In other news, we've started our slog through fractions.

[conuly]

It starts off with adding fractions with the same denominator, reducing if needed. That's easy enough, and sure enough, the same task that drove Ana to tears just a few months ago, reducing, is now the easiest thing in the world for her. WHY IS SHE ALWAYS LIKE THIS??? That isn't a rhetorical question, I actually want to know what makes it so that things that were hard become easy with a break for her. Practice doesn't do it.

In school math they're doing division, but they don't seem to be doing the long division part yet. Ana had to divide 87 by 6, and she was actually expected to draw six plates with 87 cookies divided among them. To which I say "fuck it", and she must have agreed, because she did the division first and then drew the cookies. It's faster that way, but it's still stupid. Talk about busywork, drawing 87 cookies! They've been having little intro to division assignments like this since the second grade, or maybe even the first. If they don't understand the general concept by now, drawing 87 cookies and six plates certainly won't help! You want to help them understand the idea of division and remainders, give them 25 cookies or something. But 87? Craziness.

Comments

[siderea]

That isn't a rhetorical question, I actually want to know what makes it so that things that were hard become easy with a break for her. Practice doesn't do it.

Yeah, that's a known phenomenon. I assume there's a technical term for it, but I don't know it. I just call it "fermentation". It's way under-respected in education. There are concepts that apparently the brain just has to get used to: you introduce the concept, kick it around a bit, then let it ferment for some weeks, then come back and there's no trouble.

I've also seen the effect in music rehearsal for performance.

So the question isn't "why is she like this", it's "how can we exploit this for maximal educational gains." I mean, if you know the intro-break-return thing works for her, figure out how to do it every time. And make sure she knows she works that way so she can exploit it as she develops her own self-directed study skills.

[conuly]

Well, that's largely why we do extra math. Her school uses what largely seems to be a decent curriculum, umpteen cookies notwithstanding, but if we can get to a subject before it's taught she does better.

[alessandriana.livejournal.com]

That isn't a rhetorical question, I actually want to know what makes it so that things that were hard become easy with a break for her. Practice doesn't do it.

I'm like this as well. Something that's very hard at first gets a lot easier if I'm allowed to give it some time. For me, certain things from pre-calculus that didn't make sense at first were suddenly perfectly comprehensible after the summer break, when I moved on to calculus. I suspect it has something to with letting my subconscious digest the info. There have been studies that show problem-solving is easier when you sleep on it (http://www.sciencedaily.com/releases/2012/10/121012074741.htm); maybe that's part of it.

[elenbarathi.livejournal.com]

It comes under the broad heading of 'readiness', which has not been sufficiently studied in any scientific way for anybody to give a definitive answer to your question. The public-education system would like very much to pretend that readiness doesn't exist or doesn't matter; that children can be forced to learn what other people want them to learn, whenever the other people want to teach them.

They can't, in fact. What you get from ignoring or trying to force readiness is tears, frustration, lasting antipathy and aversion to the entire subject, and strategies for getting a 'right answer' without having to actually understand what one is supposedly doing. Fifty years ago, John Holt wrote all about this in How Children Fail (http://www.schoolofeducators.com/wp-content/uploads/2011/12/HOW-CHILDREN-FAIL-JOHN-HOLT.pdf) and How Children Learn (http://www.arvindguptatoys.com/arvindgupta/hcl.pdf) (links are to full text PDF files) and his observations are just as on-the-money now as they were back then.

The problem you're running smack into here is one of cognitive dissonance. You know very well, because you've researched the topic enough, that public-school educational practices are actively bad for childrens' learning - that any time a child is frustrated to tears by her 'education', her ability and motivation to learn is impaired - but you've got no alternative to public-school education for your nieces. So you have to make the best of it, ignore the harm you know is being done by the bad practices, and try to fill in the gaps with extra work at home.

The fact is, almost anyone can learn almost anything if the learning comes at the time they're ready for it, or can fail miserably to learn it if someone tries to inflict it on them when they are not ready. Exposure to core concepts helps pave the way to readiness, which was the original principle behind Head Start and Sesame Street: a lot of underprivileged kids were starting kindergarten having never seen anybody read a book, let alone read one to them; they'd never been taught to count or say the alphabet or write their names; some had never even heard standard English spoken - their impoverished environment caused .delayed readiness, which could be ameliorated by providing them with the basic enrichments the more fortunate kids were getting at home.

Unfortunately, the parents of the more-fortunate kids got the notion that if enrichments would help get kids with delayed readiness up to speed, that they would also accelerate readiness in the non-delayed and make them into geniuses. It doesn't work that way. Kids in a math-rich, literature-rich environment will be ready to learn when they're ready to learn, and trying to push them faster is just like that old saying about trying to teach a pig to sing.