> And coming in having a fuzzy understanding of acceleration is fine, because calculus is where you learn what acceleration is.

Really? Because I learned what acceleration was a few years before I'd been introduced to calculus.

> If you're taking calculus but you don't want to learn what acceleration is, then I don't know what you're even doing.

Your statement highlights very well the point I'm trying to make.

> Even if you're doing it for finance or medicine or something, velocity and acceleration are still the most useful and intuitive ways to introduce derivatives.

I didn't point it out in my earlier comments, but I learned basic calculus in the 10th grade by two very simple (non-physics) concepts:

The derivative gives you the slope of the tangent (and I had already been taught a year prior that the slope of the tangent is the "point" rate of change). We'd already studied the relevancy to physics (or other applications) of getting the slope of the tangent in prior years (in physics courses, which is where one should be introduced to it). So I definitely did not need a math textbook to give me context.

And the integral gives you the area under the curve. I did not even need a physics application, as I'd done years of geometry up to that point to understand the concept of "area". Again, the application to things like energy was appropriately left to a further physics course.

BTW, I never said providing context in a math book is a bad idea - just that it'll help some people and hurt some people by the book's choice of context. If I were doing 1:1 tutoring, I would definitely try to provide context from the real world. The difference is that I can try to identify the relevant context for the particular student.

That alone was sufficient in motivating me to learn more. Of course, you can go from there to computing volumes, etc.

You're speaking from the perspective of how you happened to learn things.

>> If you're taking calculus but you don't want to learn what acceleration is, then I don't know what you're even doing.

> Your statement highlights very well the point I'm trying to make.

But you're missing the point I'm making. Which is that sometimes there is a simply a clearest way to explain a subject regardless of what a student is interested in.

Saying you want to learn calculus but you're not interested in acceleration is like saying you want to learn 20th-century European History but you're not interested in WWII.

I've done my share of teaching. I greatly appreciate that you need to make things relevant to students. But at the same time, you just have to teach what the thing is, using the time-tested analogies that actually work to educate students.

If a student doesn't want to learn calculus because they have no interest in what acceleration is, then I don't think they want to learn calculus at all.