For the last few years, we have been hearing about the importance of incorporating writing into our mathematics classes. It sounds like a good idea. For most of us, however, this suggestion is a daunting prospect, raising far more questions than we feel prepared to deal with adequately. What assignments? How will we grade them? How will we defend the grading of them? Do we provide enough models of good writing for our students to follow in the ways we teach and grade?
Having already committed myself to experimenting with writing assignments this term, I was pleased to find Writing in the Teaching and Learning of Mathematics just before the term began. I opened the book looking for practical advice. Happily, I was rewarded. John Meier and Tom Rishel set out primarily to answer these basic questions from their own personal experiences, and to provide guidance for "teachers who are interested in using writing assignments in their classes but who don't have extensive experience with writing assignments"(p. ix).
The book is divided into four chapters: First Steps, Listening to Others, Major Projects, and Narrating Mathematics. The section on First Steps contains the practical advice one needs in order to begin the task of introducing writing into the class, offering concrete examples of small assignments and a discussion of grading. Also extremely helpful are a discussion of not-so-good writing assignments, and some tips on ways to salvage these less than perfect assignments.
The section Listening to Others contains one piece of advice that I immediately put into practice: make the intended audience clear to the students. Upon reflection, it is easy to see that over the years students have learned to assume that clarity is not of the utmost importance since the professor already knows how they arrived at the answer. Left to my own devices, however, I might not have made this realization until after grading the first batch of papers. In general, this chapter contains advice gleaned from faculty more versed in writing than the typical mathematician.
A discussion of how to assign and mentor major projects follows in the next section. There are several examples of such projects, and some glimpses of the mentoring process. Also included is a discussion of presenting major projects in class. I will surely reread this chapter before undertaking such an adventure; it seems to make several very worthwhile points.
Narrating Mathematics is the last section of this book. It includes the authors' rationale for incorporating writing into their classes. By way of illustration, it also includes the written response of one calculus student to the statement "Prove that cubic polynomials can have no more than two maxima or minima." Along with the original response, the comments of the professor, the re-response of the student and the iterations of this process are included. Not only does this showcase what students are capable of doing, it also provides the instructor, about to embark on this process, with a tangible model.
The strongest aspect of the book, for this reader, is the use of concrete examples of assignments. Scattered throughout the book are both small questions and larger projects. While the majority of the exercises pertain to the calculus sequence and geometry, there are several examples from other courses, and several generic assignments. Throughout the book there are also exercises in the form of discussion questions for the reader. These serve to focus the reader on points which need further reflection.
And there will be points which need further reflection. In fact, Meier and Rishel consider "faculty who have used writing but would like to further reflect on their methodology" (p. ix) as a second audience for this book. If indeed you have been using writing assignments in class, but haven't stopped to evaluate your pedagogy, then you would profit by perusing this book.
Writing in the Teaching and Learning of Mathematics is a wonderful, concise book which, for this reviewer, has accomplished its goal of providing guidance in the endeavor to incorporate writing into class. Although I would have liked more discussion on grading and on the particulars of revising assignments, reading this book was time well-spent. I encourage any instructor who is giving some thought to including writing assignments in class to find a copy of this book and read it.