The case against teaching math

Bear with me here, I have to lay down some foundation to get to my point.

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.)

This story is dead on. I know this from personal experience and from teaching my own children. I could not add until I was 10. It was painful. I still remember it vividly. Suddenly everything clicked, and I rocketed through all the material I was behind on.

I have six children, five of which are old enough to be in school. We have been home schooling them, I believe I have some creds on this.

Two of them (both girls) took right to math early on. No problem there. Two of them (both boys) couldn't be bothered, no matter what method we tried.

One of the girls was doing math before she could read, because she was a late reader. Couldn't read until she was 9. But suddenly she got it, and took off, and is reading voraciously today. Her younger sister was reading at 4.

Both boys are now doing pre-algebra. One is 13, the other 11.

We decided not to sweat it when thy were way behind. We just kept getting them to do what they could. If they weren't getting some concept, we went slower, or went to other topics they could understand. Eventually everything started clicking.

Cookie-cutter education could never do this. I agree that national education standards that fit all children into specific requirements by age, are foolish and harmful. As guidelines they are fine, but if the government is behind them they are never just guidelines. They won't fix the problem of bad and lazy teachers (in fact, they make that problem worse), and they don't help good teachers teach better.

I disagree with this.

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...

Completely False. I started to learn mathematics starting in preschool and when I arrived in the US I was shocked by what passed as mathematics education in the US. The stuff American students where doing in 6th grade I had already done in 3rd grade. It might be that starting later is a good idea but the exact opposite was true for me. If I had been forced to learn mathematics the way American students learn it, well then I would have been bored out of my mind and would have given up learning it.

I learned maths AND was able to solve "story problems" in elementary school.

Looking back, the maths taught in elementary school is very basic, too. Just multiplication and division of integers, not even fractions yet.

To be honest, I don't care that much anymore if somebody doesn't want to learn maths. It's just their loss. But maths was one of the few things I enjoyed at school, so I absolutely see no point in removing it from the curriculum.

There are some school forms (like Montessori I think, quite popular here in Germany), where pupils can apparently choose for themselves what they want to learn at any particular moment. Not sure how exactly it works, but might be a good idea.

This is blogspam. The original article from Psychology Today was already submitted to HN.

http://news.ycombinator.com/item?id=1211198

But I must acknowledge that some searches for submissions of the original article that I just tried on Google failed, although SearchYC works with enough keywords.

No math until after elementary school? what? I remember doing multiplication timed tests in 2nd grade, waiting until 6th grade would seem to be catering to the lowest common denominator and doing a great disservice to many bright students.

Can someone tell me WTF "pre-calculus" is meant to mean? AFAICT, it's just a fancy word for algebra.

This is silly. He's on his way to make a good point, but fails when his main points become 1) no math 2) focus on stories and language early on.

The good point he could have arrived at is to put less emphasis on things a child is not immediately acquiring. It would be like trying to force-feed mashed potatoes down a drinking straw. Perhaps sometimes it's math. Perhaps sometimes it's music.

Instead, he just says, stories and language are the important part! Leave math for later!

What a buffoon. He started with a bigger picture that ended with a close-minded detail.

To the original author, remind yourself that "not everyone is you." Kids can grow up to be scientists, artists, doctors, lawyers, even gasp mathematicians! And we all take different paths, even at a young age.

Just a slight quibble:

> R–recitation. He wrote that by "recitation" he meant, "speaking the English language." He did "not mean giving back, verbatim, the words of the teacher or the textbook." The children would be asked to talk about topics that interested them–experiences they had had, movies they had seen, or anything that would lead to genuine, lively communication and discussion. This, he thought, would help them develop the capacity to reason and communicate logically.

He means "rhetoric." That's what the second "R" of the "Three Rs" (a.k.a. the Trivium) is supposed to mean.

This occurred to me when I took my first college psych course, and we were talking about "operational stages." The whole lecture was about how kids can't work with disconnected mental abstractions until they reach a certain level of cognitive development (the Formal Operational Stage.) It was also enforced that moving between stages of cognitive development just takes time, not more or better prerequisite education. In that light, it's kind of obvious that young children shouldn't be being taught math, any more than they should be being taught first-order logic.

I think that intrinsic motivation is key, without it, it will be impossible to really learn. If you don't have intrinsic motivation to learn something, you can always go fotr the monkey approach, where you ape after your instructor to finish a task, or solve a problem. That is by no means "learning" though.

You lost me at "Psychology Today".