When I started to go to university I really noticed how bad it was. At university the jump forward was really noticeable.
For example, at school they would show you a couple of simple explanations about derivative math or integrals, briefly and start with all the formulas.
At university I used to have a teacher that started with: history of mathematics, why they were invented, made a point about its primarily practical origins.
To explain things, he could most of the time come with real-life instances of application and there were much more often intuitive or geometric interpretations of the techniques used much more often even before starting the explanation itself to have an intuitive idea and visualization of what you were achieving.
After that, I noticed that to learn math, the first thing is to develop an intuitive, non-mathy idea of what you are doing and later formalize it.
At school and high school they just taught it as almost-memorize tables, apply formulas.
Talking about Spain, btw.
We should be explaining the story of maths and how it benefitted society. We should be asking kids about their interests and then showing them how mathematical tools can be used in those areas. We need to show kids how maths is tied to real life rather than just presenting them with a boring formulas to memorise.
I don't think this is the case. I think it's because the teachers themselves don't have a good grasp on "the story of maths and how it benefitted society".
There is a silly meme about asking high school maths teachers "how will we use this in life", and imo it's not because there isn't a good response, but rather that it requires a good understanding of the ways math is actually used. Few high school teachers have actually themselves used the math they teach for anything other than academic exercise. Someone trained in control theory or using physics equations can make things that appear almost magical using maths, and if they are talented, they can find a way to explain it to laypeople. However, people with that combination of talents are desired by just about everybody, from universities to companies, and high schools simply have no way to compete (not least because teaching high schoolers is a soul-crushing job for bureaucratic reasons)
Or do you mean mulitplying out the terms:
(a + b)(a + b) = a^2 + ab + ba + b^2 = a^2 + 2ab + b^2
?To put the blame on didactically seems to miss the more important factor that humans just aren’t that intelligent, save the one in a million genius who might have the intellectual capacity to learn something so difficult at such a young age.
Otherwise, I’d say our two thoughts are connected. With increasing difficulty in understanding new progress, there could be an inertial tendency to over emphasise the importance of old knowledge because it’s comforting/easier/pragmatic for teachers and parents.