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0 pointskazinator10y ago0 comments

I'm convinced that if I hadn't done all that mindless arithmetic homework in elementary school, today I wouldn't be able to calculate a tip. Some material just has to be practiced so that it is properly internalized.

If all you do is absorb lessons without the underlying practice, the material will evaporate from your brain within a short time.

Imagine if you had only seen division or multiplication being done on the blackboard by the teacher, and never practiced it. Today, you'd at best have a faint, dim recollection of having seen such a thing, and you'd be powerless without a calculator when confronted with some matter involving two digit numbers.

We should also look at other things that impose a "high cost" on children: spending hours playing video games or noses constantly buried in mobile devices.

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abecedarius10y ago· 2 in thread

There was an HN comment thread about an experiment: some classes with no math lessons before, like, middle school or something. (Sorry I don't have the link.) The experimental group soon surpassed the controls once they did get into math, presumably because nobody tried to cram abstract procedures into their heads at too tender an age making them think of math as unpleasant arbitrary magic. This is about what I'd expect from both the idea of Piagetian stages and actual acquaintance with average people who jettisoned most of their school math as soon as they graduated.

I agree that you learn by doing and that teaching can guide you to learn more efficiently and broadly, when it's done well. It can even benefit you when mediocre, though the vast majority of schoolwork didn't pay its freight.

kazinatorOP10y ago

That requires a follow-up: how much does the surpassing group remember 30 years later.

In 2007 I got into keyboard; I learned a whole bunch of Bach pieces on the piano in just a matter of months. I was surpassing the people who did years of piano for many hours a day as little kids to get to the same stage!

I could rip through the two-part invention #13 in A minor, #8 in F, and others. I got an old-fashioned wind-up metronome and was dropping that weight lower and lower ...

Someone---LOL---asked me where I studied music. :)

Then I somehow dropped out of it, and stopped playing. Today, I can hardly remember anything. I can get through a few bars of that Minuet in G, and then draw a blank.

It was "fake" learning, in a sense. A flash in the pan epiphany that fizzled away.

But I can wake up in the middle of the night and manipulate polynomials, remember trig identities, do arithmetic like long division (and do it fast), multiply and divide numbers in my head, manipulate fractions, logarithms, you name it. It just stuck, from the years of steady practice.

abecedarius10y ago

It doesn't surprise me that after not playing for a decade you can't remember the pieces you learned. I took a couple years of lessons and kept playing for years afterwards, and now I'd never make it far into Invention #1 from the Well-Tempered Clavier without the sheet music.

I doubt much of the math you're talking about was drilled into you in elementary school and rarely used since. As a teenager and adult I'll do most of that sort of thing in my head (not long division, normally); I didn't bother as a younger kid, but it's kept coming up enough to be worthwhile, for me; I wouldn't expect so for most people in today's society, which is sort of a disappointing fact about society, but one that matters if you think of people as free agents.

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