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5 Principles of the Modern Mathematics Classroom

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

  • Gerald Aungst - School District of Cheltenham Township; Elkins Park, PA

Foreword by Mark Barnes

October 2015 | 200 pages | Corwin

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!

Foreword by Mark Barnes
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


Goal-Setting and Planning

Maintaining Your Momentum

Appendix: Digital Tools

"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

"In this book, Gerald Aungst expertly weaves math & literacy to promote a culture of thoughtful inquiry, problem-solving, and innovative thinking. He consistently demonstrates deep respect for the topic, the teachers, and the students, carefully interspersing stories, strategies, questions, tips, and tools in just right places throughout each chapter to maximize understanding using a gradual release of responsibility model. My eyes are forever opened to an instructional world where math and literacy not only coexist – but work in concert to elevate our instructional power potential!"

Dr. Mary Howard, Author

“A dynamic read for math educators K-12, Aungst challenges the status quo and many traditional methods of classroom instruction that are still prevalent in many of our nation’s classrooms. In doing so, he makes a case for the vitality of a student-centered, rich classroom culture, filled with collaboration, problem-solving, rigorous curriculum, and high-quality communication, while celebrating student success at every turn. Moving from theory to practice, and providing a myriad of concrete methods and examples, 5 Principals of the Modern Mathematics Classroom is a must-have tool for every math teacher’s professional toolbox!”

Thomas C. Murray, State and District Digital Learning Director
Alliance for Excellent Education, Washington, DC

"Aungst ignites the magic of mathematics for his readers through five beautifully articulated guiding principles. Reminding us of what makes mathematicians so passionate about their subject matter, Gerald not only grounds his work in research but also takes us on a journey into several classrooms in each vignette so that we may take away actual, practical tips to put into practice today."

Erin Klein, Teacher, Speaker, and Author of Redesigning Learning Spaces

"Gerald has written a book about math instruction and learning, but the strategies can easily trickle to other disciplines in school.  He not only shares great ideas about how we can create meaningful learning opportunities and environments for students, he clearly articulates why this is important.  As someone who is not a math teacher, I found what Gerald wrote to be applicable to much of the work that I am doing in all areas, and really felt that the environment of math learning that he shared is much better than the one I experienced as a student."

George Couros, Innovative Teaching, Learning, and Leadership Consultant

"This is the book that teachers have been waiting for - evidence-based practices that are easy to implement. Aungst walks us through simple ways to change our mindset about math, encourage students to embrace mathematical challenges and integrate technology in our daily practices. So many ideas for every grade level!"

Annie Beninghof, Teacher, Speaker, and Author
Key features
  • Introduces a way to teach math that will inspire students and which is in line with the Common Core State Standards for Math.
  • Filled with practical tips for teachers that will infuse the magic of math into the culture of the classroom.
  • Offers guidance to teachers so that they can nurture students into becoming confident and life-long problem solvers.
  • Includes classroom routines and techniques that teachers can implement to support the five principles: Conjecture, Communication, Collaboration, Chaos, and Celebration.
  • Includes real classroom vignettes to illustrate the routines
  • Each chapter highlights how digital technology can be utilized to facilitate the learning and teaching of math
  • Each chapter will provide specific strategies targeted to five grade bands: K-3, 2-5, 4-7, 6-9, 8-12, ensuring that teachers at all levels will find useful tools and strategies for their students.
  • Provides guidance for assessing the current state of a given classroom culture, designing a plan for implementing the framework, and for creating the support system which will enable teachers to sustain the changes they want to see in their classrooms.

Sample Materials & Chapters

The 5 Principles

Chapter 3 Excerpt

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ISBN: 9781506301624

ISBN: 9781483391427

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