ive thought abt math education more over time, and have been trying to pin down whats wrong with elementary and high school math education compared to science education and higher math (not that the latter two dont have problems).
when it comes to the natural sciences, students usually learn the history behind how different concepts were discovered. biology students learn how gregor mendel's experiments led to the theory of genetics, and physics students are taught the various models of the atom that got refined over time, leading to the current quantum model. depending on the quality of the class, students may even repeat the experiments themselves. they learn the process of how these theories are produced and verified, and are thus more familiar with them.
higher math, even with its lack of intuition, at least works through the proofs of each theorem when discussing them. but elementary and high school math have neither proofs nor intuition: mathematical theorems are simply presented as is. the process by which mathematics is constructed is alienated from the majority of its students.
perhaps the culprit is the concept of intelligence (fuck eugenicists for coming up w that shit). people assume mathematical skills are "talents" ure born with (fuck christians for coming up w that shit as well) rather than the result of practice, and assume the process of inventing (fuck platonists too, for that matter) mathematics is too much for the average person, even with the guidance of a teacher.