Children should learn ‘fundamental, abstract mathematics’ such as Pythagoras’s theorem, schools minister Nick Gibb told the Schools Week/FE Week* fringe meeting at the Tory Conference last week. Pythagoras, he explained, could be ‘useful if you are buying a tall fridge in a house that has low ceilings’.**But there’s a much quicker method to solve this thorny problem than doing a calculation based on Pythagoras**. You use a tape measure to find the height of the fridge (or check the fridge specifications). You measure up the wall to see how far away the height of the fridge is away from the ceiling. If there’s still space above the end of the tape then your fridge will fit. If you can’t stretch out the tape to the measured height then you’ll need to buy a shorter fridge or put the fridge somewhere else.

Being able to use Pythagoras to solve the fridge space problem doesn’t mean it’s appropriate to do so. Why take a difficult path when there’s an easier one?**Why, then, should children learn Pythagoras?** Gibb’s correct that there are practical applications for the theorem. It’s used by architects, builders, electricians, surveyors, map makers, archaeologists, glaziers, engineers… and, of course, mathematicians. ** But the most important reason is that it’s a problem – and problems are meant to be solved.**

The first problem, and the one set by my maths teacher Mrs D over half a century ago, is to find the relationship between the squares on the three sides of a right-angled triangle using a diagram of a right-angled triangle, squared paper, scissors and glue. Present results using mathematical terms. **I realise this method might be too progressive for some - it involves pupils discovering things instead of being told. But the lesson stuck (and not just because I was using glue).**

Had Mrs D given the lesson today, she might have followed up with a short animation although I think she would have shuddered at the rap.

The second problem, or rather problems, is using Pythagoras (see suggestions here). Mrs D had scores of them which took us right up to O level. You can even laugh at Pythagoras – it’s featured in the Simpsons although Homer has to be corrected. And you can sing the chorus in Danny Kaye’s song.**The point of learning maths, abstract and practical, is that it’s exciting. It isn’t just for checking whether white goods will fit in a confined space (dull, unimaginably dull). And it isn't to climb up PISA's slippery pole. It’s looking for patterns, puzzles, challenges.**

In my research for this article I stumbled across Simon Singh talking about ‘The Simpsons and their Mathematical Secrets’. Just a few minutes in and I’m learning about Mersenne primes. Mrs D would have been thrilled. Let’s hope Nick Gibb is similarly enthused.

*See page 12 of supplement downloadable here.

(Singh)

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## Comments

"Their houses are very ill built, the walls bevil, without one right angle in any apartment; ...... those instructions they give being too refined for the intellects of their workmen, which occasions perpetual mistakes. And although they are dexterous enough upon a piece of paper, in the management of the rule, the pencil, and the divider, yet in the common actions and behavior of life, I have not seen a more clumsy, awkward, and unhandy people, nor so slow and perplexed in their conceptions upon all other subjects, except those of mathematics....... They are very bad reasoners, and vehemently given to opposition, unless when they happen to be of the right opinion, which is seldom their case. Imagination, fancy, and invention, they are wholly strangers to, nor have any words in their language, by which those ideas can be expressed; the whole compass of their thoughts and mind being shut up within the forementioned sciences. "

Perhaps those who make unfounded generalisations with nothing to support their claim should be forced to write an essay on why Pythagorus's theorem is not a matter of opinion!

Logic, precision, accuracy were her watchwords. I'm beginning to realise Mrs D had an effect on me that goes beyond mathematics.

I have also demonstrated the randomness of things taught by rote. The quotes above are from GCSE English Lit in 1960, together with "quam quam sunt sub aqua, sunt sub aquat malidiceri (?) tentant(?)" for the "O" level latin I failed hopelessly - goodness only know what it means! There is another from a Rupert Brooke in Greek which I can say but cannot write.

How useless these latter are and how useful the ability to compensate for a poor memory through understanding and an ability to learn, rather than be taught - hence, you, Janet, and I have taught ourselves how to use computers. I have taught myself how to fix electric lights and sockets (being a girl, my education was focussed on cooking and sewing). I have set up websites and a host of other things.

Education policy currently is based on being able to regurgitate information, often with little understanding, is a mark that education has been successful (as well as putting huge amounts of money into the exam boards' pockets).

And now I will just have to get that sum at the bottom right without using a calculator - is it in the times tables?

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