Here's one way that this could be transformed into an exercise: Have the instructor read a proof (or a fake proof) from, say, formal logic or set theory, and ask the students to follow along step-by-step using a simple example (a la Richard Feynman). Then, at the end of the proof, the students have to explain whether the proof is or is not valid using their example. E.g.:

Instructor: forall x. p(x)

"Ok, let's see, 'all ice cream cones are delicious'."

Instructor: not (not (forall x. p(x)))

"It's not true that 'not all ice cream cones are delicious'."

Instructor: not (exists x. (not p(x)))

"Therefore, 'there is never going to be an ice cream cone that is not delicious'. Valid!"