Hi. I'm curious to ask what methods people use to teach calculus in school. It has been a long time since I was in school, and hence I can't remember how I was taught. But, I cannot remember being taught any way apart from basically rule-based. I.e. if we have an equation f(x) = x^n then f'(x) = nx^(n-1). Note: my schooling was in New Zealand.
I've been looking at SOS Math as a resource for CompSci students to brush up on maths. I must say that for the introductory calculus section, I really like the way that they teach it, first showing how you can derive the rules for yourself, and then going onto the product rule, quotient rule, etc., once the basic process makes sense.