Before I got older and wiser, I used to see mathematicians as cold, passionless logic machines. I couldn't conceive of an emotional connection to all of those rigid numbers. It took a lot of reading in science before I realized that math can do exactly what Efrique describes:
A really clever manipulation (I can't help but think of them as "tricks") or an inspired substitution that makes a difficult problem easy can produce a tingling sensation up the back of my neck and head. A particularly beautiful piece of mathematics can, on occasion, move me almost to tears.
Then there's joy and delight. On occasion I have had the fortune to look at some neat, if modest, just-derived result and wonder if perhaps I am the first to have ever seen it (it is, obviously, rarely the case that I am - it is not unusual to find that my result has been tucked away in some mathematical corner for many decades ... on one occasion I found I had been beaten by Gauss - but the thrill of discovery is there all the same).
Mathematics can be intensely emotional. I've read mathematicians talking about math with the same passion and thrill that I experience at discovering a tremendously well-written sentence. When I understood enough physics, I finally caught of echo of the excitement and awe E = mc 2 elicits. It truly is dramatic, and beautiful.
I think that's what's missing from so much science and math education: emotion. Grammar suffers from the same disease to a lesser degree. We get so caught up in teaching kids the foundations that we forget to keep them excited about the edifice that could eventually arise.
If you're learning by rote and told there's only one possible right answer, you're not likely to understand that strong, rewarding emotion is possible. When I tutored English, I invariably discovered that all the joy'd been sucked out of it for the struggling students. They were so beaten down by rules they couldn't feel a damned thing. That had killed their motivation to master those rules to the point where the rules vanished and the beauty began. I'd usually spend a few sessions pumping them up: English is easy, it's exciting, it's really really awesome!! Once they could feel, they could punctuate. And when they could do that, I'd show them how to transcend the rules, which really got 'em going.
We need something like that with science and math. We need teachers who can make it seem simplicity itself, too exciting to stop even when it's tough, and so dramatic that you're determined to keep slogging right through to the breathtaking vistas at the top. We need drama. We need passion. We need blood, sweat, toil and tears. We need, in a word, to make it emotional.
Rationally emotional, o' course. Let's don't get carried away. But you can be utterly rational and beside yourself with emotion at the same time. The two states aren't mutually exclusive. Ask Efrique.
When people understand that, I don't think they'll see science and math as esoteric arts for emotionless experts anymore.