This sounds like some kind of zen koan, but it’s actually an integral part of learning anything within the sciences. It’s ok not to know, and it’s ok not to understand.

The process of science is the gradual chipping away at those things which we don’t understand until we uncover the truth, and it’s very important to be comfortable with the state of mind that you find yourself in most of the time: That of not knowing.

This is the third year that I’ve taught at UCT (having never taught a full lecture course before arriving here just over two years ago), and the challenges of teaching university level mathematics to a diverse and large audience are very different from what I had expected.

As I stand and teach, the act is, hopefully, a reactive one. I like to get feedback from the class as to whether they follow what I’m saying, and when I get questions I’m extremely happy. I would much rather there were questions to clear up the general understanding of what’s going on than people were completely lost.

However, and this is a big however: I actually don’t want you to come away with complete understanding.

That might sound strange, but if you walk out of a lecture theatre thinking that you understand everything, then you will not be forced to later go through and really dig into the material. Leaving the lecture feeling like you understand it all will do you a disservice.

That is not to say that I want you to leave completely confused, but I don’t expect you to follow every step of the calculations as I go through them on the board. I would really like you to copy down what I am doing (then, or from the lectures I put up here), and get a general sense of what is happening, but the details I want you to go through when you are not being rushed, on your own, or with friends, but at your own pace.

Over the last couple of weeks I find, more and more from the audience of some 200 students, that as I am going through a calculation, there will be lots of mutterings and murmurings from the class. Speaking to one of the class reps, it seems that this is because students are missing some of the steps in reasoning, and so are asking their neighbours. I want to challenge you to something now:

I want you to follow along with the general reasoning, and not be too worried about where a factor of 2 went, or why we have chosen that particular method to integrate our function. Don’t sweat this stuff. This is stuff that you can figure out in detail later. If you are worrying about this small stuff, then you are not able to pay attention to the message that I’m really trying to deliver.

That isn’t to say that you aren’t allowed to ask these types of questions to me. Please, if you find that you are really lost in what we are doing, it’s good to ask, but if you are a bit confused about one or two steps, have the confidence that you can go back through the notes after the lecture, or even watch the lecture online again that evening, and figure out what it was that you couldn’t follow at the time.

This process is a really important part of the way you truly, deeply understand something, rather than simply finding yourself able to follow along during the lecture.

Anyway, try it, let me know how it feels to be slightly confused during the lecture, but to give yourself the chance to fill in the blanks, and the moments of confusion afterwards. You may well find that that extra effort afterwards goes a long way to true understanding, where asking your neighbour during the lecture will only give you a false sense of knowing why things work as they work.