Teaching and assessing mathematics

For most of my life, I assumed, without thinking too hard about it, that when I would be within a couple of years of retirement I could just coast along, putting up with bureaucratic nonsense without complaint because I would soon be beyond their reach.

I seem to have been wrong about that.

Several documents have come my way in the last few weeks. The first one I wish to mention is from the London Mathematical Society, entitled Mathematics degrees, their teaching and assessment. It should be on their web page, but doesn’t seem to have got there yet, so I have posted a copy here.

Mathematicians in the academy are used to our colleagues in other disciplines grumbling about how often we say, “But mathematics is different.” But neither their grumbling, nor our many repetitions of the statement, change the fact that it is true.

The LMS document was produced “to support everyone teaching mathematics in Higher Education.” It is a response to a document produced by the QAA – if you don’t know what this is, you are lucky. The QAA is a symptom of the decline in the British higher education system. Its role is to police universities; once, when inspecting a French department, it sent along an inspector who spoke no French to observe a lecture in French. But at least the QAA has admitted that “mathematics is different”, and the LMS amplifies this view.

Here are the recommendations of the LMS report. Sensible enough, but should it really be necessary to say these things?

  1. A student who fails a small number of individual modules, but has an overall satisfactory average, should not be deemed to have failed a degree programme in mathematics.
  2. On occasion, a specific module should be available to more than one year of a mathematics degree.
  3. Masters degrees in mathematics should not necessarily be obliged to reach the frontiers of knowledge.
  4. Despite the agreed importance of modern computer-based teaching and learning, lectures delivered using clearly visible boards should continue to play an important role.

In fact, they will be useful to those of us who sit on University committees which try to impose different views current in other subjects.

That was the easy part. The other two documents display the kind of insanity against which the LMS arguments are of no help, and which affect all of us, not just our representatives on committees.

Back, briefly, to the value of a mathematics degree. I have always believed that a mathematics degree course produces students who can think, reason logically, attack unfamiliar problems, and know where to go for the resources they need; and that, for these reasons, mathematics graduates are valued by employers.

But listen to some of the nonsense that has come our way in two draft policy documents, one on teaching materials (produced in our department), and one a on teaching, learning and assessment strategy (which slipped out in an email advertising new administrative positions). The examples given here are merely a tiny selection from a much larger set.

From the departmental document:

  • Detailed proofs can be relegated [my emphasis] to published notes … Lecture notes are not required to include examples.
  • Module organisers should typeset teaching materials … in a sans serif font
  • We cannot simply ignore areas of student support that our students clearly want to see enhanced … students regularly ask for more examples. [If you don’t know what is wrong-headed here, you’ve probably never taught a university mathematics course.]

From the College document:

  • In these turbulent and complex times the College,[sic] needs a Learning, Teaching and Assessment Strategy that encompasses the whole student experience …
  • The College has recently undertaken extensive work to develop a distinctive set of Queen Mary Graduate Attributes.
  • [Aim 9] To increase year-by-year the percentage of Queen Mary students agreeing with the NSS questions (10 to 12) on ‘Academic Support’ so as to be in the top 10% of universities by 2015.

I have explained my misgivings about using the National Student Survey as a benchmark here before. It seems the real issue is a confrontation between

  • those who believe that students are customers, and that our job is to service them (or appease them); and
  • those who believe that students have come to learn, and that our job is to teach them.

My colleagues fall into the second camp; but a worrying number of our administrators fall into the first.

Anyway, I felt I had to take action, so I posted my critique of the departmental document and invited my colleagues to send me their views. The response was very strong. It is clear that we are committed professionals who have thought long and hard about our teaching, even those staff who are still on probation and taking courses for their PGCAP. The responses are full of comments on the lines of “If we treat students as adults, they will respond like adults … if we explain to the students why we are not providing model exam solutions they will accept our reasons” and “Can’t management stop interfering and let us get on with our teaching?”

So without ever intending to, I seem to have become a thorn in management’s side.

In response to my earlier post here about sans-serif fonts, Dima was kind enough to say that, if it all got too much for me, I would be welcome in his department. In the past, I have often wished myself elsewhere, usually because of absurdities from the Government, the funding bodies, or the College administration; never before have I felt betrayed by the people running my own department. But sorry, Dima, I think I have to stand and fight, at least for now.

But to return to my opening thoughts: here is an incident from the early 1970s when I was a postdoc. This has often given me pause for thought, and perhaps pointed to what is happening now.

Peter Neumann organised a small conference on permutation groups in Oxford. We had a party at my house, and I had the odd experience of sitting in my own front room being discussed by two great names in group theory, Ernie Shult and Leonard Scott. Ernie said that I was a very gentle person. Leonard disagreed, saying that there was a core of violence within me.

Perhaps you were right, Len!

About Peter Cameron

I count all the things that need to be counted.
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2 Responses to Teaching and assessing mathematics

  1. The LMS statement has been posted on the “Future of the LMS” blog

  2. The merits of using blackboards were not lost on at least one of my students, as evidenced by their comment on a course evaluation:

    “The way he [Dr Bailey] teaches is also clear and organized, and not at all powerpoint based which is a plus.”

    Not all the evaluations were quite so complimentary (not least the one who described me as a “jerk”!), but no-one demanded “lecturer should use powerpoint”…..

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