Quite a number of my personal students are themselves teachers of one sort or another. I teach quite a few maths teachers, interestingly enough. All this makes me think sometimes that teaching maths must be quite like teaching martial arts. After all, people come to us wanting to learn something. They want to be good – or at least better – at maths or martial arts. They expect to see improvement, and expect their teachers to help ensure that. They may very well want to ensure that they can use their maths for practical purposes – adding up the household bills, checking their change in a shop, or working out something so incredibly complicated that non-mathematicians would never even understand the problem, let alone be capable of offering the solution.
So, since the disciplines are so similar, I imagined a typical conversation between Maths teacher and student.
STUDENT: I can't really do calculus. I thought I'd just skip that part.
TEACHER: Okay, well it's in the syllabus, and there's quite a few things you need it for. And you can't do your exam unless you understand it.
STUDENT: Well I thought I could just do the rest of the stuff, and you could give me the qualification anyway, because I'm really good at some of the other stuff, and if I can't do calculus, it's not my fault.
TEACHER: Oh, well, I see. Is it just calculus, or maybe there are some other things? I notice you seemed to have some trouble adding things up last week.
STUDENT: No, I'm really good at that.
TEACHER: Great. It's just that when we did that 2 + 2 and you said you'd prefer it to be 5, not 4?
STUDENT: Yeah, that's right. I like that much better. It's a much better sum. I always use it.
TEACHER: Oh. But it doesn't work, does it?
STUDENT: Yeah, it always works. And I think it looks much better. 4 is a bit to angular. I like a few curves, you know what I mean?
STUDENT: Yeah, things with curves are better. And I'm not sure about the way you use numbers. I mean, why can't we do it like the ancient Chinese used to do? They had much cooler numbers. I read somewhere that their numbers have a kind of special power, and they're more authentic.
TEACHER: Well, I'm not sure about that, but I can see that they do look kind of cool in movies about ancient Chinese wizards and stuff like that. It's just that the movies aren't quite what we're learning Maths for. Why don't we focus on some practice?
STUDENT: Okay, but can we do some Modern Maths Applications? I mean, MMA is more, like, real. I mean, you couldn't do this adding up on the street, could you? It just wouldn't work.
TEACHER: Ah, well, the Modern Maths Applications stuff is actually what we're doing here. It just has a bit more publicity. And you've got to work really hard to get good enough to do it. It takes years of doing what we're doing here to get really ready for the MMA. So let's get to work!
STUDENT: Sure. Can we do the arithmetical points stuff this week? In arithmetical points you don't need to know about adding and subtracting and all that, because you just push the arithmetical points and then all your calculations are done, like magic. I saw this guy on YouTube, and he was trying to figure out how to build a complex algorithm and he just pressed the arithmetical point and it kind of folded down for him, right there. Can you show me how to do that?
TEACHER: I think you need to focus a bit more on your adding and subtraction for now. Let's focus on that before you think about things that might be more appropriate to a Professorial Chair in Mathematics at Oxford.
STUDENT: At the school down the road, you can be a Professorial Chair in a just a year.
TEACHER: Oh, good grief!