Oct 05, 2014 12:00
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I think she's probably right - I know I'd have done better in my maths degree if I'd spent time doing lots of example questions until it became natural, rather than coming away from a lecture with a tenuous impression of understanding and leaving it at that.
But OTOH, I have very negative memories of being made to do lots of mindless repetition in secondary-school maths - a page of about fifty variants on x^2 - 5x + 6 = 0 with only the numbers changing, and having to write out every "step" of the working (you think that's a one-step process that you can do in your head? fine, but you have to write four lines of solution for each question anyway). That felt really stupid - either you understand how to solve them or you don't, and if you don't, these exercises aren't going to help you, and if you do, they're going to bore you to tears. It would have been better to build on it, to do more advanced problems which all require solving quadratics as one step in them, and gain practice and fluency that way.
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I honestly don't know!
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That's advice I give to people I'm trying to teach to juggle, oddly enough! My usual line is, once you can more or less maintain a basic 3-ball cascade, don't spend ages trying to make it better on its own, but instead start attempting tricks as early as possible, even if they're a bit outside your skill.
Because the quality that makes a shaky cascade into a properly stable one is reliable error correction, and the fastest way to get a lot of practice at error correction is to introduce new and exciting sources of error. So, just as you say, trying more advanced stuff solidifies your grasp of the underlying thing it's based on.
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Is there any reason not to suppose that's the case? I'm not quite sure where the optimal level is, but with all sorts of skills, some I'm good at and some I'm not (solving Complex Methods problems, programming, cooking, DIY, etc, etc), I feel like I hit one level of "understanding" when I can do it once, even if that involves a lot of painstaking step-by-step work and referring to a reference example, and another level of understanding when I can do it routinely, am familiar with common variations, and can just do it without ( ... )
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Pacific Rim is also quoted as a perpetrator in the link but I don't see it at all - the female lead there is a young beginner matched with an old-time expert male.
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Hello, Freud!
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