A few days ago, I registered at bettermarks, a German startup co-founded by successful entrepreneur Arndt Kwiatkowski. I played around a little pretending I was in 7th class and looked at what they’ve built. This is certainly a very interesting project, and I hope that it will help to improve math lessons in Germany – but that is a long way to go.

Anyway, I don’t want to rant about bettermarks. On the contrary, I think bettermarks is great. But I’m worried about the content of math classes. The content that is specified by politicians. 7th-grade students in Germany seem to constantly deal with *units* in math. I guess the correct English term is “physical units”. Physical units because units are a concern of physics and, more importantly:

**Mathematics is not concerned with units.**

That’s the whole point of mathematics: You make things simple so you can handle them. In mathematics, there is no unit of area and unit of length.

Mathematicians are happy if something can be measured *at all*, a property that not too many mathematical entities have.

Take fractals for example: Suppose I drew a Sierpinski

Triangle on a piece of paper, how much space do I need to do that?

Obviously, I will need some space if I wanted to actually draw it (physical reality), otherwise I couldn’t see it. Mathematically speaking, however, it has Lesbegue measure 0 and thus, vanishing area. Not square kilometers, apples or Newton, just a number.

How about a Hilbert Curve? I can draw an approximation on some finite area. Now I can refine it, thereby increasing its length, but I don’t need to extend my drawing. Eventually, the length will grow to infinity – how can this be? In the context of soccer fields and living rooms, this doesn’t make sense – it’s purely theoretical. It’s mathematics.

I agree, it is important to teach children about the typical size of a living room, a soccer field or the distance between some well-known cities. But that shouldn’t be done in mathematics: Mathematics should be concerned with abstract thinking only. Many people believe abstract thinking makes classes less appealing to children, but honestly: Do they really think that “Martha owns a set of Miley Cyrus stickers of cardinality 8″ type of exercises make math more interesting, let alone be taken seriously by children?

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