Four Questions about Math Education

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Note: This is a post of mine from a few years ago, lightly edited.

Mathematics is probably one of the most important subjects taught in school, and schools spend a large amount of time on it. But do they teach it in the best manner? This post will ask some basic questions - Why, Who, What & How.

Why teach math?
Its useful in the real world. Its wisdom to appreciate. 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. Perhaps such students shouldn't be forced to go through such a educational curriculum for so many years. Of course, an improved system might interest many of them…

What they teach now
I never understood why so much math is taught and learned by hand, when computers have been around for a while. People give many reasons to defend the practice, but they seem to just be justifications to keep 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 would fully justify spending so many years on hand-based math. Anyways, that reason no longer applies now that smartphones are widespread.
A slightly stronger claim is that true understanding only comes when you do the math on your own without a computer. However, there’s no fundamental difference. People rarely actually understand what they’re doing, they just plug things into formulas they’ve memorized. This means 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.
In addition, much of the hand-math doesn’t even involve any true understanding, its just techniques to solve things before computers were invented. For example, most of Calculus II is learning unnecessary techniques to solve integrals. There is no reason for so many people to be made to learn such things when they can have silicon “formulas” do the work for them a billion times faster without errors.

What they should teach
I’m not even sure if it's really necessary to teach the understanding of every formula. Mathematicians may want to know such ideas, and it may be important in certain areas for other people. So people should have the option of learning it. But the main thing people should be learning is how to convert real-life situations into math so the computer can solve it. Computers cannot analyze life on their 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 Wolfram's talk, which discusses similar issues.

Current Update
On Learneroo, we plan to teach math in a different manner. We will explain clearly and visually how the math works, so people who want to will be able to truly understand it. The point of the challenges on Learneroo will be to formulate the correct formula for a question, not to solve things by hand. In fact, users will usually be able to submit the formula itself as an answer instead of the numerical result. This will save a record of their actual formula and emphasize the focus is on finding this formula, not on hand-calculating it. Programmers do not just program in machine language, they use higher-level languages and libraries. People doing math in the real-world use such tools also, and the education system should not try to restrict it.


Sample Question: If Bob earns buys D dollars of a stock and it goes up by P percent a year, how much money will the stock be worth after Y years?

Please answer the question in terms of D, P and Y (as capital letters).

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