Let me begin this review by stating that I have more than a passing acquaintance with the Moore Method. In the fall of 1989 I was a young and terribly immature first-year graduate student and I signed up for a mathematical logic course taught with the Moore Method. The instructor explained the mechanics of the course on the first day, and then handed out a list of problems and told us to get to work.
In just about every way, the course followed the teaching philosophy outlined by Robert Lee Moore almost a hundred years ago. What is now called the Moore Method is distinguished by the following features: no textbook is used, students cannot look up proofs, students cannot talk to anyone other than the professor about the problems, no group work is allowed, class time consists only of student presentations (no lectures!), and grading is based on those presentations. The only difference between this method and that used in my logic class is that my professor did allow us to talk to each other outside the classroom, but in every other way, it could have been one of Moore’s own classes.
I hated that logic class and it almost ended my mathematical career. I desperately wanted a textbook or other outside source to give me some context for the course, as I spent much of the semester completely baffled about the subject matter and how it fit into the larger world of mathematics. I deeply resented being forced to reinvent the wheel time and again, especially since I suspected that there were far better and more illuminating proofs than the patchwork ones my fellow students and I put on the board. I also resented that our professor (a very capable and affable man, by the way) was simply sitting in the back and saying nothing, especially since I knew that he had decades of experience and wisdom that he refused to share with us. Most of all, I was terrified of being called upon to present a problem when, despite my best efforts, I barely understood the question.
I left that class with (surprisingly) and A and (not surprisingly) a deep and abiding bitterness toward the very name of Robert Lee Moore and all that he stood for. None the less, I enjoyed reading this book “The Moore Method, A Pathway to Learner-Centered Instruction”, and I am sure that there is something here for everyone. To start with, reading this book has caused me to re-evaluate my feelings about the Moore Method and also to recognize that, perhaps unconsciously, I’ve adapted one or two of those same techniques to my own teaching. At its core, the Moore Method is about focusing on the student and allowing him or her to discover mathematics by doing mathematics, and this is a philosophy that to a certain extent, all of us can agree on.
On to the book under review. It begins with a few chapters that introduce the Moore Method and the culture surrounding it, then moves on to specific examples of how it is implemented (in terms of developing materials, grading the students, and so on) and finishes with some research on the effectiveness of the Moore Method, along with a chapter of frequently asked questions and some sample syllabi and course materials. A unique feature of the book is that each co-author contributed his own section to each chapter. With this, the reader can learn how four different modern practitioners of the Moore Method have designed their courses or adjusted the rules or implemented the grading scheme to fit their own teaching styles and philosophies.
For the reader who is thinking of teaching a Moore Method course in the future, there is a wealth of material here, and even for those with no such plans there are some tips and techniques they will find quite useful. My personal favorite comes from Mahavier, who didn’t want students' note-taking to interfere with their engagement in the classroom yet also didn’t want students to go home empty-handed. He now takes a digital photo of the chalkboard after a student presentation and posts it on the web immediately after class, thus giving the other students a perfect record of the proof and allowing them (during class) to focus on the mathematics rather than trying to copy everything down.
Another nice technique comes from May, who recommends keeping a daily journal of what transpired in each class—which student presented, which ones gave insightful comments, and which ones need more attention. I can only imagine how valuable this diary is when asked to write a letter of recommendation a year or two later.
The book also contains a great deal of evidence (both anecdotal and from research) as to the effectiveness of the Moore Method, and I can see how this would be helpful for those not yet sure about implementing the method in their own classroom. It also serves as a reinforcement for those already using the Moore Method. However, I find it a bit disquieting that a book which finds room for such quotes as “Keith Devlin labels Moore as ‘The Greatest Math Teacher Ever’” and “The Moore Method is the best-known and arguably the most successful way to train students to become creative research mathematicians” does not once, in over 200 pages, mention that Moore himself refused to allow some students into his class (in particular blacks and women) and also walked out of a lecture once he learned the speaker was black. No one who refuses to teach a student based on the color of his skin can be called “a great math teacher”, and while this fact does not disqualify his teaching method, it does lend some perspective.
This aside, for those interested in participatory teaching, there is much to be found in this book. While it hasn’t managed to convert me, it has inspired me to try out some new techniques in the classroom, and hopefully it can do the same for you.
Greg Dresden is Associate Professor of Mathematics at Washington and Lee University.