I went to America because I was interested in humanistic approaches to teaching mathematics – not just talking and writing about it, but practicing it – in practice (so to speak). What I found I have written about in other places on this blog. But here it is again.

I found mathematics taught in a humanistic way, sometimes with humanistic content, but certainly in a context conducive to “bildung” (the Liberal Arts environment itself). I had no idea that it was this that I should find. So I certainly know much more now as compared to before the odyssey.

But this also points to an embarrassing fact. Now knowing quite a lot about American mathematics teaching – I realize I know very little about mathematics teaching at the university level in Sweden! I say this because what has come into sharper focus for me might be obvious to everyone else in Sweden. I wouldn’t know.

Here is what:

- Focus on ideas and concepts – not formalism and manipulation. That is, make formalism dependent on ideas. The ideas and concepts of mathematics can be understood by closing your eyes and thinking with pictures and words. The symbols and the formalism then tries to capture this in a way that allows us to reason and calculate quantitatively in a reliable way.I’ve known about this for many years. But now it has moved into the center of my attention. And I realize that for almost every student I meet it is a completely new, alien and unbelievable thought.

Hey you out there! In particular in Sweden. Is this completely obvious to you? Have you been teaching like this all along? Why didn’t you tell me (yes, I’m a slow thinker)?

Now I’m so curious that I’ve started to think about travelling in Sweden to study university mathematics teaching!

- Next thing to put into sharper focus will be the
**transfer problem**. Hang on.

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