We teach it like that because we learned it like that.
We also teach it like that because states have various standards with pretentious names and acronyms ("Essential Academic Learning Requirements" = EALRs [1]) that require students to have specific bits of knowledge at specific ages. This means that, instead of students exploring various mathematical subjects in parallel, they're stuck going through them in exactly the order presented.
I remember being in a room full of math profs and TAs discussing how to get more students interested in becoming math majors. I suggested a 100-level number theory course, with the rationale that it's simple, accessible, mathematically interesting, and makes it clear that there's more to mathematics than the "progressively-harder calculus-based classes" (up to DiffEq) most hard-science majors end up taking.
We also teach it like that because states have various standards with pretentious names and acronyms ("Essential Academic Learning Requirements" = EALRs [1]) that require students to have specific bits of knowledge at specific ages. This means that, instead of students exploring various mathematical subjects in parallel, they're stuck going through them in exactly the order presented.
I remember being in a room full of math profs and TAs discussing how to get more students interested in becoming math majors. I suggested a 100-level number theory course, with the rationale that it's simple, accessible, mathematically interesting, and makes it clear that there's more to mathematics than the "progressively-harder calculus-based classes" (up to DiffEq) most hard-science majors end up taking.
[1] 252 page, 8+ meg pdf: http://www.k12.wa.us/Mathematics/Standards/K-12MathematicsSt...