First Day Plan: Math teaching as Improv

I had a job interview for a summer program a few years ago, and as part of the application I had to submit a lesson plan for a random day in the middle of the summer.  I chose to do a lesson I had successfully run in a few classes exploring Conway's Tangles.  I carefully wrote out a step-by-step plan (3 minutes on this, then 5-7 minutes on this, and so on.)  Then it got to a point in the lesson where I needed some student to have a flash of inspiration -- it's never failed to happen, but I didn't feel like I could write "Student has a flash of inspiration (2 min.)" on my lesson plan.  So I became vague and unclear as to what would happen next, and my lesson plan meandered from there.

I realize now that the lesson plan communicated at best little information about what happens in my classroom, and at worst a disorganized teacher.

I am not disorganized, even as my classroom can sometimes seem chaotic.  I know where I want to start, and I know what my goals are.  What happens along the way is often a mystery to me until it happens -- not unlike an improv performance.  I've seen many teachers write of the importance of "yes, and..." in a classroom, and I will add myself to those voices.  If I am offering up "yes, and..." it means students are guiding what we are doing.  I need to be flexible and quick on my feet, but those are my strengths.  (And also my weaknesses -- sometimes "flexible" becomes "taking a random unnecessary tangent that distracts."  I continue to grow and learn, though.  But, predictably, I digress.)

So to my first day plan. It was inspired by this vSauce video .(The relevant section starts at about minute 14).

I'll shuffle a deck of cards (at least seven times) and claim that never before in the history of cards has a deck been in the exact order I've created.

Students are to agree or disagree and defend their answer.

The goals:

• Discover that n! describes the number of ways to order n things.
• Review of scientific notation.
• What mathematical rigor looks like.
• How to accept something that violates your intuition.
• How to resist using the internet to solve problems.

Students will work alone, then in groups, and then we will .... improvise!  I know that kids will stand and move and talk to different people and have cards and whiteboards available if they want.  In the end, each student will have to write a summary and defense of their answer using mathematics.  Our first class period is 30 minutes, so we'll see how far we get.  I suspect we can finish sometime during the second class.  Then, we're off!