Contents

Foreword by Mark Barnes

Foreword by Mark Barnes

Preface

Preface

Acknowledgements

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

Appendix: Digital Tools

References

References

Index

Index

Additional materials

SAGE Publishing Logo

5 Principles of the Modern Mathematics Classroom

Creating a Culture of Innovative Thinking


October 2015 | 200 pages | Corwin

Format Published Date ISBN Price
Paperback 01/02/2026 9781483391427 $37.95
Lifetime 01/02/2026 9781506301624 $35.00

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

Take a look at Gerald describe why you need this book!


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

Recent Product Reviews:

"One of the major strengths is that the book is written in teacher friendly language and that it gives practical examples. This content is much needed for today’s teachers who are either stuck in a traditional way of teaching OR wanting to change and are looking for ideas . . . I would definitely purchase this book and would strongly consider it as a supplementary, recommended text for classes I teach as an adjunct faculty member."
Barbara Fox, Adjunct Faculty, Lesley University, University of Boston, Regis College
"This book is great for our educational world right now. There have been many who are talking about the changes in our math classrooms to help promote more problem solving and not just answering questions. This is a great start for teachers to begin to make changes in their classrooms for students to become great problem solvers . . . I would purchase this book for the math team to have them begin the discussions of helping students become problem solvers."
Anthony Purcell, 6th Grade Math Teacher, Longfellow Middle School
"This book is practical and forward thinking. It should be required reading for undergraduate college math methods classes."
Christine Ruder, 3rd Grade Teacher, Truman Elementary School
"I absolutely recommend publication! Elementary teachers are overwhelmed with how to teach multi-step problems to young children. Knowing they (the teachers) don’t have to be the Know-All of the class, but to allow the students the opportunity to think, possibly fail, repeat, provides the teacher time to watch the students and help direct their learning.”
Lyneille Meza, Coordinator of Data & Assessment, Denton ISD
"Math is an area in which critical thinking skills are vital. This book will assist educators in encouraging students to think critically when dealing with math problems. Learning to incorporate the 5C’s into the math classroom is sure to enhance both teaching and learning! . . . I would purchase this book. We always welcome material that will enhance our students’ ability to learn and develop critical thinking skills! (And even have some “fun” while learning!!!)"
Susan E. Schipper, First Grade Teacher, Charles Street School

Recommendations