I wasn't aiming to criticise the particular set or scope of topics taught at each stage, more so the fact there's no provision to ensure students are aware of what branches of mathematics even exist. There's no formal introduction or grounding or broad strokes.
It's like teaching science where there's no innate notion of biology, chemistry and physics as three separate disciplines... or teaching history without putting everything in its place on a timeline and your students end up not knowing whether Tudor times ended before or after the Ottoman empire fell.
It's the big picture exposure that I think maths lacks, and I personally never bothered to step back and actually look for that big picture until I was already in my 20s. The way maths is taught makes you feel like it's suddenly going to open up, but all that actually happens is you follow one branch.
If you took additional math along with basic/elementary math, they do go into more detail about the branches of mathematics. There's also further mathematics and combined mathematics, both are A level subjects.
I think basic math focuses more on arithmetic than math theory, which could explain your frustrations a little.
It's like teaching science where there's no innate notion of biology, chemistry and physics as three separate disciplines... or teaching history without putting everything in its place on a timeline and your students end up not knowing whether Tudor times ended before or after the Ottoman empire fell.
It's the big picture exposure that I think maths lacks, and I personally never bothered to step back and actually look for that big picture until I was already in my 20s. The way maths is taught makes you feel like it's suddenly going to open up, but all that actually happens is you follow one branch.