Coming This Fall

Now Available!

5 Principles of the Modern Mathematics Classroom: Creating a Culture of Innovative Thinking. Order now directly from Corwin. Also available on Kindle from Amazon.

Everyone can be a "Math Person"

Mathematics instruction is frequently conducted under a false assumption: that mathematics is a fixed, linear sequence of skills. This leaves out what makes mathematicians pursue their subject with passion and drive: the mystery and magic of math. This book will help every teacher, from Kindergarten to high school, bring that magic back into the classroom. By learning and applying five simple principles, you can inspire students, teach them how to think like innovators, and make them believe they are all “math people.” The 5 Principles let you build a classroom culture that emphasizes the most important part of any mathematics curriculum: the processes, practices, and habits of mind. In order to embrace the magic, the classroom must be a place where problem solving happens daily and is deeply embedded in its culture. This book will enable you to make that a reality.

Bravo! 5 Principles of the Modern Mathematics Classroom brings a conceptual framework for K‑12 mathematics to life. As a parent of a struggling math student and as the executive director of Edutopia, a source for what works in education, I commend Gerald Aungst for sharing his five principles of the modern mathematics classroom. This book 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 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 Aungst is as innovative as he is refreshing in his approach to mathematics instruction. The strategies he describes will make an average teacher excellent and an excellent teacher outstanding. The examples in this book can be used immediately in 1‑on‑1 conversations with teachers, small group professional development, or large group workshops. Each chapter resonates with his approach to the modern mathematics classroom. This book is an excellent resource for every teacher who teaches mathematics. 
Sean Gardiner, Ed.D.

Director of STEM Education, Upper Merion Area School District

The 5 Principles


In a traditional mathematics classroom, the primary goal is for students to get the right answers to questions and exercises. In a classroom where conjecture is encouraged, students ask most of the questions, and the answer to a question is very often another question. 


In a traditional classroom, communication is primarily one way: the teacher explaining a procedure or algorithm to students. In a problem-​​​oriented classroom, students must learn to communicate frequently about problems and how they solve them. 


In a traditional classroom, students work alone, and the emphasis is on an individual’s skill fluency. Problem solving classrooms are all about the “we”.


Though this sounds sketchy, it is simply encapsulating the idea that real math work is messy. In a traditional classroom, neatness and order rule the day. Real problems, on the other hand, require experimentation, false starts, mistakes, and corrections, sometimes over and over again. 


In a traditional classroom, recognition is given for right answers and high grades. In a problem-​​​solving culture, anything that leads towards a solution is celebrated: finding one small step of a complicated problem, thinking of an innovative approach even if it doesn’t pan out, or even making a spectacular mistake and asking for help. 

Supporting the Principles with Digital Tech

Digital tools can support and enhance all five of the Principles. For a list of the tools found in the book, visit the 5CMath Digital Tools page.