This was a question on Quora. Here is an answer I wrote:
In the US, judging strictly on what I’ve seen from my time in the classroom as both a student, a teacher, and a visiting mentor of other math teachers, I find that math and science was very often taught as sort of cookbook recipes without any real depth of understanding. The recent National Council of Teachers of Mathematics prescriptions have attempted to correct that, but results have been mixed, and the Common Core has ironically fostered a weird mix of conceptual math marred by teachers being *OBLIGATED* to follow a script, word-for-word, if they want to remain employed. Obviously, if students are really trying to understand WHY a certain mathematical or scientific thing/fact/theorem/theory/law is true, they are going to have questions, and it’s obviously the teacher’s job to figure out how best to answer said questions — which are not likely to have pre-formulated scripts to follow in case they come up — and which are going to take time.
Another thing that is true is that not everything in mathematics has real-world applications in every single person’s life. I taught a good bit of computer programming (aka ‘coding’ today), geometry, arithmetic, probability, algebra, statistics, and conic sections, and in fact I use a LOT of that every week fabricating telescope mirrors to amazing levels of precision, by hand, not for a living, but because I find telescope-making to be a lot of fun and good mental, aesthetic, manual, and physical exercise. But I’m a pretty rare exception!
Most people obviously don’t dabble in math and physics and optics like I do, nor should they!
In fact, I have made it a point to ask professional scientists and engineers that I meet if they actually use, on their jobs, all the calculus that they learned back in HS and college. So far, I think my count is several dozen “Noes” and only one definite “Yes” – and the latter was an actual rocket scientist / engineer and MIT grad and pro-am astronomer (and wonderful, funny, smart person) who deals/dealt with orbital rocket trajectories. (IIRC).
In France, when I went to school there 50 years ago and in my experience tutoring some kids at the fully-French Lycee Rochambeau near Washington, DC, is that they go very deeply into various topics in math, and the sequence of topics is very carefully thought out for each year for each kid in the entire nation (with varying levels of depth depending on what sort of track that the students elected to go into (say, languages/literature, pure math, or applied sciences, etc), but the kids were essentially obligated to accept certain ideas as factual givens and then work out more and more difficult problems that dealt with those particular givens. No questions allowed on where the givens came from, except to note the name of the long-dead classical Greek, French, Italian or German savant whose name is associated with it.
As an American kid who was mostly taught in American schools, but who also took 2 full years of the French system (half a year each of neuvieme, septieme, premiere, terminale, and then passed the baccalaureat in what they called at the time mathematiques elementaires, I found the choice of topics [eg ‘casting out nines’ and barycenters and non-orthogonal coordinate systems] in France rather strange. Interesting topics perhaps, but strange. And not necessarily any more related to the real world than what we teach here in the US.
Over in France, however, intellectuals are (mostly) respected, even revered, and of all the various academic strands, pure math has the highest level of respect. So people over there tend to be proud of however far they got in mathematics, and what they remember. Discourse in French tends to be extremely logical and clear in a way that I cannot imagine happening here in the public sphere.
So to sum up:
(a) most people never learned all that much math better than what was required to pass the test;
(b) only a very few geeky students like myself were motivated to ask ‘why’;
(c) most people don’t use all that much math in their real lives in the first place.