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

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.

 

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*

"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*

"This book is practical and forward thinking. It should be required reading for undergraduate college math methods classes."
*Christine Ruder, 3rd Grade Teacher*

"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*

"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*

"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*

"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*

"5 Principles of the Modern Mathematics Classroom is an easy-to-read and use book that provides educators with practical strategies and solutions to immediately incorporate into their mathematics classrooms. The design of the book provides classroom teachers an opportunity for deep reflection of their current mathematics instructional practices to ensure that they are creating students who are mathematical thinkers and problem solvers. 5 Principles of the Modern Mathematics Classroom offers teachers strategies to allow their students to wonder freely, work collaboratively with their peers, communicate efficiently, and participate in experimentation and celebration. Using technology as a way to incorporate the principles of a modern mathematics classroom is briefly explored with short explanations of specific tools for each principle. Overall, Aungst has provided his readers with a five principle framework that when incorporated into a classroom, will transform students into mathematicians."
*Stephanie Schwab, STEM Program Administrator*

"What does it take to be an excellent teacher? With so many ideas about teaching floating about, it is necessary to capture the essential components and package them for careful consideration. While perspectives for what it actually takes to ensure all students flourish are manifold, it is certain that the aspiring teacher must be constantly reflecting on her practice and expanding her awareness of productive beliefs and actions. To this end, Gerald Aungst has developed a guide ideal for any teacher hoping to find the sweet spot between theory and practice that can easily translate to the classroom.    Capturing a very complex and hopeful view the nature of a classroom that promotes the success of all students, Gerald Aungst presents illustrations, research, and classroom activities. Simple and engaging, the stories and resources inspire the reader to delve into an entirely unplanned investigation of a new ideas at every turn. The 5 Principles of the Modern Mathematics Classroom are engaging, perplexing, and ripe for exploration and discussion. I′d recommend the read for any teacher looking to better understand what being an excellent teacher means through the lens of the classroom culture and for any PLC looking for a head start in casting a vision for a strong mathematics culture in their school."
*Levi Patrick, Director of Secondary Mathematics Education at the Oklahoma State Department of Education*

"In 5 Principles of the Modern Mathematics Classroom: Creating a Culture of Innovative Thinking, Gerald Aungst comprehensively describes the characteristics of an environment for mathematical learning which integrates the math practice standards and actively involves students in higher level, inquiry-based thinking.  Aungst’s book holds value for the beginning teacher, who will find a multitude of resources and ideas for establishing an effective mathematics classroom, and for the seasoned teacher, who will be challenged to reflect on her own practice and incorporate the five principles into her math instruction. Coaches and other instructional leaders will find the book well-suited for book study or PLC discussion, with contemplative questions at the conclusion of each chapter. Gerald Aungst’s 5 Principles provides a framework for propelling math learning forward in the twenty-first century."
*Louise Kirsh, Math Coach, North Penn School District*

"Math is linear... Math is neat and tidy... Math is about getting the right answer... Not in this book! Gerald has done an awesome job of showing us what math learning can look like in a way that embraces the messy inquiry and problem-solving that accompanies real world math. Put this book to work and watch your students be amazing!"
*Scott McLeod, J.D., Ph.D., Director of Innovation, Prairie Lakes Area Education Agency, and Founding Director, UCEA Center for the Advanced Study of Technology Leadership in Education*

"Mathematical thinking critically impacts a learner′s capability to process the world around her. The typical math instruction actually degrades a child′s capability to see math in the world and to find delight in the messy construction of analytical, critical and creative processes through mathematical thinking. In 5 Principles of the Modern Math Classroom, Gerald Aungst provides a learning path for teachers that leads them to think together and to practice math instruction that makes math real. And that′s what great math teachers do – at any age."
*Pam Moran, Superintendent*

"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 W. Gardiner, Ed.D, Director of STEM Education*

"Gerald masterfully reminds us that math education must be more than a "recipe" and challenges us to aid our students in thinking like mathematicians. With practical advice and inspiration, you’ll again find the beauty in math and be empowered to reveal it for your students. Regardless of the age you teach, this book offers a fantastic breakdown of the role of conjecture, collaboration, communication, chaos, and celebration play in transforming your classroom into one where students engage free-range thinking every day."
*Kelly Tenkely, Architect of Learning, Founder and Administrator*

"Take a good, hard look at your teaching practices! If your math classroom resembles your childhood classroom, then you need to invite Gerald Aungst to the party. His 5 practices will help you transform your teaching so you can develop the critical thinkers of tomorrow. Gone are the days when mathematics instruction was focused solely on procedures. As Gerald describes so astutely in terms of music, we must train our students to be ready to work through unique problems just as we train music students to sight read. Gerald provides sound research and examples from all grade levels, including websites and apps for incorporating technology. He addresses the pressures of state tests and the long-term benefits of an actively-engaged classroom. He supports the premise that ALL students can learn math. Gerald guides you along with reflective questions and suggestions for how to begin. This book is an inspirational must-read, and includes insightful questions for use in a book study. Put it on your reading list and begin the journey."
*Mary Palladino, Math Coach*

"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*

"Gerald Aungst reframes mathematical thinking for the reader, giving space for teachers to go beyond the usual airtight methods for math pedagogy." 
*Jose Luis Vilson, Educator and Author of This Is Not A Test*