Invitation to Didactique offers a glimpse into a field of research that has been ongoing in France for the past few decades. The concept of Didactique stems from the research of Guy Brousseau and the classroom work of his wife, who has been a primary level school-teacher in France for several years. The term Didactique, as developed by Brousseau, is not easily defined in a sentence, not even in a paragraph. Hence the decision of Warfield to write this short volume.
The majority of Brousseau’ s research seems to have been focused at the primary school level. His work centers on the use of classroom activities to help students gain understanding of specific mathematical concepts. This does include the construction of new activities for classroom teachers, but that is not the goal of Brousseau’s research. His main focus is on the way a particular activity affects the students and the teacher. He is interested in answering, among others, the following questions. What demands do students place on the teacher during an activity? What demands does the teacher place on the students? Are there separate explicit and implicit demands? How do these demands affect progress through an activity? How does progress through a particular activity affect student acquisition of the desired mathematical concept?
The opening pages of this short book are a difficult read. After a short description of a classroom situation that provides a brief glimpse of what didactique is about and an interesting history of Brousseau’s research, the rest of the first chapter left this reader wondering if there is any insight to be gained by reading the book. I found myself feeling lost in some of the language and terminology. Somewhere before the end of chapter one, I determined to choose one of three paths. I could press forward in the text without fully understanding what I was reading, I could give up on reading the book, or I could begin rereading chapter one while looking up terminology as needed until I felt that I had absorbed the material.
I presume that Warfield has written the book for those, such as myself, who are not familiar with many of the concepts or much of the language surrounding Didactique. With this in mind, I determined to continue to read chapter 2 although I felt uncomfortable with some of the insights that Warfield had intended chapter 1 to provide. My plan was to read as far as I could, see if the material would eventually reveal itself in the writing, and stop to reread if at any point I felt that I was totally lost.
Fortunately, the readability quickly improves. Chapters 2 through 4 provide four specific examples of didactique. Each example yields specific insight into Brousseau’s development of the concept of didactique and what he refers to as the didactique contract.
I found the last 60 pages to be a quick and pleasant read. I developed an interest in pursuing potential research that might be applicable within the United States educational system, but based on Brousseau’s work. Although the latter pages of chapter one had been difficult to read and left me unsure of what I might gain from the book, those pages were necessary and provided an important base from which to draw when the examples were presented. I did not need to reread much, but I did refer back to these pages as needed while reading through the examples.
I believe that the latter half of chapter one could have been written in a manner more accessible for a novice to Didactique. However, the reader who is willing to press through this section will be rewarded. I hope that the work of Brousseau and Warfield will gain a following in the United States.
If you are interested in research concerning how educators can induce a student to acquire a piece of mathematical knowledge, then this book is a must read. It will provide you with an introduction to a long history of related research from France. It also provides a reference list for those who want to investigate this research area beyond an introduction.
Stephen Lancaster is Assistant Professor of Mathematics at California State University Fullerton.