He had us implementing an interpreter, and step-by-step we were adding more features. Eventually we added continuations (building a CEK machine). It wasn't until I actually used the interpreter and played with it after finishing the homework that continuations started to make sense.
But they really solidified for me a year later when I took a course in operational semantics from him. We walked through the evolution of semantics in various languages through history, and had to write out the evaluations of expressions step-by-step (by hand, on paper). Then continuations really made sense.