This is deeply incorrect. If it were correct, mathematics education would have to begin with set theory and physics probably could not begin with F = ma. Our p

This is deeply incorrect. If it were correct, mathematics education would have to begin with set theory and physics probably could not begin with F = ma. Our pedagogy is cumulative but it is tellingly built on some hand-waving and "you'll have to trust me on this part". This means that we can take a different approach to it pretty easily. For example, why does set theory often wait until college and probability until... never? These concepts are much more analytically useful to the average person than is the quadratic equation (which you can look up as needed) or (heaven help me) angle-side-angle. We teach math through loaded down problem sets instead of heading right after the most conceptually useful (and therefore) meaty chunks first. We don't even teach children mathematically-grounded science for the most part; that's a missed opportunity to take those problem sets and make them analytically powerful and memorable.