when a freshman college student tells me that he was always good at math, it translates to “I was very good at following obscure steps to manipulate mysterious symbols, without any real understanding of what they mean.”
The most common complaint I hear about undergraduate students is that they aren't able to blindly manipulate symbols, and consequently get hopelessly confused when they have to deal with "unintuitive" concepts.
That's who the current system panders to, because they're the ones who scream loudest when it doesn't. And they find it morally offensive if you ever ask them to solve a problem that isn't extremely similar to an example they've already seen.
And they're the ones who think they're "good at math". That's who highschool caters to because that's what standardized testing caters to and that's what the noisiest parents and students want... and teachers that have higher ideals are swimming up-stream if they want to actually challenge the kids.
High school teachers, please make your students manipulate mysterious symbols more.
It's funny because when that article started I was totally on board with him, then we got there and I just laughed.
"The trick to flying is to be able to throw yourself at the ground, and miss."
The quote does appear in HHGTG.
[edit: I don't have a copy of the original radio scripts on hand, but from the book:
"The Guide says there is an art to flying," said Ford,
"or rather a knack. The knack lies in learning how to
throw yourself at the ground and miss." He smiled
weakly. He pointed at the knees of his trousers and
held his arms up to show the elbows. They were all
torn and worn through.
"I haven't done very well so far," he said. He stuck
out his hand. "I'm very glad to see you again, Arthur,"
he added.
-- Life, the Universe and Everything
Isolating a variable is, in some sense, a blind manipulation, but so is, "I see a plus sign, that means I have to subtract". As a first thought about a problem, they represent very different understandings.