I had the opportunity over the last month to work with some math teachers at JD Smith Middle School. This sort of fell on my lap at the last minute, but it seemed like a good chance for me to try something new and expand my perspective on education in the region.
During the past few weeks, I visited classrooms and made observations of the individual teachers. I then compiled a short list of topics that I felt were relevant to department as a whole, and then presented my findings to them. I also wrote up a short summary of my thoughts on the individual teachers.
My first point was about the careful use of spoken and written mathematics in the classroom. The teachers were using "solve" as a universal instruction for "do what you're supposed to do." This is fine when the students already know what to do, but the ones who don't know get confused because this one word means many different things in different contexts. I suggested to them that there is a clear distinction between solve, compute, simplify, and other word they might use in the future like factor, reduce, expand, and so forth.
The second topic was to look at arithmetic. Arithmetic is really an exercise in bookkeeping, not anything deep or profound (except the fact that we *can* do bookkeeping, which is truly deep and profound). So I talked about doing addition as "big-to-small" instead of "small-to-big" and explained why it works better once students understand the basics of the place value system.
The third topics was more exploratory, which was the topic of fractions. This is probably the most difficult topic because of the breadth of pictures we use to discuss them. Unfortunately, these pictures are not all compatible with each other. This leads to students being confused because they think about the same picture in different ways. I didn't have a lot to say in this area, but opened the door for them to discuss it among themselves. I hope they are able to go somewhere with it.
Overall, I think it is a net positive given the amount of time spent with them. I intentionally stayed away from pedagogy specific ideas because I'm not a pedagogist. I'm just a pure mathematician, but I think this is a helpful type of "outsider" perspective for them. I'm done with that project for now, but I left the door open to come back and talk to them about a different topic if they choose to invite me back.
