What's a derivative? (Where does it come from and what is it used for?)
(aka my way of seeing if they're paying attention in class or just using a formula)
This girl's answer:
A derivative is a simplified form of an equation that can be derived from the original and can be used to find the answers for different equations.
She had a lot more issues than this... every single one of her difference quotient expressions had x -> 0.
This girl also cried after my first semester exam. Apparently she didn't learn a lot from that experience.