So, I completely agree with this, though I think it misses a few points. I don’t want to go into it here, though.
Lets say I totally agree. Then what?
I can’t just pick up a random calculus book, because that would not let me use my programming skills. Or, at least, I feel that “tension”.
Project Euler is great, I guess, but it feels more “fun” than useful.
So, where to next?
What’s wrong with not being able to use your programming skills?
What points do you think it misses?
Well, I’m not sure that wrong is the correct word. “Less optimal” might me more on target.
When I took math classes, the ability to “visualize” problems really helped in my understanding. I really liked working with Maple, even though it was painful (because we had no good resources on program manipulation). I would love to do the same, today. I think a curriculum that is “designed” around the use of a computer to understand and math would be really interesting.
I have that problem a lot, and it’s one of the reasons I’m ill-suited to school. I usually learn better by actually doing useful things. However, I see mathematics as a language, and time has to be spent learning the “primitives.” Whenever I start learning languages, it can be difficult to get started because of some of the initial time it takes to get enough of the basics to do anything really useful. It takes on average at least a month before I can even hold a modest exchange with someone in whatever language assuming a solid effort. I can do “toy problems” (“hi”, “my name is”, etc…) in the meantime, but I find there’s a lot of precursor knowledge that has to be learned first.