Unfortunately I do not think that the author of the article nor the board member who is its subject wants to replace current mathematical education with something more useful. They likely just want to dumb it down so that more students pass.

What math did you learn in high school that you believe is so worthless? My school taught algebra, trig, and calculus. Some of these are useful for everyday life and some are useful for academia.

Read the linked PDF. Schools teach calculation, not mathematics. Some of the calculations occasionally manage to be useful, but if you developed a mathematically mature mind it sure didn't come from your schooling.

If you did not take multiple classes that consisted almost entirely of writing many proofs per week, you never took mathematics. If all you did was problems 6-32 evens due next Tuesday, that's not math.

Putting kids through years of proofs would not improve the situation. They would still call it dumb. They would still hate it. They'd probably hate it even more, because it's harder.

Moreover it's necessary to teach kids the basics before you teach them advanced concepts. Despite what the article might have you think, we do teach musical notation first. Kids learn that as they are first learning to play. Composition is reserved for the university.

Also, the inefficiency of math education in schools does not mean that what they teach is worthless. Certainly they could do better. And maybe making teenagers do hundreds of proofs would be better. But at the end of they day, the student who took calculus in high school is better prepared for college (and a scientific career) than a student who did not.

I think jerf isn't really phrasing his position in a palatable way, even though he's right. Since he's referencing Lockhart, I'll go with that. The crux of Lockhart's argument is that math is actually really beautiful, intriguing, and exciting, and the legalistic, browbeating manner in which it is currently taught basically takes all the beauty and excitement out of it.

Assuming your high school was like mine, when you learned algebra, trig, and calculus, you were probably taught a few of the whats, some of the hows, but almost none of the whys. It's only in upper-level undergrad and graduate courses that the beauty really starts to be taught in earnest.

You're absolutely right to say that putting kids through years of proofs would probably make them hate math even more. Again, that's largely due to the way proofs are taught, especially at the secondary school level. They're all just a bunch of rules listed one after another, "doing a proof" is basically like explaining all the rules of chess to someone who's never played before, and then asking them to put the board in a particular state, thirty-two moves into a game. It ends up as a bunch of trial-and-error guessing... it's frustrating and it's boring. Sure, there are a few savants or folks whose brains are wired in such a way that it's either easy or interesting, but it's just painful for most folks, because there's no intrigue.

It's not until three or four years into college that most people are exposed to proofs as an intellectually stimulating game, where intuition plays an even bigger role than "looking at a list of rules and deciding which one fits".

But we don't get that in high school. We're not taught how to intuit something and then map the rules to our intuition. In fact, we're usually taught that this is wrong!

I get that Lockhart thinks math is beautiful. I don't think the average student agrees, though, and not just because they were taught it in a poor fashion. Similarly, I personally think programming is super-nifty, but most people don't agree. They find it difficult and tedious.

The fact is that we can't convince someone to find programming (or math) beautiful. So we teach them enough that they can hopefully 1) pass the tests, and 2) absorb enough to be useful. We do that through repetition and exercises. This is why beginning CS classes are often so tedious. They are aimed at a fairly general audience. In contrast, later classes are aimed at students who are specifically interested in CS, so the teaching methods are different, and better for those students.

I think you're wrong, and I think distaste with math is entirely due to poor teaching and/or poor/limited exposure.

If we were talking about music, would you let me get away with saying "The average student doesn't like music, in any form whatsoever"? Music is something human beings just like. We're wired to like it. Certainly there are forms of music we prefer, but I think you'd have a hard time finding someone who didn't like any music.

Math, numbers especially, can resonate in the soul in the same way that music does. It's more abstract and much less visceral, but just as beautiful, once you've really learned how to comprehend it.

I think your argument about math classes being tedious is orthogonal to whether or not math can be beautiful for everyone. Entry level music classes can be tedious, too. No one repeatedly hammering out "Frère Jacques" on the piano would say that it was beautiful, but they could hear someone playing some Chopin and easily acknowledge the beauty. Again, I maintain that this is due in large part to music being much more visceral -- you don't have to understand it to appreciate it, while in math you often do.

I upvoted both of you because you each raised some interesting points. The thing that piqued my interest was the analogy of "feeling" math like you "feel" music.

Early in high school (late 1980's mind you), I decided to take up percussion to play in our award-winning marching band. I started out on cymbals, but that was too simple. Then, I worked on the rudiments of percussion/snare drum. I had to work hard on the "math" of the musical notation, but I soon realized that I had a feel, an "ear" for complex percussion rhythms. And it jived with my already attuned ability in singing. There was something natural that "just clicked."

I see this same pattern in African spiritual music performed by people with no formal education. There's a natural mathematically knowledge they possess without any formal math education.

To me, music is just a higher abstraction of math. One that people with no math education can appreciate without even knowing why.

It's only when educated in math, that the "resonation of the soul" takes place. And I'll superficially agree with the reasons of the other commenters about why the education is lacking.

My point is that we don't have to teach them to feel anything about math. Some people will grok it at a deeper level than others and come to that realization on their own. But I think the overall analogy to music is pretty good. Mozart grokked music theory better than anyone alive today, but that doesn't mean I can't appreciate his genius (given no formal training). And I couldn't integrate an equation today (15 years out of college), but that doesn't mean I can't appreciate math in my life.

> If we were talking about music, would you let me get away with saying "The average student doesn't like music, in any form whatsoever"?

This is kind of a ridiculous comparison. As you said, "Music is something human beings just like. We're wired to like it." On the other hand, we are not wired to like math. We don't go to math concerts. We don't listen to math when we drive. We don't typically do math in the shower.

And sure, some people feel that math "can resonate in the soul", but most do not. We certainly don't teach people to feel that way about music. On what basis do you claim we can teach them to feel that way about math?

Yeah, it always annoyed me that we would be presented with something like sin, cos and tan. Shown how we can hit a button the the calculator and combine this with some equations to find out angles and lengths of triangles but never really taught how the magical sin, cos and tan work.

What I found weird about Lockhart's lament is that my music theory classes were pretty much like the "nightmare" he describes in the intro. I didn't really consider them such a nightmare, so I never read the rest of the essay.

The difference with music theory is that you've listened to music and you already know the magic. Now you can take the time to take it apart and study it, and you probably won't forget the magic. To understand Lockhart's metaphor, you must also understand that in his metaphor, this is the student's only exposure to music. They don't listen to music three hours a day, it's not in the background of every movie they watch, etc. And instead of only interested people seeking out the theory, as in your case (and as it turns out, mine, I took 2 years as well), it's forced on everybody. For more than two years in college, too. You can't possibly have been in his nightmare.