The case against teaching math

The case against teaching math
ordinary-gentlemen.com

Sure, kids don't like math. I myself didn't like math when I was a kid. Why? Well, because math takes work. Sometimes lots of work.

I believe a solution to this has to do with how math is taught, as opposed to just abolishing the subject altogether. I don't hate math any longer - I can sometimes see the beauty in it, and I sure as hell know that it comes in handy, especially when working with computers.

But even if it isn't taught properly - there is something to be said for doing math at an elementary level. Working on math problems tend to give you a certain kind of mental tenacity, that would come in handy later. The question, really, is how to make math seem fun/relevant - especially when it gets more abstract.

Steven Strogatz has some cool ideas: http://opinionator.blogs.nytimes.com/category/steven-strogat...

Bias has a specialized definition in machine learning; in a (really thin) nutshell, it represents the set of concepts a given technique can represent. If your banana vs. ball classifier can only represent "roundness" and "yellowness", the bias will prevent it from seeing a yellow cube as anything but a banana. (If you really dig in, I find this concept is really a superset of the traditional meaning of "bias" and find it a lot more edifying, but that's beyond this post.)

A learning agent, even a human, can only learn what their biases permit. Much of intellectually growing up is the process of learning better biases, for instance putting away "magic" and replacing it with "chemistry". If you've ever felt your brain stretching as you learn something (a foreign language, Haskell, etc), that's your biases growing. Characterizing growing biases mathematically has been a great challenge for machine learning, but it clearly happens to humans.

Alright, getting up to the payload here: I have actually had similar concerns about our educational patterns before because you can't effectively teach something until you have the necessary biases in place. Unfortunately, you can't stop learning, you are always learning. So what happens when you "teach" something to students that lack the ability to apply the correct biases? You get the square yellow cube effect above... one way or another it will fit the biases you have (give or take growth, which takes time). The result is semantic gibberish. Now, by itself it is inevitable that you will go thorough quite a lot of gibberish as you grow up (see also "Kids Say the Darndest Things"), but why are we using precious school time to do that for math?

Furthermore, it is transparently obvious that things can be taught too soon. My 18-month-old is frolicking around my feet now, and he can't add. There's not much I can do to correct that right now. At some point he will, but this suffices to prove the point that there is a "too soon". So, when is it no longer "too soon"? Are we really sure that our traditional answer is anything more than traditional, that it has any actual truth?

Teaching things early is not harmless, either. Think about it; how many adults have downright childish issues with math? Childish misunderstandings, childish opinions, childish beliefs? Coincidence? Bad motivation? Or a schooling system that jammed it into their brains before they were ready. And those that don't have childish problems... is it merely because we were ready soon enough, rather that necessarily any actual unique skill? Some people never recover.

It is at least a question worth research and thought before we knee-jerk an answer of "if it was good enough for my grandpappy it's good enough for you".

(Getting a little more controversial, this is why I don't support really early sex education (i.e., elementary school). You will accomplish nothing except hilarious misunderstandings on a very important topic. This can have real, negative consequences, and the intentions count for nothing.)