Well, the way I understand the US system is that all children basically get the same education, and they are divided only by grades. In the NL and I think other European countries also, children go in separate highschool tracks depending on their performance in elementary school. A child that exhibits weakness in logic/maths/puzzle solving in the last year of elementary will likely be recommended to go into a vocational track and only ever receive basic maths education unless they opt in to a higher education track afterwards.
In the NL often these tracks are even in separate schools, but always separate classes. So my sister went to a different highschool than I did because I was showing more proclivity towards scientific education. After her highschool if she wanted she still could've opted for a track that would qualify her for scientific education, but since she had a preference for arts she went to an arts academy instead.
FWIW, your understanding is incorrect. While true that in US schools, all students are expected to complete a full 13 years of schooling (Kindergarten + 12 grades), students receive individualized courses of study. By high school, there may be 3-4 levels of instruction for Math ranging from remedial to college-bound, to college-level coursework. Additionally, non-college-bound students at most schools have the option of taking classes that prepare them for more traditional blue collar work (like automotive repair, etc) and often students have the option to go to a different school more aligned with their talents/skill level.
The primary difference between US and European education is in the US taking particular courses of study is the decision of the student/parents and not of the state.
Yes, it's similar in Belgium. But, derivatives are really considered basic knowledge, so I doubt there's a track you can pick in Belgium that does not expose you to this. I will check.
update: combining www.onderwijsdoelen.be and the distribution of students across the different tracks, 69% of the students are required to be exposed to this.
In the NL often these tracks are even in separate schools, but always separate classes. So my sister went to a different highschool than I did because I was showing more proclivity towards scientific education. After her highschool if she wanted she still could've opted for a track that would qualify her for scientific education, but since she had a preference for arts she went to an arts academy instead.