In the fall, I am teaching one undergraduate and one graduate course, and in planning these courses I have been thinking about alternatives to the "standard math class". I have found it much easier to find different models for undergraduate classes than for the graduate classes.
There are many blogs and other online resources focusing in large part on math pedagogy, often taking "nonstandard" approaches to the math course (Moore method, inquiry based learning, flipped or inverted classroom, Eric Mazur's "Peer instruction",...). For instance, Robert Talbert's blog discusses the practicalities of the "flipped" classroom, and here Dave Richeson discusses teaching undergraduate topology using the modified Moore method. Note that although Moore originally used his method in a graduate topology course, most discussions of it and its adaptations are at the undergraduate level.
Of course, the basic principles of the methods would still apply at the graduate level, but I still find myself wanting to see specific examples of different approaches people have used to teach a graduate course.
Are there similar discussions of teaching a nonstandard math course at the graduate level? Or at least links to syllabi, course webpages, etc. for such courses?
First, it is of course hard to pin down exactly what is meant by "standard math class"; for the purposes of this question, let us highlight the following:
- In class meetings, the vast majority of time is spent with the professor lecturing.
- Nearly all the assessment is done via problem sets and quizzes/exams.
- The textbook runs in parallel to the class lectures. Although lip-service my be made to reading it, there is little structural dependence on it, except perhaps as a source of problems: lectures do not depend on students having read the book, and problems are not asked on material not presented in lecture
Second, though descriptions of the form "I once took a course where..." could be interesting, It would be particularly valuable to have links to course webpages with syllabuses/etc. describing in more practical detail what happened, or discussions from the actual professors doing the teaching about what they did, their reasoning behind it, how it went it practice, etc., as opposed to just a collection of anecdotes.
Finally, though what I have discussed above tend to be rather drastic changes from the "standard math class", of course things run on a continuum, and smaller deviations are possible. For example, I have taken graduate courses where student presentations of selected material played a role, and where a part of the grade was given to an expository paper. But in the courses I took these were usually rather minor deviations from the standard structure. Examples of similar smaller variations would be valuable if they were particularly well documented, or had explanations of why these variations were particularly important and not just window dressing.