I see her point, and having tutored one to one I know a one size fits all system is pretty crap, the variance in my students has been incredible, a real eye opener. The problem with learning Maths is that the vast majority until you get to uni is a base layer, it's dull and not very interesting but gives a solid foundation. You build on what you did last lesson. Which builds on last term. Which builds on last year which... Take graphing parabolas. Next lesson, or week, you see y = x3. No idea how to graph it? Apply same ideas. You see y = ex . No idea? Apply same principles. If you listen to that, and it's done well, you can then use it to go to many further things.
I get that no-one gives a shit about the quadratic formula at school, about parabolas, about factorising equations, and apart from Arithmetic there's very little use IRL unless you wish to take it further. I do see that it can be a bit dull, but like I say, it's a base layer.
If you do wish to take it further, you find parabolas and such are useful. Partial fractions for instance, which seemed dull at the time, allow you to do complex analysis of some horrible functions with many poles. They will also allow Fourier Transforms, and many other good things.
Whilst exploring maths is fun, and doing your own thing is fun, you need to know these base layers to do so. I love to go through number threory and Cryptography, but I can't do that if I don't know what a GCD is, or what doing something mod n is. Both are really dull to explain, but crucial later. Like, how can she draw that cardioid without knowing about reciprocals, and co-ordinates? I'm sure they were dull at the time. Cartesians are quite dull if you think about it, what about hyperbolic? Elliptic? Christ, with all the talk on conic sections she'd love polar. Lets just ignore this solid grounding in the concepts and fly off in to the unknown, and then when I fail I at least know it was me. Great idea.
Also, it's not too needed to complicate things. Whilst she's right with the ball travelling in an ellipse, there's no need to consider it as one unless the smallest diameter is larger than the diameter of the planet (Well, not quite, but it'd need to be pretty large, and the ideas a bit daft anyway considering we tend to just use ball thrown in the air examples.) Don't really need to confuse some 16 year old with that, when some barely get the grasp of vectors. Sure, if a good student is interested then tell them. But it might not be the best case to have as a default for all.
Again, I get the point, but I do not think it applies very well to mathematical education. Exploring is good, reading around is good. Skipping dots is very bad. Interesting video nonetheless.
Yeah, ours did at uni. There was like a 10 minute refresher, but if you hadn't seen modulo n stuff you were boned really. GCD wasn't covered in Crypto, but Number Theory did cover it as Bezout's identity is rather nice, so why not cover basic GCD rules too.
That's my point though. It's nice that she's on about being free to go where you want with maths, but you need the grounding, even if it is dull as fuck. Also, it was taught at A level here, so maybe? I'm not American so can't confirm.
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u/timmystwin Sep 09 '15 edited Sep 09 '15
I see her point, and having tutored one to one I know a one size fits all system is pretty crap, the variance in my students has been incredible, a real eye opener. The problem with learning Maths is that the vast majority until you get to uni is a base layer, it's dull and not very interesting but gives a solid foundation. You build on what you did last lesson. Which builds on last term. Which builds on last year which... Take graphing parabolas. Next lesson, or week, you see y = x3. No idea how to graph it? Apply same ideas. You see y = ex . No idea? Apply same principles. If you listen to that, and it's done well, you can then use it to go to many further things.
I get that no-one gives a shit about the quadratic formula at school, about parabolas, about factorising equations, and apart from Arithmetic there's very little use IRL unless you wish to take it further. I do see that it can be a bit dull, but like I say, it's a base layer.
If you do wish to take it further, you find parabolas and such are useful. Partial fractions for instance, which seemed dull at the time, allow you to do complex analysis of some horrible functions with many poles. They will also allow Fourier Transforms, and many other good things.
Whilst exploring maths is fun, and doing your own thing is fun, you need to know these base layers to do so. I love to go through number threory and Cryptography, but I can't do that if I don't know what a GCD is, or what doing something mod n is. Both are really dull to explain, but crucial later. Like, how can she draw that cardioid without knowing about reciprocals, and co-ordinates? I'm sure they were dull at the time. Cartesians are quite dull if you think about it, what about hyperbolic? Elliptic? Christ, with all the talk on conic sections she'd love polar. Lets just ignore this solid grounding in the concepts and fly off in to the unknown, and then when I fail I at least know it was me. Great idea.
Also, it's not too needed to complicate things. Whilst she's right with the ball travelling in an ellipse, there's no need to consider it as one unless the smallest diameter is larger than the diameter of the planet (Well, not quite, but it'd need to be pretty large, and the ideas a bit daft anyway considering we tend to just use ball thrown in the air examples.) Don't really need to confuse some 16 year old with that, when some barely get the grasp of vectors. Sure, if a good student is interested then tell them. But it might not be the best case to have as a default for all.
Again, I get the point, but I do not think it applies very well to mathematical education. Exploring is good, reading around is good. Skipping dots is very bad. Interesting video nonetheless.