I was reading Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity by Loren R. Graham and I came across a great little quote, but we will get back to that later. The book was like Paul Erdos book The Man Who Loved Only Numbers style of quick writing. It was a fascinating book with history of some of the most famous Russian mathematicians of the 19th- 20th Century. This book reminded me of a professor that I had at the University of Nebraska at Omaha.
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A quick quote gave me inspiration to get students up to the board.
He would begin a proof at the blackboard, pause, and then say, "I cannot recall the proof; perhaps one of my colleagues could remind me." This was a challenge that the class felt obligated to meet. One student would jump up, go to the blackboard, attempt the proof, fail, and then sit down with a red face. Another would get up, perhaps a 17 year old, successfully write the proof on the blackboard while the entire class stared enviously, and then sit down. Professor Luzin would turn to that student, bow slightly, and say "Thank you, my colleague." Luzin treated the students as intellectual equals, and his teaching led them to prepare for and anticipate coming lectures.
One of them later ask, "Had Luzin [really] forgotten the proof, or was it a well-constructed game, a method of arousing activity and independence?" They never knew.
This small process of accidentally forgetting the proof or answer to an example is a great way to get students up to the board and motivated to do mathematics. I especially love the part where the instructor bows to the student and offers a sincere Thank you and recognizes the student as an equal, in mathematics you are always trying to get students to enjoy math and approve of their mathematics.
How could you incorporate this small idea of forgetting proofs in to your teaching? What benefit do you think would this have in your classroom? How do you do this now in your room?