Saturday, February 2, 2008

Stopping learning fractions?!

I just read an excellent article on the Good Math, Bad Math blog. The author, Mark Chu-Carrol, is a PhD Computer Scientist, who works for Google as a Software Engineer. His blogging goal is, as he puts it: "Find the fun in good math, squash bad math and the folks who promote it".

It appear that there is a "innovative" idea floating around- to stop teaching fractions at school. This idea was proposed by an award-winning professor Dennis DeTurck. This idea is of course about as innovative as stopping to use electricity.

DeTurck does not want to abolish the teaching of fractions and long division altogether. He believes fractions are important for high-level mathematics and scientific research. But it could be that the study of fractions should be delayed until it can be understood, perhaps after a student learns calculus, he said. Long division has its uses, too, but maybe it doesn't need to be taught as intensely.

In his post Mark "squashed" both this idea, and also the position of those who oppose DeTurck, and claim that: "Math is hard. The idea that somehow we're going to make math just fun is just a dream."

In my opinion fractions, long division, calculation of square roots and by-hand multiplication of long numbers are the building blocks of our understanding. It is not possible to really understand the world of numbers without it. There are many examples of people who do totally unbelievable mistakes because of this. Not so long ago I read about a woman who when asked to pay 100 dollars for her purchase gave the seller four 20$. She was completely sure that 4*20=100 and even went to complain to the manager, when told that she needs to add 20$. At this part you are probably thinking: well that can happen to her but not to me. If it didn't happen to you yet it probably won't, but with such changes in education as DeTurck proposes it is more than likely to happen to your children.

There is also a very interesting claim, that was put both by DeTurck and by one of the readers of Mark blog - that fractions should be taught in college after the student already knows calculus. Perhaps we should also teach them how to read and write after they will graduate? It is also not very exciting to learn. Even better, I think only the professors should be able to know how to read and write. And for the rest of the population we can make computerized readers that will be able to read them what ever they need.

How much time is needed to go back to the stone age? It took a long time to get up, but it is always easier to go down than to go up.

Eventually we get what we are paying for. If we don't want to know math, we will not know it. The problem is, we are not gaining anything by not knowing math. If fractions will not be taught in school the children will not gain anything - except perhaps a headache when they will try to figure how to divide a pizza into three halves.

It is good that we have calculators but we shouldn't depend on them. In one of the comment to the article high school teacher says that he has students who come to him and don't know how to calculate 3+5 without a calculator. This sound weird, but there is no reason to think he is lying.
Even if we do know how to use a calculator, there is no guarantee that it will help us. About a month ago I heard a story about a second year physics student at the Hebrew university. He needed to calculate the wavelength of a wave, in an exam. The calculator told him that it was 10^40. This is impossible - the diameter of our galaxy is only about 10^20 meters. However he wrote it, confident in the calculator.

It may sound surprising to you but my calculator often "lies" me. I noticed that sometimes when I put in simple calculations with fractions, the result is not correct. It happens because the calculator doesn't know how to treat infinite decimal fractions, so when I do:

It might show that the result is not zero, but 10^-6 for example. I know why it happens, but obviously it would be insane to trust the calculator after this.

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