I recently observed some of our City maths PhD students teaching a problem class, and it reminded me that often the simplest techniques can be really effective. There was a whole sheet of problems for the class to work through, but rather than go through them one by one, in the order they appeared on the sheet, the tutors asked the students which one they’d had the most difficulty with. There was a consensus that many students had struggled with a particular question, so the tutors stated with this one. Not only did this mean that they could devote more time to the questions where students required more explanation, but it also meant students were immediately engaged as the session had been tailored to their needs.

Something that will repeatedly crop up in this kind of teaching is students declaring that they don’t know how to do a particular question or task, or that they’re just stuck. How can you help students in this situation?

• You may need to go back to the principles of the question, as problems can often be at a fundamental level, or stem from a basic misunderstanding
• Break the problem down into parts, to make it easier to understand – sometimes this might involve translating the problem into mathematics
• Check a students’ prior knowledge by asking them what they know, and follow up by asking them what they want to know – this might move them forward from a frozen position of not knowing where to start
• Before a session, read through the course textbooks to find out how concept/topic is introduced or taught, and take a look at any lecture slides or other material on Moodle
• Be aware that maths has both a how and why – an acceptance of an argument (e.g. a proof) is not the same as understanding what it means and how it fits in.

Students may be able to repeat a definition perfectly, but will use their ‘image’ to tackle problems. To find out about a student’s concept definition, ask a direct question. To find out about their concept image, ask an indirect question. Definitions are verbal and explicit, and revealed by direct questions such as “what is a function?” or “what is a tangent?”. Images are non-verbal and implicit and revealed by indirect questions such as “is there a function such that/where..?”.

What issues have you encountered during problem classes? What suggestions do you have for dealing with them?

This post has adapted materials from Dr Giles Martin, Bath Spa University and the University of Western Ontario’s Graduate Handbook.