You know what part of the problem is? All of the "reforms" to get students ready for technology, and the push to test certain skills so young create a situation where context is not developed. Lists of formulas are given to students; they don't actually memorize or develop much.
The good students today are fabulous technicians. They don't, however recognize things in different contexts or know how things connect.
My favorite is traditional Trigonometry...just develop all of those wonderful concepts by starting with the right triangle. My experience is most teachers out there today don't know the subject. They just hand students lists of formulas, many very complex, and have them plug in values and get results. It leaves them really deficient in recognizing and developing things.
It's very simple: they cannot solve difficult problems. They cannot do any task that requires them to put together 2 or more concepts. And the reason they cannot do this is very simple: Everyone gets good grades. And they feel good about themselves. The teachers tell them exactly what will be on the exams, they memorize that, and regurgitate it.
BTW: Euclidean geometry is no longer taught in many high schools. It just isn't "useful." Which I find ironic, considering a few very famous lawyers, such as A. Lincoln and J. Garfield knew Euclid by heart.