So, this is something that constantly comes into my mind.
During elementary school, one is thaught arithmethics, the base for every other areas of mathematics, since all of them rely, in any amount, on arithmetics. One is taught the basic operations with natural numbers, and, eventually, the set of real numbers.
At least in my country, middle school is where one starts with basic algebra, I mean, solving linear equations, coloquially called “finding x”. This is still no problem, since showing how equations work is pretty self-explanatory.
The messy part on education in mathematics starts when one reaches high school, that is the part when students ask “Why does that happen?” when they are thaught trigonometric functions, identities, limits, derivatives, integrals, et cetera. However, it is not precissely easy to answer those questions. One cannot explain the linearity of calculus operators to their students if they have no idea of linear algebra concepts such as linear transformation. Whan cannot explain the reason of integrals to a group of students if they have no idea of mathematical analysis. Then, what is the point?
I personally believe that, in mathemathics, theory is first. This means, high school should first teach formal logic and set theory (instead of having a recap in middle school topics), and notions on geometry and abstract algebra, at least, defining functions, binary operations, notions on group theory and analysis, since one can construct every topic in mathematics by knowing that, and then, reasons for concepts seen later would be known. And then, math wouldn’t be seen as “the hardest subject in school” (well, perhaps at the beginning).
Yet, again, it’s just me drabbling and ranting on a topic that will never be concluded.