[wycx]

A good first step is to come up with some possible reasons for why we suck.

I know I felt that mathematics was completely devoid of context during my high school and undergraduate years.Now that I have problems to solve, I have a real purpose when I go back and relearn what I was taught years ago.

Perhaps we should not have mathematics classes at all. Instead, we should just expect to encounter mathematics every subject, and the mathematics is taught where appropriate.

[calibraxis]

Also, I'd use the natural explanation, which the evidence points to: schools are reasonably successful at inculcating conformity and ignorance. (http://www.youtube.com/watch?v=pFf6_0T2ZoI) If they didn't fulfill this social function, they'd be dismantled or fixed.

(Thinking otherwise is like thinking that invading Iraq was about WMDs and the US gov't was noble-but-fumbling. Contorting ourselves into logical pretzels to preserve an illusion.)

I wish people like Edward Frenkel well. (Author of "Love and Math: The Heart of Hidden Reality", who tries to undo the damage done by math education.) But they're fighting an educational system which is inherently opposed to supporting critical thought, which fires effective teachers who refuse to work in the correct ideological framework.

[XorNot]

The point I was driving at is we still end up with people who don't understand basic algebraic manipulations. So the issue isn't "you never did math", the issue is we're failing to get people to understand it.

The converse side of the idea - which I'm presently experiencing - is to definitionally heavy and try and show the proofs for all sorts of things. From my personal experience, this is equally as bad - I have real difficulty following proofs, where applying the results of said proofs is straightforward - easier to memorize, and apply, and slowly from that work backwards to figure out what the ramifications are elsewhere. But that's a process which takes years - I have 1 semester so in a practical sense memorization is the key.