Drawing a Circle

Can you draw a perfect circle?

I know that I couldn't, but with help from a SmartBoard game it became easier and my students loved to draw circles on the Smartboard for a great end of the year activity.

I had students put their name with their high score and by the end of the day we had a leaderboard and by the second day students were inching closer to my high score.  (Yes, I did practice for 2 hours to beat some of my students.)

It was a great competition to get students engaged and motivated in the classroom.  I hate to see teachers only using a SmartBoard as a presentation tool, it is there for students to use and manipulate.  I had some students up there for 20 minutes trying to get the tips and tricks down and finally making the leaderboard.

Check out the game here: Circle Drawing

Some of my students didn't know what the cat was there for, but it is a great reminder to tell the students how close they are to 100% like a badge.  If the students do poor enough, they get an angry cat that all the students laughed at.

Forgetting Proofs

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?