Going through some old papers, I came across a summary of student feedback from Relations & Functions, a course I team-taught at Lincoln-Sudbury (L–S). This was more-or-less equivalent to today’s Honors Precalculus, and it’s instructive to consider the similarities and differences. The title was more informative then (I’ve always hated the word precalculus, as it tells you nothing at all about the course; all it tells you is what the next course is), and the content has changed only slightly over 46 years, as you would expect. Emphases on trig, vectors, transformations, analytic geometry, and limits all remain. We no longer do matrices or 3-D analytic geometry, but now we include iteration and fractals, which couldn’t really have been in the curriculum in 1972. A very noticeable difference is the schedule: that year the L–S course met four times a week for only 35 minutes a day! In our feedback only ten students out of 51 recognized that 35 minutes was too short.
Because of the excessively short blocks, we ended up doing too much lecturing. Although a majority of the students liked that emphasis, we didn’t; we remarked that “we don’t want to train sponges — we want kids to be doing mathematics.”
You may be wondering who ”we” are. As I suggested in the first sentence above, I team-taught the course with a colleague, Phil Lewis; officially each of us was assigned a single section, but we made sure that we were each free during the time the other section met, so we were able to teach both sections together every day.
Here’s another similarity and difference: When asked about the pace of the course, out of 51 students 1 found if “a little too slow,” 26 OK, and 24 “sometimes too fast.” Nobody found it “much too fast” or “much too slow.” Those numbers are very close to today’s in terms of percentages, and they still seem appropriate to me. But the big difference is in the actual numbers. At L–S in 1972 we had 51 juniors in honors math out of a junior class of 400; at Weston in 2017 we had approximately 95 juniors in honors math out of a junior class of 190. You can do the math. Roughly twice the number in honors out of a population half the size. Does this tell you something about the communities or something about the decade? Or both?
A few of my favorite comments from the open-response part of the student questionnaire:
- Make the class smaller.
- The course should be called Functions & Other Relations, not Relations & Functions.
- It was too hard to follow sometimes — while one teacher caught his breath, the other taught, and vice versa — it was very easy just to sit back and watch the show.
- I really like the whole Math Department. It’s the best department in the school, mostly because of the teachers.
- The course provided a new perspective on mathematical problems.
- All math teachers are generally friendly and helpful.