I actually appreciate the way math is structured at the university level in the states. I think introductory math (calculus) should focus on use rather than add

I actually appreciate the way math is structured at the university level in the states. I think introductory math (calculus) should focus on use rather than addressing the "why", as long as it's clear that there is a "why" that can be learned later. In your example, I would hope there would be more than just a formula (i.e. some hint at justification). There are several reasons for this. 1) Misplaced rigor, especially at the wrong level, can cause students to lose interest, 2) Addressing "why" concerns does not necessarily bring any intuition on use, 3) people can develop intuition at a higher level (I'm sure you have experience using programming functions which you don't necessarily understand), 4) the economics of education (there is only so much time you can be in the classroom).