Calculus I—Day 8

I got locked out of the classroom a few days ago (fortunately, there was one other person in the building at 5:30 on a Wednesday afternoon in the middle of July, and he happened to have a key which opened the door, so all was not lost), and because the university is run by a massive bureaucracy, it is going to be another week before I get a key. Thus, in order to ensure that I can get into the room, I have been wandering over to the classroom an hour or two early (while there are still people with keys hanging around) to make sure I can get in. Surprisingly, on the day before an exam, several students had the same idea. Heh.

What I Taught

Since I am giving an exam during the next meeting, I scheduled this class as a review day. For review days, I tend to let the students run the show for the most part. I didn’t prepare any lecture notes, and I had no set plan. If the students hadn’t had questions, we would have been out in 20 minutes.

Fortunately, the students had questions.

First, I handed back quizzes. There was one question in particular that students didn’t really understand, so I went over that. Then I handed them a quiz, and asked them to work on it in groups. I like giving group quizzes every once in a while for a couple of reasons: people on the top of the curve end up in groups with people on the bottom, which tends to benefit everyone; it generally helps to bring the average up a bit[1]; and it allows for another learning modality.

The rest of the session was spent going over old homework questions and sections material that were of interest to the students.

What Worked

Since I didn’t have much of a plan going in, it is hard to say what worked or didn’t. Group quizzes are generally a good thing in my book (see above), and it seemed to well. The 25 or so students sorted themselves out into five or six groups (one large group; several pairs and troikas; a few singletons), and I heard a lot of really good collaboration as I wandered around the room and checked in on progress.

The remainder of the class was what it was intended to be. The students had questions, we addressed them, and I spent some time talking about my expectations. All-in-all, we had a good evening.

What Didn’t Work

This is a minor point, and I think it speaks more to the exact role that I am supposed to play in a college classroom than to what worked or didn’t, but it was a frustration for me, so I’ll mention it in this section.

I explicitly told the students that they were taking an open-note, open-book, collaborative quiz. Any resource that they could come up with was fair game, except for me—I was not going to answer any questions about the content (one does not always have an authority figure to refer to, thus it is good practice, right?).

Most of the students immediately grouped up, but there were a couple that decided to work on their own. This was, I think, to their detriment. There is one woman in particular who sat through most of the quiz staring blankly and looking really frustrated. I approached her a couple of times and suggested that she refer to the text or try to join with one of the groups that had formed. I even asked a couple of students if it would be okay for her to join them. She was invited in, but continued to stew.

In a high school setting, I probably would have planned out the groups ahead of time (to mix ability levels, to control behaviour issues, and so on). That is obviously the role of a high school instructor. At the advanced undergraduate or graduate level, students are on their own, but have learned to collaborate outside of class (or not), and are free to sink or swim on their own. This batch of students is in transition, and I am not entirely sure how much I should babysit them, and how much I should let them figure it out.

Ultimately, I tend to be pretty hands-off. They are adults, and should be able to figure out what is in their own best interests. Thus, I didn’t force anything on this young woman (though I made strong suggestions) and allowed her to fail. I think that is the right thing to do. Either she will learn from the experience or not.

Notes:

[1]
I assign grades at the end of the semester by looking at the peaks in the distribution of grades. Generally, there is a big cluster in the middle, and at least one clump on either side of the middle bump. People in the middle group get Cs, the bumps on either side get Ds and Bs, and tails get Fs and As. However, the syllabus says that 90% is an A, so if the distribution is looking low, I like to throw an easy assignment to bring the average up without altering the general shape of the distribution.
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