The Moore Method: for Undergraduates?

by Jean Joseph

In my daily morning walks, I’ve managed to read R. L. Moore’s biography (R. L.Moore: Mathematician and Teacher by John Parker (MAA)), where I learn about his famous method of instruction: he would give some axioms to his students and assigned them theorems to prove. The students are not allowed to communicate to each other, nor are they allowed to consult any book; they must sweat on the problem until they get something that they can call a solution that they are expected to present in class, where the penalty of not getting the right answer is to listen to another student who has gotten it right. It seems he used this method mostly with his graduate students (I don’t think I’ve read that he used it with his undergraduates although he was known to have a special flair to recruit undergraduates who would become great mathematicians); nevertheless, I think this method could be implemented in undergraduate math classes because it emphasizes problem solving and hard work that, I think, many undergraduates need.

When it comes to presenting the solutions in class, it would give the students an opportunity to perform some mathematics the same way a piano student not only is expected to learn music theory but to also perform for an audience. Nonetheless, it seems there are many challenges that would preclude one to reasonably use this method. For example, many undergraduate math classrooms are overpopulated; it seems even a class of 40 is too big for such an experiment. Also, there is a rigid plan that some instructors have to follow when it comes to what students are expected to learn. Ultimately, (I think it’s probably the most crucial one) many students would probably drop a class that uses such a method because they might realize that they would have to work too hard. Albeit these challenges, I think some aspect of this method could more or less be applied such as assigning challenging problems as extra-credit or have advanced version of some classes where less students are present. As many of us will teach or have already been teaching, do you think such a method would be successful at your institution?

It was serendipitous that I picked this book to read, which I find interesting not just because it explains the Moore method but because it mentions many other anecdoctes (e.g. tensions between mathematicians) that, in some way, draw a picture of the mathematical profession. Next on my list is a biobraphy of Gödel, which, I hope, will be as insightful as Moore’s biography.

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