[Animats]

There is that.

One approach to calculus is to teach it alongside Newtonian mechanics, with lots of experimental work. Those go together.

The problem is, it's too hard for high school teachers.[1]

[1] https://www.compadre.org/portal/pssc/pssc.cfm

[vlmutolo]

My public high school offered a combined physics-math course (basically two different teachers and courses that coordinated with each other), and it was definitely an excellent way to learn calculus.

We learned derivatives for mechanics around the same time as limits for calc. So everything in calc was properly motivated. I think we moved into E&M around the same time as we got into integrals in calc. We had done basic integrals in the mechanics portion of physics, but got into it formally in calculus and into trickier applications in E&M.

IIRC, the class as a whole did very well on the AP exams. I’m often frustrated by courses that don’t offer similar motivation for math concepts. I think it makes the material far more interesting.

[Animats]

Nice. Once you see how acceleration, velocity, and position are related and how integration and differentiation describe them, what calculus is for becomes clear. After all, that's why Newton invented it. Not because he liked to sum infinite series.