Teaching Multiplication with Lesson Study

Whether you are an elementary school teacher, a curriculum director, or a college mathematics education professor, this book offers valuable insights about teaching multiplication and about lesson study. Part I of the book focuses on the Japanese approach to understanding the concept of multiplication and how students learn multiplication through lesson study. Part II of the book reports on multiplication in ethnomathematics programs in Latin America.

 

Japanese lesson study has been valued internationally but not always successfully implemented in other countries because “it is a kind of cultural practice”. This book seeks to unlock the mystique and deeply analyzes the teaching of multiplication with lesson study beginning with the concept definitions. It describes various commonly used definitions of multiplication and shows how the preferred Japanese “definition by measurement” provides a foundational idea that can mature with the children whereas other definitions can cause misunderstandings. The book also describes problems that originate from language including inconsistencies of expressions and inconsistencies which occur when mixing natural language and mathematical language. 

 

Japanese children memorize the multiplication tables up to 9 x 9 in second grade as an opportunity to learn how to learn. This focus on students learning mathematics by and for themselves is actually an important component of the lesson study. The objectives have been embedded in the teaching materials in such a sequence that the students are well-prepared for future learning with sense-making. Because of the consistency in terminology, extensions from whole number to fraction and decimal multiplication can be considered by the students themselves based upon what they already understand. 

 

The book offers several exemplars of lesson studies, for example, multidigit multiplication which demonstrates the importance of vocabulary and structured activities so students can consider the ways of calculation by themselves. URL addresses are provided so the reader can see on videos what is described in the text. Subtitles help English speakers to understand what is happening in the Japanese classroom. Chapter 7 includes excerpts from the lesson study group to show how a teacher prepares the lesson materials.

 

Part II of the book seems like an afterthought. The chapters present proposals and reflections by researchers in Ibero-American countries. Ethnomathematics projects using nature and art are discussed as well as classroom research using a “necklace” didactic sequence of the type 1:3 :: x:24. The final chapter reflects on students’ failure to learn multiplication in the Ibero-American countries and supports the Japanese method of careful attention to terminology and lesson study.

 

I highly recommend this book as an excellent resource for those involved with teaching multiplication or teaching elementary teachers. It provides compelling justification for the importance of using proper and consistent terminology, understanding the definitions of multiplication, posing open-ended tasks, and having an insightful questioning strategy.  The illustrations, examples, and web addresses furnish valuable insight into Japanese lesson study. Each chapter ends with a lengthy listing of references for further exploration and the book ends with a helpful index. 

---

 

Mary Beth Rollick is Professor Emerita at Kent State University, in Kent, Ohio. She continues to tutor undergraduate students and enjoys helping them to understand the “why” as well as the “how” of mathematics.