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Chronological Archive • April 20, 2003 - April 26, 2003
April 25, 2003
Prime bear

Dave Barry (archiving mess scroll down to Wed April 23) calls this his "educational site of the year". Yes it's Alkulukuja Paskova Karhu, the Prime Number Shitting Bear.

I actually learned quite a lot about Prime Numbers from this eccentric animal, like how around 1,000 they are a lot more frequent than I had supposed, nearly as close together as they start out being.

I don't have to have it explained why mathematicians find Prime Numbers fascinating, because they find anything mathematical fascinating by definition, but do Prime Numbers have any uses other than as something for joke bears on joke websites to emit from their recta? I've heard they're used for encoding things, or maybe for making it impossible to decode things. How does that work?

And do primes have other uses? Surely they must. Commenters who know maths? Here's your chance to broaden the minds of all the maths-phobic humanities snobs who flock here by the thousand.

And linguists! What language is "Alkulukuja Paskova Karhu", and what does it mean? I'm guessing it's Russian, and it's the bear's name, but what do I know?

Posted by Brian Micklethwait at 02:11 AM
Category: Maths
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April 24, 2003
Party titbits

I've just done a quite long posting on Samizdata about the influence of children's toys on later artistic tastes, so I haven't time for much profundity here. But I did attend a social event last night at which I picked up a couple of titbits of interest here.

First, I learned that however interesting a figure Maria Montessori might be in herself, not everyone admires her influence, in the form of your average Montessori school. On the contrary, I encountered the opinion that Montessori schools are employment opportunities for dimwitted women who would otherwise have no place whatever in the teaching profession, and that in general they tend to be extremely disappointing and unsatisfactory places, full of kids being bored to death with pointless objects and just meandering around doing very little. Well, I'm just passing on what I heard.

The other little titbit I gathered up has a bearing on the bilingual raising of children. One of my friends told me last night that she knows of an Anglo-Dutch couple, with a kid. Dad talks to the kid entirely in Dutch, and Mum talks to the kid entirely in English.

The kid is not yet at the stage of talking. He's only at the repetitive nonsense words stage. Nor does he read books yet, for real I mean. But he is at the stage where he turns over the pages of books he already knows from them being read to him. Now, get this. When he "reads" books that his Dad has read to him (in Dutch) the repetitive nonsense noises are Dutch noises, with lots of "ch"-ing from the back of the throat, but when he "reads" Mum books, English books, the noises he makes are different, more of the "Grrrrh!" variety. I love that. I've no idea what it proves, or if it proves anything at all, but I love it.

At the party I also met up with occasional contributor here Julius Blumfeld, who had some very interesting things to say about the role of bias in education (he's for it!) which I urged him to write down and send in. If he doesn't do this reasonably soon, I hereby serve notice that I myself will attempt here to summarise what he said.

Posted by Brian Micklethwait at 10:23 PM
Category: LanguagesParents and children
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April 23, 2003
Don't reward!

Yesterday I linked to this site and at it I today found this piece, which includes the following quote from Maria Montessori herself:

Like others I had believed that it was necessary to encourage a child by means of some exterior reward that would flatter his baser sentiments, such as gluttony, vanity, or self-love, in order to foster in him a spirit of work and peace. And I was astonished when I learned that a child who is permitted to educate himself really gives up these lower instincts. I then urged the teachers to cease handing out the ordinary prizes and punishments, which were no longer suited to our children, and to confine themselves to directing them gently in their work.

Of all the notions I've so far got today from my further reading of Paula Polk Lilllard's book about Montessori, this is the one that has most intrigued me.

I don't yet know whether Montessori intended this idea to apply to older children as well, but it certainly makes sense to me that it might.

When someone rewards you for what you've done, it is as if they have taken possession of your work. They've made it theirs rather than yours. Accordingly, you lose interest, because it isn't yours any more.

