Interesting Links for 05-10-2014

[andrewducker]

• Couples converting from civil partnerships will get backdated marriage certificates
  (tags: relationships lgbt marriage UK )
• What women want (from their porn)
  (tags: women porn viaBartCalendar )
• Call of Duty Players 'Aren't Hardcore Gamers', Says Infinity Ward
  (tags: CallOfDuty gaming )
• Satellites detect 'thousands' of new ocean-bottom mountains
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Comments

mathematical fluency

[woodpijn]

Interesting.

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.

Re: mathematical fluency

[andrewducker]

I also have negative memories. But I'm not capable of distinguishing between "Things that I didn't like doing" and "Things that were no good for me". So I'm prepared to believe that doing the same thing over and over was still useful. Or that it was useful for a bit, but the amount was too much. Or that it wasn't varied enough.

I honestly don't know!

[simont]

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.

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.

Re: mathematical fluency

[cartesiandaemon]

I was thinking both halves of that. But I assume there's an optimal level of practice which is somewhere between those two extremes? I don't know for sure, but I think when I was younger I did lots of practice at problems which were basically trivial for me because that's what I was supposed to do, and then by A-level when I had some freedom with how much work I did, I automatically went to the opposite extreme and did only enough to understand it once, which I think was a problem after I went to university.

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

Re: mathematical fluency

[andrewducker]

My general feeling is that if you can teach something to someone else then you understand it.