As someone who took both a stats and newtonian physics course before taking a calc course, I wish I hadn't. It was a waste of time. They can't explain why you use the formulas they do, they have to just say "trust us, and be able to regurgitate it on the exam". For me, learning means developing an intuition, which means resolving/building new facts from other facts I have already accepted. Being handed seemingly random formulas to memorize goes directly against this. Yeah, I can use my car without knowing how every piece inside works, but the moment something goes wrong, I don't know what to do. I would never say I am car-literate, and someone who hasn't taken calc cannot be stats-literate.
But how would you "motivate" the formulas without knowing where they came from? Why is this the formula we use and not something else?
To go back to the car analogy, I know why I need an engine, you might even say I know how to use the engine, but if the engine dies or I want to use the engine for some other purpose, I'm not equipped to do anything.
I don't have "literacy" with engines, I have rote memorization of a series of steps. I don't have enough information to know why the steps are what they are, nor could I know under what conditions the steps should change or what they should change to.
Sometimes they'll need formulas they don't understand (can't motivate) for doing work things?
Then what? Are they going to incorrectly use anther one, a wrong one, because they understand it better?
(Searching not where one lost the key, but where the light is stronger)
Hmm, I wonder if you studied stats? It sounds as if you studied lots of math.
I did long ago, mostly forgotten, and, hmm, I don't think there's a single real life useful probability function one can understand, without knowing the underlying calculus? Except for understanding in the sense of trusting the teacher.
