Mathematical Structures, 6.5

I wasn’t planning to post about the course this week, since it is revision week. But there are a few things to report: we had the test (more about that later); and I got back the summary of the student questionnaires.


As you will not be surprised to learn, the formal questions are much less use to me than the free-form comments.

The questions

Like all of our first and second year modules, assessment of coursework is formative (comments only) rather than summative (a mark). I have views about this, but never mind, it is a fact. So what is the point of a “question” which asks:

The criteria used in marking on this module have been made clear in advance.

This question got the lowest approval rating of any of the seven. Why? Logically (and these are maths students, we do want them to be logical), it was made clear to them that they won’t get marks; that should be enough. I suspect that what is going on here is that students are a little confused about what is required of them in a mathematics degree, and this module is the obvious target. They are saying, I don’t really know what I have to do to get high marks on exam questions. But if that is the case, why is the coursework submission rate rather low? That is where they will learn how to write mathematics clearly!

The comments

There is much more meat in the comments. Modesty compels me not to talk about the approving comments I got from the students. (Two of them told me that I shouldn’t retire; too late, I’m afraid. They should tell this to the Vice-Principal.)

Well, all right then, here are two. The first I like, the second I don’t quite understand:

  • Professor Cameron makes the lectures interesting by adding some history/philosophical thoughts in.
  • Professor Cameron has a profound ability to flow and engage with students.

The most important issue was the small-group tutorials. Eighteen respondents commented favourably on these. (Conversations with the tutors bear this out. Mostly they are finding the tutorials very enjoyable; hard work, but work they might prefer to some other things they have to do. The fact that attendance has kept up also bears it out.) Fourteen thought that they could be improved; but these were divided among people who didn’t specify how, people who didn’t like their tutors, and people who thought that the tutorials should be longer.

This raises an interesting point, reflected in other comments. Anyone who has read student comments on a mathematics course will be familiar with the most common requests: “more examples” and “more sample solutions”. I don’t believe that these actually help learning, after a point. But, sadly, these students have been spoon-fed to too great an extent at school; I am trying to wean them off the spoon. They don’t have small-group tutorials in any other module we teach; so, for good or bad, they have to get used to doing without them.

As to the point that there is not enough time to discuss all the questions in the tutorial, I reckon the answer is in their hands: they should tell their tutors which questions they really want to discuss, or what parts of the course material they want explained.

Curiously, five asked for MyMathLab to be introduced into the course resources. They use this in Calculus, where it is a valuable tool, and can give them lots of practice questions. I don’t think that Mathematical Structures fits the MyMathLab model very well; fortunately I don’t have to implement this.

The test

There is nothing like marking test papers to bring you back to earth with a bump after reading student comments.

Actually, they are not doing so badly. When he checked the test paper, the second examiner (who also happens to be the Director of Teaching, and the driving force behind this module, and also of course is giving tutorials) made an optimistic prediction about what the average mark would be. I don’t know whether he will be as accurate as Nate Silver, but now I’ve marked about one-third of the papers, it seems he won’t be too far off.

I won’t talk here about the good and less good things the students have said; I am going to give them the chance to do that first. Next week they will get their test papers back from their tutors, and will be encouraged to discuss about ten statements that people actually wrote on their papers. I want them not just to say what the right answer is, but to diagnose the misunderstanding of the person who wrote the statement, and to try to correct this misunderstanding by giving a clear explanation.

It is a truism (no less true for that) that the best way to learn something is to teach it; this is the nearest I can get to giving the students the opportunity to learn by this method.

I will reveal one of the misstatements, made by several people, and distressingly familiar to anyone who has taught proof by induction:

n = n+1.

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About Peter Cameron

I count all the things that need to be counted.
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