Teaching mathematics
Nov. 20th, 2025 04:53 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
baroque_mongooseI am currently doing a BSc (Hons) in mathematics with the OU. I've tried to do a degree on two previous occasions, once at the usual time and then again some years later; but on both occasions I was rendered unable to complete it by circumstances beyond my control, so I am very keen to finish this one before I shuffle off my mortal coil. And the reason I specifically picked maths, despite the fact that I have a lot of interests and it isn't the one at the top of the list, is that I already have quite a lot going on in my life, and at this stage of proceedings I don't want to be busting a gut doing a degree. I chose the subject I knew I could get a First in with minimal effort.
At which point, my audience is going to split neatly into two groups of people. There will be the ones who are nodding their heads because they know exactly what I'm talking about, and then there'll be the ones who are going "what?!" If you're in the latter group, I know what you're thinking: you're thinking maths is hard.
Don't get me wrong. I do 100% get why you've been finding it hard. But I'm still here to tell you that, intrinsically, it isn't, unless you have dyscalculia. Bear with me for a little while, and I'll explain why.
Maths, more than any other subject, builds on itself; and for something to build on itself, you do need all the bricks to be there in the lower courses. If you're trying to build a wall and you have one brick missing at the bottom, that brick should be helping to support the two bricks on top of it, but it's not there so you can't put them in. That means you now have two bricks missing in the next course, and in the same way three in the third, and so on, till after a while you can't build the wall any higher because you have a massive triangular gap and nothing there to build on. And this is exactly what learning maths is like. If you were ill when they were teaching how to divide fractions, and you didn't have another way to catch up, that won't have made a lot of difference at the time, but it would have caused increasing problems as you went on.
Anyone without a specific learning difficulty can learn maths perfectly adequately, provided they have a teacher who can go back and find where the initial brick is missing. I once demonstrated this with a friend in Sheffield. She said she couldn't do maths. I said she could, showed her a first-year university maths textbook, and assured her that I could explain to her any topic in there that interested her and she'd understand it. So she took me up on that. It's a long time ago now, so I forget what the topic was, but very soon we got to something she didn't understand. So I worked back a bit (to where the next two bricks should be, if you like), and found out which one of those was missing. And again, and again, quite a long way back, till I finally got to the basic problem: she didn't know what square roots were. I explained square roots, then built it all back up again and took it from there. And, lo and behold, she understood the whole topic.
My friend had missed square roots in school due to illness; unfortunately there is also a lot of bad maths teaching about. (For two or three years I had a bad maths teacher myself - she was lovely, but she had no idea how to teach; fortunately I had both a solid existing foundation and a really good textbook, so I was able to teach myself during that period.) When I was growing up it was just the odd poor teacher, but these days I suspect that even some good teachers are not teaching maths very well because a) they don't have the time to give pupils enough individual attention, and b) there's so much pressure on getting good exam results that there is a huge temptation simply to teach black-box techniques without giving pupils a proper mathematical understanding. Here's the quadratic formula, stick your numbers in, crank the handle, and you'll get the right answer. We, however, were taught how to derive that formula; I can still do it. And, consequently, I don't forget the formula, but I also know that if I did forget it, I could just derive it for myself with a little thought. Someone who has only been taught the formula and not how it works is going to have no clue what to do if they forget it.
Anyway. This is the point in my degree where I get to do a non-maths module, so I'm doing one called "Making your learning count" in which you get to do a whole slew of short OpenLearn courses and discuss them. You can choose anything, so I've picked mostly courses in two areas of interest I'd like to bring up to date (cosmology and linguistics), but the one I am on at the moment is called "Teaching mathematics". It's about how younger children learn mathematical concepts, which is interesting as I haven't taught anyone under about 15 or 16; it's useful to see exactly what sort of things children are likely to get hung up on, and why, and how you'd address that.
And the authors of the course are very clear that the aim should be to get the children to understand why things work at all points, so that they aren't just memorising formulae and techniques by rote. I'm delighted that we're on the same page!
