Tuesday, March 07, 2006


How the hell can the kids learn when the teachers keep making the most glaring mistakes?

My son is a maths whizz, but for once he wanted my help. “I can’t work this one out, Dad,” he said plaintively. It was a bit like David Beckham asking me to take a free kick. He had been working on an old Key Stage Three paper by way of preparation for a forthcoming examination. It was a multi-part question and in the middle of it you had to be able to come up with a simplification of (n +1)² in order to progress. It was clear, looking ahead to the next part of the question, that the examiners expected you to write: (n +1)² = n² + 1.

Now anyone who studied with the late great J P C (Jake) Cole (MA, Cantab) will know that this is a classic schoolboy howler. It was the kind of thing that used to make him go red in the face and snap the chalk in his hand. Every now and then we would give him answers like this just to enrage him (for which I apologise and ask the Cole family to take several dozen similar offences into consideration). We knew — since Jake had drummed it into us — that (a + b)² = (a + b) (a + b) = a² + b² + (crucially) 2ab. Therefore (n +1)² = n² + 2n + 1, not n² + 1. The authors of KS3 had omitted the 2n.

I have come across another transgression against all that J P C Cole held sacred. This is the question of 9 ÷ 0 = ? Jake could have demonstrated that any number divided by zero must give infinity. How many times can you get zero into 9 (or, to put it another way, subtract 0 from 9)? 1, 2, 3? Obviously an infinite number of times. Therefore 9 ÷ 0 = u221E and n÷ 0 = u221E.

Some authorities maintain that dividing by zero is just an impossible operation (when in 1997 the computer of the USS Yorktown tried to divide by zero the ship shut down for three days and had to be towed into port). Or that dividing by zero produces the Big Bang, the infinite energy of the vacuum, and shakes the whole structure of mathematics. The commissars of Key Stage One mathematics think the answer is 9.

Case, the Campaign for Science and Engineering, recently highlighted the case of a father who discovered that his child was being taught that 9 ÷ 0 = 9 (as if zero were equal to nothing and the 9 wasn’t really being divided at all). Amazed, he complained about it to the school. They said it was perfectly correct. Incensed, he took it to his local education authority — and they said it was fine, too. Now really determined to get this sorted, he took his problem to the Numeracy Bureau and they said thank you for his concern but that the answer was spot on.

With a highly developed sense of infinity, especially in the higher realms of bureaucracy, this single-minded father finally had to go all the way up to the Department for Education, who checked with their Supreme Mathematical Adviser, who said yes, of course it was bloody wrong and what stupid idiot had been putting this about?

These mistakes can be fixed, but it strikes me, having witnessed young high-fliers being systematically ground down by years of sheer plod at school, that there is a larger problem threatening to immobilise the whole stately QE2 of mathematics.

At my older son’s school, the top set in maths is disproportionately packed with boys and girls from Asia, mostly Chinese, and some from Singapore and Korea (a situation borne out, at the global level, by the Trends in International Mathematics and Science Study — Timms). How come? A lot of the British children think the answer is that Asian children are just better at mathematics than we are. They are Manchester United or Chelsea to our worthy Conference cloggers. And they are right, not because of any inherent genetic advantage, but simply because in the Far East good young mathematicians are cherished and nurtured and coached in the way good football teams are. In Singapore, for example, the highly fluid and flexible web-based HeyMath system allows you to be as good as you can be.

If Team UK is hovering around the relegation zone, it is partly because we still have a misguided if well-meaning idea that everyone is or should be or could be equally good at maths. They aren’t and never will be. Mathematics, like music and chess, is one of those fields in which some kids are just amazingly gifted —Mozarts or Grand Masters of maths — and they have to be given the freedom to play at their own level.

The numeracy strategy may have been effective in making the innumerate numerate, but it tends to condemn to stifling, mind-numbing repetition those who are already — almost instinctively — mathematically fluent. This feels like punishment, being shot down for flying too high too soon. Kurt Vonnegut has a story about a perfectly egalitarian Utopia in which all the fast runners have weights chained to their ankles and fast thinkers have to wear headphones that send a regular buzz through their brains to sabotage all coherent thought. Under the guise of numeracy, our schools are tending to hold back the hot young mathematicians and lock them up with a numerical ball and chain so that everyone else can catch up. And buzz their brains, every so often, with manifest absurdities.


The never-ending decline of Australian public education:

One of Victoria's newest government schools is a homework-free zone. Students at Point Cook's Carranballac Prep to Year 9 College are not assigned any homework. Instead, the school's 820 students are encouraged to spend more time with their families including playing board games, gardening and learning how to sew and bake cakes. College director Peter Kearney said he wanted students to bond with their families and improve their general knowledge and lifestyle skills, instead of locking themselves in their bedrooms to do hours of homework.

Mr Kearney said it was "absolute rubbish" to give students as young as Prep daily homework of up to 30 minutes a day as recommended by the Department of Education. He said schools were giving out homework only to "appease parents". "Parents think homework means success, but there's no link between academic performance and homework," he said. "Nine times out of 10 the homework doesn't help kids, it diminishes them." Mr Kearney said the school curriculum belonged in the classroom with students needing to learn from other sources outside school including reading and playing sport. "The world we live in is full of stimulation. We need to have more of a general knowledge and understanding," he said. "Some of the kids in our school thought carrots grew in supermarkets." But Mr Kearney said his school may give some "purposeful" homework to Year 9s next year to prepare them for VCE.

More here

Keith Burgess Jackson on inteligent design: "What a strange world! I'm an atheist and a Darwinist, but, because I'm also a philosopher and a conservative, I find myself on the side of design theorists on the question of science education. As I've said many times in my blogs, I respect religion and am grateful for my Judeo-Christian heritage. I see no harm in allowing science teachers to raise questions about Darwinism. Isn't that what education is all about? Shouldn't students be urged to think critically about every theory? Sadly, there are some Darwinists who want to shield the theory from criticism. This is nothing more than indoctrination. If philosophers and scientists can debate design theory, why can't high-school students?


For greatest efficiency, lowest cost and maximum choice, ALL schools should be privately owned and run -- with government-paid vouchers for the poor and minimal regulation.

The NEA and similar unions worldwide believe that children should be thoroughly indoctrinated with Green/Left, feminist/homosexual ideology but the "3 R's" are something that kids should just be allowed to "discover"

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