Of course, any attempt to improve math education gets screamed at ("New Math! Common Core! Blah!") and the whole thing just becomes political.
Another problem is that the discovery learning approach can lead to some horrible failure modes for math. I've seen cases where an hour of proper instruction can go further than a whole term of trying to see if they can find it out for themselves. Case in point: the rule of three. If 10 apples cost $20, then 5 apples cost ___? You can spend ages thinking about what it "means", or you can learn that you write down a 2x2 table, multiply across the diagonal and divide by the number in the corner.
given enough time to read and debug, I suspect I could eventually figure out how any piece of code worked. but if you give me a book and ask me to pick a good topic for an essay, I might not finish before the end of time.
A lot of capable people are mathphobic, and it's strange to watch (as someone who took naturally to math). The expressions on the page (or the attempt to produce those expressions from a model in their mind) causes them to seize up. It's like watching an anxiety attack happen. Something about math (the subject, their experience when taking the courses, whatever) has left them with a severe discomfort or level of fear when dealing with it.
Computers illicit the same response from many people, regardless of background, education, level of experience with computers. They develop an understanding by rote, or with a rudimentary (but likely totally wrong) mental model. As soon as something is slightly different, the fear or discomfort rises and their mind blanks. They cannot figure out the next step. At an extreme, a color changes and they think it must mean something, but really it's just that that control is now "transparent" (pulling in the background color but blurred) and they happen to have a bright red object behind it, when normally it's a more neutral gray or blue. For some it's that things are no longer in the right place or that display differently (think of the changes in the Windows start menu over the decades). They'll have different thresholds, but once they hit theirs they cannot proceed without great difficulty.