There's a quote that's been making the rounds on the internet and elsewhere. Attributed to Albert Einstein, it says, “Everybody is a genius. But if you judge a fish by its ability to climb a tree, it will live its whole life believing that it is stupid.” (I very much doubt Einstein actually said this, as I've never been able to find a source for it. If you know where this quote comes from, please tell me in the comments.)
I have very mixed feelings about the "everybody's different" meme in education. On one hand, it's (trivially) true -- everybody IS different. On the other hand, I think it causes people to internalize their limitations as part of their identity. "Oh, I'm just not good at art/math/writing/music." Worse, it can cause teachers to give up on certain students.
I've been on the receiving end of this. In seventh grade, I started algebra and went from getting A's in math to getting C's. After a while, I concluded -- with ample support from people around me -- that I simply wasn't a "math person". This lasted until my fourth year of college when, for some reason, I decided to take a mathematical ecology class. To make a long story short, I bombed the midterm and was going to drop the course. When I went to see the professor and started talking about dropping, he just said, "Don't do that. That would be a mistake". He then sat down with me and we spent half an hour going over what I had gotten right on the test and what he thought that meant about my thinking. Result: I got help from a friend who was excelling in the course, earned a B+, and then went back and relearned the algebra and calculus I hadn't mastered earlier. In grad school, I successfully took several undergrad math classes and a large part of my research is now theoretical. So much for being a fish!
The fundamental flaw in the "fish trying to climb a tree" metaphor is the hidden assumption that people have fixed abilities and talents. But this is just wrong. My favorite example of the flexibility of our abilities is John Mighton, who was interested in both math and creative writing as a child, but was discouraged from pursuing them by some low grades and the belief that he would have to have been born a prodigy to do well in either field. Eventually, though, he became an award-winning playwright by deliberate practice, following the example of Sylvia Plath. While trying to make ends meet in theater, he started tutoring kids. His first student was a teenager who had been told by his teacher that he was too dumb to do well in math. (We'll return to him later.)
Mighton ended up creating a program called JUMP Math that allows kids who were far working below grade level to catch up and excel. Even more remarkably, when used as a full-class program, JUMP both increases achievement and drastically shrinks the gap between "stronger" and "weaker" students. It does this by combining careful step-by-step instruction with a strong emphasis on developing self-confidence.
Confidence in one's ability to learn is absolutely critical to learning. My grandfather, a retired engineer who was appalled at my calculus grades, once offered to pay for a tutor for me -- and I declined because I didn't think it would do any good. When a student doesn't believe their work will pay off, doing the minimum amount of work necessary to get by isn't laziness but a perfectly rational strategy. Why waste your time? Conversely, experiments have found that kids who are taught that intelligence can be developed with practice do better in school.
The bottom line: Most of us have the ability to excel in many fields and they can inform each other. While letting kids have time to explore their interests is certainly valuable, we should err on the side of educational breadth. So let's work to find worldchanging ways of teaching that work for everyone!
Oh, and about John Mighton? He ended up going back to school and earning a Ph.D. in mathematics. So did his first student.