Monday, July 25, 2011

Math Education

Intro - Education & Math
Mathematics is probably one of the most important subjects taught in school, and the school system does spend a large amount of time on it. But they do not teach it in the best manner. There are a few basic questions that need to be asked, such as Why, Who, What & How. 
Why teach math? 
Its useful. Its wise. But how well do are these reasons applied in practice? 
Who to teach math to? 
Many people barely use or appreciate any of the math they learned after division, so they don’t get much from it. There’s little point in causing them all that trouble. Maybe people who have no mathematical inclination, should not  go through such a system. Of course, an improved system might interest some of them… 
What they teach now
I never understood (at least since elementary school) why they have to teach so much by hand. What is the point when there are computers? People give many reasons to defend the practice, but they’re mostly just attempted justifications for keeping things as they are. For example, some people used to say ”What will you do if you don’t have a computer/calculator?” I’m not sure that rare occasion ever really justified spending so many years on it though. Anyways, that reason has become obsolete now that everyone has cellphones, and soon all will have smartphones.
A slightly stronger claim is that true understanding only comes when you do it on your own without a computer. Except there’s no real fundamental difference. People rarely actually understand what they’re doing, they just plug things into formulas they’ve memorized. In which case, they are just like a mindless computer, generating an answer. I bet many people don’t even know why the most basic formulas work, such as multiplication of 2-digit numbers.
Also, much of the math learned doesn’t even involve any true understanding, its just techniques to do things before computers. For example, most of calculus II is learning unnecessary techniques to solve integrals. There is no reason for so many people to learn such things when they can have silicon “formulas” to the work for them a billion times faster without errors. 
What they should teach
I’m not even sure how much of a value there is teaching the understanding of every formula. Maybe for mathematicians, or in certain areas. But the main thing they should be teaching is how to convert life into math so the computer can solve it. Computers cannot analyze life on its own, and wont be able to for quite some time. Students need to learn how to take questions in life and mathify them. People can focus on the higher-level interesting and useful questions, and let computers do their calculating thing. 

For more on this topic, see Conrad's Wolfram talk, which discusses similar issues.


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