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I have been going to beginner’s dance classes for seven years.
Am I terrible at it? I don’t think so.
Do I keep forgetting what I’ve learnt? Not particularly.
Am I impervious to teaching? You’d have to ask my teachers. Plural. And that might give you one clue as to why I’ve been learning at this level for so long.
Learning something brand new is hard, isn’t it? Some seven years ago, I was ‘voluntold’ into trying my first ever Lindy hop class. The first few lessons made me feel not only as if I had several left feet, but that they were pretty much unconnected to my brain in any meaningful way. The basic steps looked so easy and effortless when done by others but took so much of my brainpower to do that it was agonising. If you’d have seen me dancing then, you’d have seen me hunched over, bouncing upwards instead of downwards (a key facet of the dance, difficult to explain unless you’ve seen it), gawping at my own feet as I desperately tried to make them comply with the rhythm I was hearing. To compound the difficulty further, Lindy hop is generally a social, spontaneous partner dance with lead and response, meaning I was also learning to have a choreographical conversation. In those days, I was limited to doing the equivalent of shouting ‘hello’ and nodding like a maniac, such was my tiny if hard-won repertoire. Phew.
Fast-forward to now: I have a sense of the basic steps that is fluent and automatic (I can even have an actual spoken conversation while dancing, which would have seemed as extraordinary as being able to run a marathon to me seven years ago). I can do multiple styles of the dance and transition between them fairly easily. I rarely tread on anyone’s toes, or kick them; I can do some impressive things like aerials and fancy styling; I can (and have) rocked up almost anywhere in the world and danced confidently with strangers with whom I don’t even share a language.
I’ve also taken, by my estimate, about 300 beginners’ classes.
Lindy hop has an extremely interesting model of social learning. As I travel a great deal, I’ve been fortunate enough to try classes in many areas of the UK and even outside it, and the basic premise seems common: an evening of Lindy hop consists of a beginner class, then a break with social dancing, then an intermediate class, then more social dancing (sometimes with a live band if you’re lucky). Remarkably, it is pretty usual for even quite experienced dancers to attend both classes. That is, the expectation is that non-beginners will be present and active in the beginner’s class. This seems to have several effects:
Even more than that: in my own experience, I can say that of those hundreds of beginners’ classes I’ve taken, I’ve made new connections, understood something more deeply, or looked at something afresh almost every single time. Some of that is undoubtedly about having new teachers (Lindy hop typically has two teachers at a time, dancing together) – I’ve probably learnt from somewhere in the region of one hundred teachers in the last seven years. That has been a rich and satisfying experience in itself.
But one of the most important things I’ve learnt from my Lindy hop classes is that you can learn the same thing with a differently angled focus to your attention and it can feel revolutionary. You can practice the same basic steps in a different way an almost infinite number of times and just get really, satisfyingly good at those very simple steps, adding layers of flair, and this can still qualify you to be an expert in some sense. In other words, the lens(es) through which you are able to view something, and the ability to assimilate multiple and complex representations of that thing – not the complexity of the thing itself – can move you great leaps forward in your learning.
What on earth would this look like in mathematics?
Imagine being a maths teacher in a lesson where there was a real mix of expertise like this (and it was unknown to you). You are doing ‘simple’ mathematics but adding layers of flair and complexity, trying to give those with real experience of the subject something thought-provoking and fresh to consider while ensuring the very fundamental principles are amply covered. You have to trust that conversations breaking out at times are productive ones and that those with more experience are giving useful feedback to those with less; but you listen in at times to make sure and adjust where necessary. You are sowing seeds and watering and weeding all at the same time; but it also means the flowers are evident for everyone to enjoy. You also allow plenty of time at the end for learners to play and explore together; some rehearse the lesson’s work, and others relate it to other things they have learnt previously or make unexpected leaps into something pleasingly creative. Most of all, the focus is on dialogue – creating conceptual understanding through narrative, questioning, collaboration, critique, and conversation: first in a series of small tutorial-rehearsal steps, and then in a series of longer exploration-creation sections.
Utopian, or the very opposite? How might it work in terms of concepts to focus on (my first thought was something like ‘equivalence’ or ‘angle’). I’d love to hear your views below, or you can tweet us @CambridgeMaths.