*A confession and example of a teaching transformation.*

A Confession: As much as I talk about teaching and ideas about ‘good’ teaching both here and with colleagues, I don’t really practice what I preach as much as I could or should. I’d say I’m a good teacher, but in the very traditional sense, i.e. in a way that my colleagues and students would recognize as good teaching. After teaching for many years (30!) I realized that I could keep refining my technique but that it wouldn’t really increase the impact I had on student learning. So I tried to figure out what I could change, and that lead me back to the very beginning, and here’s a result:

An Example: For Fall 2010 I was assigned to teach a new course, a course for current high school and community college faculty that wanted or needed graduate work in mathematics. The topic was Analysis, a.k.a. Calculus. From what I knew of the course and what I had learned in my search for changes to my teaching, I realized that this course was both a good place to try these new things and a course that really required a new approach to teaching.

First point: If you ever get the chance to teach teachers, do it. If you give them the respect they deserve, they are the most understanding, accepting, and encouraging students to teach. Most of my students worked all day and then took time to spend 3 hours of their evening learning about math, *because they wanted to.*

Second point: This course transformation I’m about to describe, breaks all the rules that I usually give to someone interested in changing his or her teaching. (1) I had never taught the course, nor anything like it, before, (2) I changed everything that I had ever done in teaching rather than just a part, and (3) all I really only had a small set of good ideas that I had never tried, to go on.

Details: The main idea was that the students were going to do all the work, including choosing what work to do. The only parts I set were that they had to document it all online and that they had to ‘make sense’ of Calculus as a whole. And I told them so, a little bit at a time. I didn’t answer any question that I could avoid answering.I didn’t evaluate their work, but made them evaluate it themselves. I did teach some to the whole group, as needed, on topics usually prompted by student questions or my or student interests. Most of the teaching was done one to one or with small groups.

Results: It was the best course ever. Between the students and the way the class ran, it was the most enjoyable teaching I had ever done. For the final evaluation (i.e. grades), I had each student review and reflect on the body of work they had done. The work the students had done was very diverse, each organized according to the students needs and interests. The reflections showed appropriately deep learning, greater understanding, new insights, and many other wonderful things. Sure, some students were frustrated by the course structure, and some may have done less than they could have, but I would again risk that to see the kind of growth and excitement that the course encouraged in most of the students.

Conclusion: I believe, as I wrote a couple of days ago, that development as a teacher requires not just incremental improvements, but an occasional review of the foundation. This experience, where I risked disaster while trying to create true and deep learning, only confirms this belief, and encourages me (and hopefully you, the reader) to reflect, plan some core changes, and then take the plunge.

Good luck and good teaching!