How to teach Maths

The recent debate in the Czech republic about the Maturita exams in Maths and quality of Czech Maths teacher gor me thinking – what does it actually mean to be a good Maths teacher? I myself teach Maths, this semestr I have two great students – Lachlan and Liat. And I have to confess, often I struggle, because it is not easy to explain abstract idea as someone, for whom is hard to imagine someone does not understand it, to someone who has totally oposite feeling about the situation.

My teachers here in Aberdeen are, in my opinion, very good and really try hard to pass everything they know on us. But each Mathematician has his/her own way – one draws a picture, another tells a story and another does not tell you much, because he thinks that you must understand it by yourself and not through his understanding. And all these ways are valuable, although most of the people would say the later is bad and does not lead anywhere.

Despite all this, it is I think clear that in general the Maths teachers lack the ability to motivate Maths, to show why does it make sense and why is it really important. And that is the most needed thing at elemetrary and grammar schools.

I have read a very nice essay by V. I. Arnold recently. He writes there about Mathematics and how to teach Maths. According to him the main problem is in separation of Maths andd Geometry. Geometrical problems are surely easy to motivate. Everything around us has some shape, these shapes are transforming and changing, thus everyone understands immediately the importance of knowing such stuff. Most of the high school Maths can be easily transformed into real-world problems, the only problem is nobody does that. For example Arnold at one point of his essay writes: “ It is only possible to understand the commutativity of multiplication by counting and re-counting soldiers by ranks and files or by calculating the area of a rectangle in the two ways. Any attempt to do without this interference by physics and reality into mathematics is sectarianism and isolationism which destroy the image of mathematics as a useful human activity in the eyes of all sensible people.”  On many other examples Arnold shows how ridiculously and uselessly was great part of trivial Maths covered by the cloak of complexity.

And I think he is right. Maybe the only right solution how to make students be interested and like and love Maths again is by showing that Maths was created as an abstraction of the world and is still based on the real world, whatever that is. Thus it must be taught with emphasis on the Real and not the Abstract. Lets try to do that!