Next: Supervising women Up: text Previous: Preliminary organisation

The supervision

< It is of course essential to know that material thoroughly before you give the supervision. This means working through the problems⁵ and may also mean reading up the theory, since your students may want you to explain difficult bits of their lecture notes. Do not be discouraged if something proves difficult for you; it is perfectly acceptable to seek help from other supervisors or from the lecturer.

<

All lecturers hand out problem sheets. These are supposed to relate to their own treatment of the material.⁶ Unless you are particularly confident of the course as it is given by that particular lecturer, you will probably want to set work from these sheets. In an ideal world, the number of sheets per course would match the number of supervisions generally allowed by colleges for a course of this length and the sheets would consist of basic questions followed by some supplementary questions intended as extras for the good or well-prepared students. However, even the world of Cambridge mathematics is not always ideal, so you should try to get sight of the sheets before you set the work in case it is necessary to pick a selection of questions. In any case, unless you are a genius, you will want to work through the material thoroughly yourself before the supervision. Some lecturers provide written guidance for supervisors, to indicate how some of the problems on their examples sheets should be tackled to be consistent with the approach of the lecture course or what the significance of a problem is in the context of the lecture course. In any case, do not hesitate to approach the lecturer: he or she will often be glad to have the feedback.

All examples sheets should be viewable on and downloadable from the departmental websites (http://www.damtp.cam.ac.uk/ and http://www.dpmms.cam.ac.uk/) and should also be available from pigeon holes in the relevant bit of CMS.

For revision supervisions in the Easter term, students usually like to prepare past Tripos questions. It is sensible to select them yourself: it is not safe to assume that last year's questions are suitable. Choose those which are pedagogically valuable, but not pure bookwork. Eight questions is about the right number for a third year course. The solutions to all Tripos questions are available in the DAMTP and DPMMS librarians' offices for inspection by supervisors. These should not be photocopied and handed to students.

<

Most courses are 24 lectures (three/week) or 16 lectures (two/week). Lecturers are supposed to provide four examples sheets for a 24-lecture course and three examples sheets for a 16-lecture course. Since these are likely to be distributed evenly over the course, you should not arrange supervisions before the middle of the third week of lectures for a 24-lecture course and not before the fourth week of lectures for a 16-lecture course. Students find it extremely dispiriting to be asked to do problems on material that they have not yet covered in lectures. Often, it is best to arrange the last supervision for the beginning of the following term, when the students will have had time to learn the material in the last few lectures.

<

Stephen Leacock (a Canadian economist) described the Oxford method of supervision as follows. (His description dates from 1922 but things change slowly in that university.) `I understand that the key to this mystery [the Oxford method of education] is found in the operations of a person called the tutor [i.e. supervisor]. It is from him or rather with him, that the students learn all they know: one and all are agreed on that. Yet it is a little odd to know just how he does it. `We go over to his rooms,' said one student, `and he just lights his pipe and talks to us.' `We sit round him,' said another, `and he simply smokes and goes over our exercises with us.' From this and other evidence I gather that what an Oxford tutor does is to get a little group of students together and smoke at them. Men who have been systematically smoked at for four years turn into ripe scholars.'

Many arts subjects rely on the pipe-smoking method of supervision (speaking metaphorically of course: nobody smokes in supervisions) but most scientists believe that only non-scientists (if anyone at all) can successfully smoke at students. Generally, in a mathematics supervision, you sit at a desk⁷ with your students (preferably two of them, one on either side of you so that they can read what you write) and write out solutions to exercises or explanations of pieces of mathematics on paper (not on a blackboard). The students should be persuaded not to take notes themselves; they need to leave their minds completely free to concentrate on understanding everything you supervisor say. At the end of the supervision, the students should take away what you have written and (best) use it to annotate, correct or complete their own supervision work or (second best) file your notes with their own work. It is worth telling them a few times that they should go over the supervision as soon as possible, while it is still fresh in their minds.

What you actually do in the supervision will depend very much on your students. It is a good idea always to start by handing them back their (marked!) work, allowing them a minute or two to look over it. Often, it is worth then asking the students how the lectures are going and whether there are any problems arising from them. This is useful for breaking the ice; and there may not be another opportunity once you get to work on the set problems. With the very best students, the supervision can turn into a general discussion of the subject, but most students are anxious to go over the work they have done in detail, question by question.

For problems which one or both of the students did not manage to complete, unless there are just small points of interest, it is often best to write out the entire solution, explaining the derivation of each line. You should make sure that what you write is not scrappy; the students should be able to recognise which question is being answered (write the number on the paper) when they come back to it later and be able to reproduce the entire solution from what you have written.

Generally, students are not interested in your neat and elegant solution (which you may well have learnt from your supervisor, or from some other source); they will accuse you of just performing mathematical tricks. They want to know why you thought of tackling the problem in this way and what features are common to a class of problems.

You should try to use each problem to explore the extent to which they have understood their lecture notes, perhaps working in a bit of the theory in your explanation (or getting them to).

Remember that showing students how to do problems is not the main purpose of a supervision. Most students seem to prefer a problem-based learning process This means using the problem as a tool to illustrate, and enhance the student's understanding of, the theory. The solution is not an end in itself.

<

You are expected to mark students' work. There is a limit to the amount of time you should spend on marking: it is not realistic to aim to find every single missing sign or arithmetic error (though your students will appreciate it if you do). However, it is important to get a good idea of whether the student has understood the material or merely copied it from the lecture notes, from a book, from a pal, or from the solution you wrote last week for another student. You should write congratulatory comments on the good bits,⁸ but you should not be too damning of the bad bits: it sometimes takes as much time and effort to produce poor work as it does good work, in which case, your student might be very upset and discouraged.

It is a very good plan to tell your students to mark in the margin of their work any step they are unsure of. This not only saves your time, but is also very good discipline for them.

Some students like to know whether their attempt at a question, especially a Tripos question for a revision supervision, would have earned them an alpha or a beta. You may be able to judge this for yourself; alternatively, you may find that the model answers kept by the Faculty Office include a marking scheme. As a rule of thumb, and alpha corresponds to 3/4 correct and a beta to 1/2 correct.

Subsections

• Supervising women