In my last post, I reported on Avery Pickford's exciting presentation at the Asilomar conference. The idea of student-created problems was thought-provoking — here are some thoughts it provoked.
I have no doubt that pursuing student-created problems is worthwhile, but a skeptic may not be convinced by the argument that we should do this because it is what mathematicians do. Only an infinitesimal fraction of the students we teach will become mathematicians. A larger number will use mathematics, and of course, they will use it better if they have a deeper understanding. But it would be useful and interesting to articulate what habits of mind are supported by this, and how they transfer to life outside of math and its applications. That would help sell this idea to students, to fellow teachers, and to parents. (Of course, just doing it is the best selling point!)
Doing this routinely almost certainly makes it more difficult to "cover" specific topics, as student initiative may take the class far from what was intended by the teacher. This becomes more of a concern at the high school level, given the massive content we are expected to teach. I am not arguing against a problem-solving approach, as there are lots of ways for the teacher to select the right problem to introduce or apply a given topic. I'm just saying that I find it difficult to visualize a high school class working on student-created problems much of the time and still staying on track content-wise. (Avery has been doing this with 5th and 6th graders, I believe. I used to teach at that level, and I felt like I had a lot more freedom there than I did in high school.)
A further challenge is that if there are different sections of a class, what they end up doing is likely to diverge. This problem is more manageable if it is the same teacher for all the sections, as he or she can manipulate things as needed. Again, this is does not take anything away from the value of this sort of approach, but it does complicate its implementation. Like anything worthwhile, it takes some time and some teacher energy to figure out how to use it. Certainly more of this can be done in electives and singleton classes. That is certainly what I observed at my school.
A year or two ago, we had a discussion in our department about giving students one opportunity each term to pursue work of their own choosing. The idea was that this would happen outside of class, as an at-home assignment which would give us a different window into the student's thinking and likewise, it would help the students to self-assess. Unfortunately, we never followed up on this idea. Part of it was probably because of our lack of clarity on how to set this up. Also we probably would need a rubric to clarify our expectations, and that itself would be a bit of work. Being nearly retired, I won't get to try this, but it does seem like combining that plan with some of Avery's ideas would probably yield something workable. Sticking to this for a few years would help that practice take root, and would end up influencing department and school culture.
More on the workshops I attended at Asilomar in my next post!