At which point, my audience is going to split neatly into two groups of people. There will be the ones who are nodding their heads because they know exactly what I'm talking about, and then there'll be the ones who are going "what?!" If you're in the latter group, I know what you're thinking: you're thinking maths is hard.
Don't get me wrong. I do 100% get why you've been finding it hard. But I'm still here to tell you that, intrinsically, it isn't, unless you have dyscalculia. Bear with me for a little while, and I'll explain why.
Maths, more than any other subject, builds on itself; and for something to build on itself, you do need all the bricks to be there in the lower courses. If you're trying to build a wall and you have one brick missing at the bottom, that brick should be helping to support the two bricks on top of it, but it's not there so you can't put them in. That means you now have two bricks missing in the next course, and in the same way three in the third, and so on, till after a while you can't build the wall any higher because you have a massive triangular gap and nothing there to build on. And this is exactly what learning maths is like. If you were ill when they were teaching how to divide fractions, and you didn't have another way to catch up, that won't have made a lot of difference at the time, but it would have caused increasing problems as you went on.
Anyone without a specific learning difficulty can learn maths perfectly adequately, provided they have a teacher who can go back and find where the initial brick is missing. I once demonstrated this with a friend in Sheffield. She said she couldn't do maths. I said she could, showed her a first-year university maths textbook, and assured her that I could explain to her any topic in there that interested her and she'd understand it. So she took me up on that. It's a long time ago now, so I forget what the topic was, but very soon we got to something she didn't understand. So I worked back a bit (to where the next two bricks should be, if you like), and found out which one of those was missing. And again, and again, quite a long way back, till I finally got to the basic problem: she didn't know what square roots were. I explained square roots, then built it all back up again and took it from there. And, lo and behold, she understood the whole topic.
My friend had missed square roots in school due to illness; unfortunately there is also a lot of bad maths teaching about. (For two or three years I had a bad maths teacher myself - she was lovely, but she had no idea how to teach; fortunately I had both a solid existing foundation and a really good textbook, so I was able to teach myself during that period.) When I was growing up it was just the odd poor teacher, but these days I suspect that even some good teachers are not teaching maths very well because a) they don't have the time to give pupils enough individual attention, and b) there's so much pressure on getting good exam results that there is a huge temptation simply to teach black-box techniques without giving pupils a proper mathematical understanding. Here's the quadratic formula, stick your numbers in, crank the handle, and you'll get the right answer. We, however, were taught how to derive that formula; I can still do it. And, consequently, I don't forget the formula, but I also know that if I did forget it, I could just derive it for myself with a little thought. Someone who has only been taught the formula and not how it works is going to have no clue what to do if they forget it.
Anyway. This is the point in my degree where I get to do a non-maths module, so I'm doing one called "Making your learning count" in which you get to do a whole slew of short OpenLearn courses and discuss them. You can choose anything, so I've picked mostly courses in two areas of interest I'd like to bring up to date (cosmology and linguistics), but the one I am on at the moment is called "Teaching mathematics". It's about how younger children learn mathematical concepts, which is interesting as I haven't taught anyone under about 15 or 16; it's useful to see exactly what sort of things children are likely to get hung up on, and why, and how you'd address that.
And the authors of the course are very clear that the aim should be to get the children to understand why things work at all points, so that they aren't just memorising formulae and techniques by rote. I'm delighted that we're on the same page!
no subject
Date: 2025-11-20 06:37 pm (UTC)You know, I do understand your friend that said she was bad at math but isn't- because inherently, as you've said, math is about knowing how each brick is built. And inherently that was my problem with math. After square roots, I'd just. Forget what the next brick, or get confused with the amount of numbers. This also was part of my problem- math was the subject I couldn't bullsh*t in a way I could with english or history, (I feel its understated to say that everyone that uses Dreamwidth likes reading, and that + the fact that I am genuine history nerd meant that I would never study for history tests, I would get to the school 20 minutes before the test, crank open the chapters, and just. Read. and get above 85, every time.) so having to work in a slower pace frustrated me. Especially during high school, where they added more bricks, and taking my time with the bricks meant that I couldn't finish on the designated test times....
no subject
Date: 2025-11-20 06:42 pm (UTC)