How do we learn: inside that mystery called “learning”

I spend a lot of time thinking about how it is we learn things. In particular, how people learn mathematics. I spend too much time thinking about it and not enough actually doing it – although last term I changed this by moonlighting as a first year undergraduate maths student. I attended all 1st year, 1st term mathematics lectures, two weekly support classes (in mathematical analysis), plus a more advanced lecture in history of mathematics (for 3rd and 4rd year students) and lots of talks by internal and visiting lecturers. I have not solved the riddle of how we learn, but a friend linked me to a new mathematics blog today and my experience was very similar to this post in which Baez talks about “levels of exellence. I love his idea of playing “teacher/student”. I’ve done that so many times without being able to put an accurate label on it. I would say, however, that there are many more intermediate levels (or “stripes”) in the large ones such as “mastering elementary algebra”. And that you undergo changes during all of those microlevels. Before we know something, it can seem scary and unattainable – but that is because we fail to recognise that with each thing we learn, we change a little and become a little more able to go forward.
One of the central insights in my experiment in learning some mathematics as an adult is the importance of giving up hang ups and learning to get on with stuff without getting stuck on something I don’t understand. It made me realise that people who do science are just like everyone else, apart from the fact that they didn’t stop when they hit their first (or thousandth) wall, and just kept on going. I studied sociology for so many years and I still think I don’t know much. Yet I know much, much more than someone who hasn’t studied it at all. In that sense, sciences are a lot like sport. Learning develops your learning muscles (if you are careful not to get injured). Baez talks about that, too, with the example of swimming.


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