When You Really Really Know Something

With my boys, we got into a discussion this morning about math, the way it's taught, and learning in general. I thought it was worth talking about in more depth because it's a subject dear (!) to my own heart, and I know it is with some of you too. I know we've talked about it here before.

I was good at math when very young, but I reached a level at around the age of 13 or so where it got very difficult, and I pretty much gave up. I actually remember at the time thinking "I used to be good at maths*, what happened?" I scraped through. I passed, but only just. 

I have spent my life ever since hating and avoiding it. There are two reasons. One, it only really crops up or has any relevance these day in accounting, i.e. taxes etc, which I hate with a passion. I can do it. It's just basic arithmetic, it's easy, just tedious. 

Now and again I have to add a few fractions (recipes, woodwork, etc) or work out an angle when I'm constructing something, but let's just say math doesn't play a big role in my life. 

I have been heard many a time complaining about the time spent on math in High Schools, but more so in colleges. About kids who fail only on the math - but therefore FAIL, and kids in college who can't get past the math, despite the fact it's not relevant to what they went to college for. I'm angry about it. You pay a lot of money for further education, and these compulsory general courses.............don't get me started. Just don't. 

Because I've been studying things recently where advanced math would have been useful, I've been forced to change my attitude. 

You see, I used to believe that the way advanced math is taught in High School is a waste of time, unless you needed it for more study in future, where the advanced math would come in useful. 

So, now I believe that the way advanced math is taught in High School is a waste of time, even if you do need it later on for further study. Because you won't remember it. 

The only kids who benefit from advanced math the way it is currently taught, are those who enjoy it, and intend to immediately go on to further education, and continue it. 

The only kids who get anything out of it are those who really really understand it.

Most do not. They scrape by. They struggle, cram, and get just enough of it right to pass the exam. 

Even Tom, who has a very special brain, and picks up math concepts as easily as most people pick up earworms, admits that the last math course he did in High School didn't make much sense, and he only passed because he has a good memory. He never really understood it. He gave me an example too. 3D parabolas. He learned how to use the formulas, but he didn't really understand it, because they weren't taught to do that. They were taught how to use formulas. And by this time he was just trying to graduate, and GET OUT. His interests lay elsewhere. He scraped by. 

If, in a few years time, he wanted to study something that required understanding 3D parabolas, he'd need to start over. 

So what was it all for? A taste? Busy work? I've heard all sorts of explanations. But all over the world, kids are not understanding this stuff, scraping by, barely passing, and then forgetting it. Subsequently they either never use it again, or have to repeat the entire bloody course later on. 

It is quite clear to me that if I wish to continue studying certain things, I will need to do a math course or two, or I'll be floundering again. 

That time, hours and hours of time, spent in secondary education, struggling though a subject I never really understood, didn't enjoy, and took so long to use I'd forgotten it all anyway, could have been put to so much better use. I think literacy, the state of which generally I am DISGUSTED with, is far more important. But that's dumbed down in schools. And as some of us have discussed elsewhere this morning, in many places nutrition is not taught at all. You know, basic maintenance of your own bloody body. OK, before I get all riled up, I'll move on to what the boys were saying. 

Michael said that he has done better in his most recent math course because his teacher was smart. Michael had been getting all the answers right, but not showing his working out. Yeah, that old chestnut. The teacher must see how you arrived at your answer. Michael does it in his head. I remember going through this with Alex, who, if he's reading this, which he probably is, is nodding furiously. Alex is officially a genius. He went to a school for gifted students and all. Then he flunked math. Makes no sense until you know all the details. Gifted kids are encouraged to figure things out for themselves, it's a totally different process really. But standard High School math requires that you follow the steps, show your working out, follow the herd.......dum de dum de dum. And Alex did it in his head. Even as a very small child, he told me he could see the numbers in his head, and he really really understood what was going on. 

Michael's teacher did a test. He gave Michael a completely different set of questions to all the other students. He still got them all right. This teacher, this wise wise teacher, has decided that the boy understands the work, and can do it in his head. He's not copying other people! That's the first reason they want to see the working out. But the other reason is that they think that if you follow the steps you are taught, you are understanding. No, you are memorizing steps. If you really really understand, you can skip steps, or do it another way altogether. 

The way we are taught math is not the only way. Watch this, as a simple example:

I had a hell of a time learning long division. When I met Martin he showed me a new way to do it. It made sense, and I've used it ever since. Now, I see they teach it yet another way, which looks bloody stupid to me. I have taught my kids the way I know, they prefer it, but they would lose marks at school if they showed my method. 

With far more advanced things, there is still more than one way to arrive at your answer. That really is the heart of mathematics, after all. Devising ways to get from problem to solution. Perhaps if more emphasis was placed on working things out for yourself, instead of following steps, you'd actually understand it? Or am I being radical? 

OK, that's math. But I think this may apply to other things too. Soup, for example. No, I'm quite serious. I have lost count of the times I've had the soup discussion with people. Making soup appears at first to be an arcane art. People who make good soup are greatly revered. Many people, who patiently and carefully follow a recipe, can come up with an enjoyable soup. But they don't really really understand soup. If they did, they wouldn't need a recipe. OK, it's not the best analogy, but I think you see what I mean. 

I think when a thing is being taught, it should be taught from the inside out. It might take a bit longer, a bit more effort, but it's better. It sticks. Of course, if you are interested, you can take it upon yourself to study deeper, find it yourself. IF you are interested.

As somebody once said "Education is wasted on the young". When you want to do it, you try harder. But when you need to do it, you rely on teachers. 

*Because that's the English short form, with an s, so I used to think that. Now I think it without an s. One adapts.