What Makes a Good Mathematics Lesson (The Theory)

Have you ever wondered What Makes a Good Mathematics Lesson?
For many years, this has been a topic of conversation between American mathematics educators Douglas Corey and Blake Peterson, and their Japanese colleagues Hiroyuki Ninomiya, Kazuhiko Soma, and Susumu Kunimune. This conversation led these Japanese mathematics educators to articulate “key considerations” that should be addressed when preparing a good mathematics lesson and the “criteria” that can be used as guidelines when reflecting on the quality of a lesson after it has been taught.

The three considerations are:
Make the Goal of the Lesson Clear
Thoughtfully Decide on the Problem and its Presentation
Plan Ways to Incorporate Students’ Ideas

And the questions corresponding to the criteria are:

Were Students Proactively Engaged and Did They Continue to Think for Themselves?
Were the Objectives Appropriately Set and Achieved?

In this book What Makes a Good Mathematics Lesson: The Theory, the Japanese authors discuss the conceptual underpinning of the three key considerations and two criteria. This book also includes an introductory chapter written by the American mathematics educators contextualizing Japanese mathematics education for an English-speaking audience.

In What Makes a Good Mathematics Lesson: The Lessons, 27 Japanese middle school teachers describe lessons in which they implemented the key considerations and two criteria. At the end of The Lessons, four US teachers each describe their adaptation of one of these 27 lessons in their classroom and contextualize the key considerations and criteria for their respective situations.