This idea also reminds me of an earlier posting I did here about a lecturer who once visited my school. Intrinsic to the enormous pleasure I remember taking from this event was that nobody tried to test me later to see if I'd been paying attention to it properly. I decided what it meant and which was the best bit and why it was so good. And I recall once refusing a prize for some work I did during a holiday from the same school, about town planning, as if shaking off the unwanted attentions of an over-affectionate relative.

The organisation Taking Children Seriously also makes much of the notion that there is something deeply manipulative about rewarding children from doing "good work", an idea which I must say didn't make that much sense to me when I first encountered it, but which I think I get better now. I wonder if this lady, the leading light of TCS, had read lots of Montessori before she got into her TCS stride, or whether it was just a case of a good mind echoing a great one independently, or perhaps just breathing the air that had been perfumed by the great one.

If Montessori has been as influential as I surmise, this might also account for some of the fierceness with which many teachers oppose the current government-lead enthusiasm for academic testing. What such critics presumably have in mind is that lots of literacy testing, for example, may indeed create a generation of children who certainly do know how to read and write, but it may also create a generation of children who don't actually like to read and write very much.

Taking the same idea into early adulthood, it is a familiar story for recent university graduates to be repelled by the whole idea of intellectual activity for about two years after they leave university, because while there they forgot how much fun thinking seriously and systematically can be.

Posted by Brian Micklethwait at 06:59 PM
Category: Parents and children
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April 22, 2003

No less then one email flooded in noting my absence yesterday. An American. The mistake I made was that what with the Monday after Easter being a bank holiday, which may not register over there, I was in Sunday mode, and only realised this morning my omission. Apologies to all who had their day ruined by being without their fix of Brian rambling educationally.

However, I have not been ignoring education. Last Friday evening I was given dinner by friends, one of whom is a Montessori teacher. And they also lent me a book on the subject.

Until now, Maria Montessori (1870-1952) has really only been a name. I expect to have more to say about matters Montessorian over the weeks, months and years to come, but in the meantime I note how very influencial this lady's ideas have surely been.

A core Montessori notion is that you mustn't expect to start children straight away with academic 3Rs type teaching. They must instead be allowed to explore their physical environment and to develop their various senses, of sight, sound, touch, and so on. And now that stuff is so cheap and ubiquitous, almost every child in the West now possesses a cornucopia of toys and educational objects of all imaginable shapes and sizes. Meanwhile, children's TV shows have encouraged children to explore their physical capacities and senses by playing with all the useless yets perfectly safe and clean detritus of the modern food and toiletry packaging industry. Here in Britain, the TV show Blue Peter has become the object of endless good natured and nostalgic teasing for its various schemes to convert toilet rolls and fruit juice cartons into houses, dolls and spaceships. I'm guessing that Montessori had a lot of influence on all this kind of learning by playing.

There was, you might say, an interlude between a world in which children lived a rural life surrounded by the stuff of nature, and our own world where stuff also abounds. Unlucky children during this transitional period would sometimes spend their entire early lives in unstimulating places like orphanages, with no stuff to play with and effectively not doing anything, and as a result they grew up permanently stunted. A key Montessori insight is that by "playing" of this sort (although she actually called it "working"), often very repetitively, the child is developing its own brain. Children, said Montessori, have short periods of intense focus on particular topics, so to speak, and if their eagerness to explore colour, for example, meets no response in the form of a colourful environment with colourful stuff in it, their lives are rendered permanently less colourful. (As Montessori realised, a child who grows up without hearing language spoken can never later get to grips with it.)

The book I've been reading is called Montessori: A Modern Approach, by Paula Polk Lillard, and it was first published as long ago as 1972. However, I am already very struck by how many of Montessori's ideas chime in with the latest fashions in evolutionary psychology. I'm also currently reading Steven Pinker's The Blank Slate, and the intellectual overlap is remarkable.

I haven't got to the bit where I learn about Montessori's views about reading and writing, but I'm looking forward to it very much.

Once again, my apologies for the blip in service here. I wish I could be sure that it will be the last. I will leave it at promising that such interruptions will be rare.

Posted by Brian Micklethwait at 08:32 PM
Category: Education theory
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