Unnecessarily difficult

A few years ago, one of my former students from Honors Precalculus informed me that my course had been “unnecessarily difficult.” An interesting phrase. “What does that mean?” was my puzzled response. Let’s call her Rachel (not her real name).

It turned out that Rachel interpreted the name of the course rather too literally; she saw no reason for us to do anything more than the bare minimum to prepare her for calculus. This was AB Calculus, of course; she wasn’t interested in all the parts of my course that would have prepared her for BC Calculus had she chosen to take it. So I explained that to Rachel, but I also pointed out that every math class has many goals, only one of which is the need to prepare students for the next course in sequence. What else did she get out of precalculus? (I thought she might say “a B minus”…but in fact she just shrugged and repeated her criticism.)

This all made me wonder yet again about the value of feedback from students. I learned something about Rachel, but I learned almost nothing that I could use in rethinking the course. (Actually, I did learn something useful: I realized that I should be more explicit about the goals of the course when talking to students.) Nevertheless, when it came time recently to give questionnaires to students, I of course complied with this requirement as did all Weston teachers. (Question to my current students: They all did, didn’t they?) We were allowed to develop our own questionnaires, and we could share as much or as little of the results as we felt appropriate. I chose to share all the results, both with my students and with my department head, and I’ll present a few interesting excerpts here.

First, as I have already mentioned Honors Precalculus, let’s see what I learned from the 43 students who responded (that’s a 100% return from both sections — one of 23, the other of 20). It’s hard to tally open-ended responses, since a prompt like “The best things about this course so far have been…” can elicit anything from a topic to pedagogy to teaching style. I would surely have gotten different results had I prompted for responses to a particular topic or a particular type of lesson. Nevertheless, it intrigued me that 5 students listed groupwork among their “best things about this course” and 6 listed it among their “worst things about this course.” Hard to know what to do with that. So let’s abandon the four open-ended questions and move on to Part Two, which presented students with a couple of dozen statements, each of which they could agree with or not. Here are a few thought-provoking numbers, showing how many agreed with each statement:

28 I feel I have worked as hard as a reasonable person could expect of me.
  8 I feel I have worked harder than a reasonable person should expect of me.
  7 I feel I have not worked as hard as a reasonable person would expect of me.
  6 More class time should have been devoted to working on assignments/worksheets individually.
12 More class time should have been devoted to working on assignments/worksheets in groups.
23 More class time should have been devoted to lectures/discussions.
30 More class time should have been devoted to going over homework at the board.
  6 More class time should have been devoted to going over homework in groups.
  8 More class time should have been devoted to tests and quizzes.

One student agreed with all six of this last set of statements! Where would we find the time? Anyway, the rest of these numbers may be thought-provoking, but it’s not necessarily clear what to do in response.

Now let’s turn to my other course, Algebra II, which is a “college-prep” course at Weston. (As discussed elsewhere, all non-honors courses at Weston are “college-prep” and tend to attract an enormous range of students: by definition all those who choose not to take honors or are unable to do so. Since Algebra II is a graduation requirement, no one escapes it, even those who are weakest at math as well as those few who are not intending to go to college.) I have two sections, one of 21 and one of 24; 41 of the 45 responded. Here are some numbers from those 41 in response to the same statements quoted above:

24 I feel I have worked as hard as a reasonable person could expect of me.
  6 I feel I have worked harder than a reasonable person should expect of me.
11 I feel I have not worked as hard as a reasonable person would expect of me.
11 More class time should have been devoted to working on assignments/worksheets individually.
20 More class time should have been devoted to working on assignments/worksheets in groups.
  7 More class time should have been devoted to lectures/discussions.
12 More class time should have been devoted to going over homework at the board.
12 More class time should have been devoted to going over homework in groups.
  8 More class time should have been devoted to tests and quizzes.

What do these results tell you (if anything)?



Categories: Math, Teaching & Learning, Weston