historical order versus pedagogical order

Historical order is not necessarily pedagogical order. For example, the only reason integration preceded differentiation is because the notation needed for differentiation was lacking. Another example is General Topology. Historically, metric spaces were the first topological spaces considered, but the student is best served by a cold-turkey presentation of the general topological space, leaving metric spaces as a footnote for the students to explore on their own. Indeed, some simple things discovered very late, such as the 6-People Theorem and Kaprekar’s constant, should be presented in elementary school.
keywords: Mathematics, Calculus