Right now, I’m a teaching assistant in a course on discrete mathematics. Almost every PhD comes with teaching duties, and for good reasons. Teaching well is surprisingly challenging – just because you know the material well doesn’t mean you’ll be a good teacher – and requires years of practice.

I’ve naturally reflected on the nature of teaching, partly because I’m now on the other side, partly because of AI. In my view, the goal of the teacher should be to transmit a mental model from their head to the head of the student as efficiently as possible.

My current guiding principle when teaching is to reduce cognitive load. This is a common piece of advice for mathematical writing (recall distant definitions, use notation judiciously, say what’s being omitted), and it can also be applied to designing exercise classes. When giving talks, I’ve also noticed a surprising number of questions just concern the conventions formulated at the beginning.

The cognitive load rule isn’t just pop psych, though. I recently listened to a podcast where a professor in pedagogy, Jonas Linderoth, described the student’s working memory as the fundamental bottleneck in learning. Moreover, when I ask Claude for five evidence-based principles of good teaching, it cites ’explicit instruction that manages cognitive load’ along with retrieval practice, spacing and interleaving, frequent checking of the class’ understanding, and connecting new material to prior knowledge.

Yet, I wouldn’t pick any of the four other principles as my teaching credo. While I incorporate some active recall into my classes, I cannot control the frequency of reviews. Spaced repetition naturally lends itself to self-study. The last two principles mentioned above seem relatively straightforward – ask questions, scan for confused faces, draw parallels. If you’re a good explainer, this will come naturally to you¹. By contrast, minimising cognitive load requires a good deal of preparation.

Beyond this – slight digression, sorry – I also try focusing on the human, non-automatable aspects of teaching. For example, I aspire to be more promptable than Chat-GPT. While I haven’t trained on the entire internet, I can read your face and I know what you were lectured this morning. I should be able to give a more personalised answer; if not, I’ve failed. Another example is the performative element to teaching: solving an exercise at a blackboard is like a performance. If done well, it can be infinitely more engaging than AI output.

But these are minor details.

If you have basic social skills and your explanations go easy on working memory, you’ll probably be a decent teaching assistant, at least in mathematics. In practise, before giving a solution, one can recall definitions, auxiliary results or notation, and present information step by step² in a logical way. It’s also a good idea keeping relevant preliminaries visible on the board, and writing enough on the board so someone – like that normal human who got distracted for 30s – can follow the argument.

The teaching problem – communicating a sliver of your worldview – is intricate. A simplistic but perhaps useful way to think of it: identify the key bits of information, then permute them in whichever way minimises the receiver’s cognitive load.