Apparently someone came to this blog by searching for “active learning in maths good or bad”… I wish I could tell them, without active learning there CAN BE no maths. Maths is all about DOING it yourself. But what do I know, I’m just a sociologist who thinks maths is fun.

## Passive learning in maths!?

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Reading James C. Scott’s discussion of the ancient Greek concept of ‘metis’ in his book Seeing Like a State, it struck me that maths seems to involve a lot of it: an intuitive feel for the game, acquired only through practice, that enables an experienced practitioner to look at a problem, as an experienced general looks at an enemy fortress, and think that there’s a good chance of being able to attack it in such-and-such a way.

Hi Benjamin,

I only just saw your comment – sorry it took so long. Indeed! I like your fortress metaphor, mathematicians often use similar ones to describe what they enjoy in their work. This is also an aspect which mathematics shares with complex games.

What does ‘metis’ mean?

As far as I understand, in ancient Greek, mètis meant something like a combination of wisdom and cunning. Scott uses it to mean the “intuitive feel for the game, acquired only through practice” that I referred to above. I highly recommend his book, especially since you’re a sociologist. It’s one of the few academic books I’ve read recently that really presents an original idea in an enjoyable way. I have a feeling that his exploration of the relationship between mètis and rational, systematic problem-solving could perhaps be unexpectedly relevant to the sociololgy of mathematics.

thank you! I looked him up, really interesting work. I’m just writing a paper about how mathematicians work and play with mathematical objects, so it’s very relevant at the moment.