Calculus really should be thought of as dependent on linear algebra (the derivative of a function is the best linear function that approximates it; it just happ

Calculus really should be thought of as dependent on linear algebra (the derivative of a function is the best linear function that approximates it; it just happens that in 1D the only linear functions are multiplication by a single number). Linear algebra seems like it would be far more useful than algebra 2 (things like conic sections?), trigonometry, and "pre-calc". It's possible that you could do something like algebra (middle school)->geometry (maybe introduce the notion of a group here and focus more on symmetry and not so much on figuring out the missing angle/length in a complicated diagram)->linear algebra->probability/statistics. Concurrent with linear algebra, have kids learn calculus in physics class. After physics 1, they can do chemistry and/or e&m. Do vector calculus in e&m. Basically trim all the useless stuff out of high school and add the first couple semesters of college instead. Offer analysis as an elective after linear algebra/physics 1, and put a proper account of the n-D derivative and things like the Newton–Raphson method there. Obviously that's a STEM bound curriculum, but at least in my school growing up, you only needed algebra 1 and geometry to graduate, which the honors kids did in middle school. So I assume any curriculum more advanced than that is for STEM bound kids.