Agree about the Elements. I was once enrolled in a small class that proved all of the props in order. For a given meeting, a set of props were assigned (fewer and fewer as they got longer and more complicated), and a student's name would be randomly chosen to prove the prop at a chalkboard without the book or any aides-memoires. One did not have to reproduce Euclid's proof exactly. We quickly learned the value of (a) making mistakes, and (b) being able to think things through logically. It was a transformative experience for me.