“F is not prime because 151 and 157 are primes and the set of prime numbers is not closed under multiplication.”
Mathematics needn’t be fancy
Dr. Chris Brownell

Maybe I am a product of said eduction system, as I would probably have gone for this one rather than the simpler alternative you propose (assuming I had remembered the proper terminology, that is).

I guess the desire to speak in math language rather than plain English is that it partially lessens the worry to say something inaccurate. When interacting with my colleagues in physics, it matters a lot and often shows who has a proper understanding of the material and who does not.

Yet, the simpler the math language, the better.

So, on second thought, I think I agree with your premise and ended up nitpicking on the specific examples.

So to answer your question, the best way is probably the obvious one. Clearly explaining your concerns and lead by example in your own lectures. On an exam, explicitly asking for the simplest explanation possible, with possible bonus points.

And if the students can carry on that attitude in real life, that would be even better. Weed the posers from the real ones. If you can’t explain it to a 10 year old in simple terms, you probably don’t understand it well either.

There must be a Feynman quote related to this somewhere…

I should probably rewrite these few paragraphs into one clear thought. The irony.