For example, I gave an exam earlier today with a problem that ended in the sentence
Use the chain rule to find $(f\circ g)'(3)$.
During the exam, one of the students asked me what the circle between the $f$ and $g$ means, and I answered that it represents the composition of functions.
Later on, another student was working on a question that contained the phrase
. . . where $V$ represents the volume of water in the tank.
and also the phrase
Given that water initially drains from the tank at a rate of $2.0\;\mathrm{L}/\mathrm{min}$ . . .
The student asked whether $2.0\;\mathrm{L}/\mathrm{min}$ is the value of $\dfrac{dV}{dt}$, and I said I couldn't help with that.
Would you have answered these students' questions? How do you decide what to do in these situations? I usually handle these on a case-by-case basis, but I'm curious if anyone has any good general rules for deciding what information to give.