> [0] Sometimes it can be helpful. Adding a relevant layer of physicality to help reason about the problem can be nice, especially in calculus.

I think you've hit the nail on the head here. I had tremendous difficulty with Calculus in High School. Everything was introduced via mathematical derivation an proof. I'd gone over halfway through the year with Cs and Ds and, even though it was almost 30 years ago, I remember the moment it clicked. I was sitting the library working on some problem about pools draining and "OMG, it's just about how fast things are changing" popped into my head. That made derivatives, area under a curve, and all of those things make sense to me.

Ironically, I ended up being the only person in my class to get a 5 on the AP test and then ended up as a EE major, which was very calculus heavy.

I think that act of translation is pretty helpful; it's not often irl math is presented nicely, but rather as a scenario that one has to solve. Translating a scenario into a math problem is practice for that, I think.

To try and inspire people, though, maybe word problems could be written to be more relevant

I always found the context in which I’m solving a word problem to be the most critical piece to accurately solving it —- and the reason they aren’t that great.

Oh, I’m taking a test it over polynomial expressions —- I already know how I’m going to solve whatever word problems I run across.

Adding the extra physical descriptions to calculus actually helped me better understand what the equations meant and represented. Definitely beneficial in some scenarios to some people

Same here - that experience is why I aded that exception.

Until Calculus/Physics though, I don't think there's much added benefit - except maybe an occasional "here's how algebra helps while grocery shopping".

One other thing I find super helpful is understanding exponential growth and decay. That gets used in quite a few places besides just the sciences

When I tutored elementary kids, physical examples really helped with fractions.

That makes sense.

Seems reasonable that as you introduce new concepts having a physical equivalent would make it easier.

This rings true to me. I was only able to get an intuition for calculus when I was able to conceive of it in geometric terms. I later learned that this was how Newton originally derived it.

This helped me to “trust” it in more advanced contexts where geometric intuition becomes exceedingly difficult.