Next month will see undergraduates return to Cambridge for the first term of a new academic year, keen to get back to face-to-face, interactive learning. As well as a fresh start for the students, this is an opportunity for reflection and perhaps innovation on the part of their teachers.

Undergraduate supervision is a form of small-group teaching as practised at the University of Cambridge. Students bring solutions to Examples Papers of problems set by their lecturer, and discuss them with a supervisor (such as me) in groups of two or three. The strength of this system comes from the individual, personalised help that students receive.

I have written this post to clarify my present thoughts on supervisions: what I aim to do, and what I would like my students to be doing, to facilitate the most effective learning. I shall first discuss the value of setting explicit expectations. I will then set out my expectations in the form of advice to the students, suggestions of “how to get the most out of a supervision”. Finally, I will discuss the problem of cribs, and what a supervisor can do to mitigate their detrimental effects.

Explicit expectations

I have come to realise over my years supervising that I cannot rely on my students to take the initiative. I have taught many proactive, brilliantly eager supervisees. However, a fraction of those that could benefit from my help do not ask for it, or do not attempt all of the problems set for that session, and so on. It is my responsibility to try and encourage everyone to take full advantage of the teaching time laid on for them.

A small step is to send a short email before each supervision, confirming the date and time, and explicitly stating which Examples Paper will be discussed. Surprisingly, I have found this measure to reduce the number of ill-prepared students. All students know that they should bring a completed Examples Paper to each supervision, but setting and resetting clear expectations seems to provide a sufficient nudge to finish their work.

Regular contact outside of the scheduled sessions provides an additional opportunity for enrichment. I keep a list of relevant YouTube videos, interactive web pages, and further reading, then distribute a link relating to the current Examples Paper in advance of each supervision. This provides motivation and illustrates wider applications of the Engineering topics we cover, complementing the more technical work during supervisions.

Following the success of my reminder email, I plan to tell my students what I would like to see from them more generally over the coming academic year. Different students can reach the same answers in a myriad of ways, but by requesting certain specific outputs I can encourage a logical approach to problem solving that will serve well in future. Students already have some idea of what to do to prepare for supervisions, but my hope is that making my expectations explicit will prompt all students to raise their game a little.

How to prepare for a supervision

Below, I describe my approach to undergraduate Engineering supervisions, and offer some suggestions for you, the student, to get the most benefit from them. I am here to help, but preparation on the part of the supervisee makes this much more efficient.

During a supervision, my first priorities are to:

• Assist with stumbling blocks in solutions to Examples Papers; and
• Clarify difficult concepts from the lecture notes.

Correspondingly, the student should:

• Read through the lecture notes and identify any gaps in their understanding; then
• Attempt all Examples Paper questions covered so far in lectures; and
• Make a list of issues arising from the above, or anything else to be discussed.

This enables the best use of supervision time — by the end of the session you can expect that we will have discussed and hopefully sorted out all of your problems. If we get to the bottom of your list, or you don’t bring any specific queries, I will:

• Ask you to justify your workings;
• Quiz you on important material covered in lectures;
• Talk about extensions of the material and its practical applications;
• Go through fundamental derivations or an unseen problem.

It is in your interest to lay out your solutions to the Examples Sheets clearly. Show intermediate lines in algebraic manipulations. Annotate your work with the mathematical technique, physical principle or assumption used at each step. Highlight final answers. This will make it straightforward for you to later remember and explain what you were doing. Your Tripos examiner, who must mark over 300 scripts, will also be thankful if you make their life easier.

Clear expression of mathematics is an important skill for a professional Engineer, just like spoken or written communication. It is not enough for you to be confident in reinterpreting your scribbles, because Engineers do not work in isolation. Your colleagues will need convincing that there no risk of the pressure vessel you have just designed exploding. Your manager will not sign off on that bridge if you have plucked a formula or safety factor from nowhere!

A note about cribs

I would rather you make a persistent but unsuccessful attempt at a problem than copy the solution from a crib. The Faculty of Mathematics Study Skills guide reasons,

“Once you have seen someone else’s solution to an example, then you are deprived, for ever, of most of the benefit that could have come from trying it yourself.”

Ultimately, examples papers exist for your own sake, to give you the opportunity to develop your understanding of the concepts and methods described in lectures. They are not assessed towards your degree. It is absolutely fine to come to the supervision without all the answers — In fact that is almost the point of the whole exercise!

For difficult examples papers, I provide hints to help guide you towards the answers and reduce the temptation to crib. If you are still stuck, try these steps first:

• Reread the question to confirm what information is given, and what you are seeking;
• List the physical principles or definitions you think might be relevant;
• Check that equations are dimensionally consistent (e.g. we cannot add length to time);
• Carefully verify algebraic manipulations, particularly expansions or simplifications;
• Write down in words what you have tried so far and why you think it is not working.

Once you have done all the above, there is really no point looking at a crib, and you might as well wait until the supervision to discuss the problem with me.