Opening up to new ideas

This is something from my clog or computer log.  A clog can be defined as a blockage which stops things from going out in the pipe.  I wrote a few ideas over the last year before I was brave enough to actually post anything on-line.

Unlike many classrooms where activities are used mostly to introduce a topic or to consolidate a concept, most of my math lessons are centered on activities, a picture or a news article. My colleague Al and I are often asked where we get our ideas from for our activities. That's a good question.

I remember Al looking at me one morning with wild eyes.  He took a plastic tumbler and rolled it on the floor.  “Fantastic, isn't it?”  It immediately made me think of the newbie mail room employee played by Tim Robbins in The Hudsucker Proxy.  He proudly shows off a circle drawn on a piece of paper that he pulls out of his shoe.  

“Take a look at this sweet baby. I developed it myself.”  Without giving the movie's plot away, the Robbins character rides his idea to the top of the corporate ladder.

When Al rolled his cup on the floor and it formed an arc of a circle, he saw all the mathematics in an activity that could span a number of days and a number of curriculum expectations. (Note that this was not Al's original idea but he recognized it for all its potential.)

I drove my son to his rowing practice this morning.  I had been up until midnight to submit a grant proposal and I was still buzzing.  I figured that I should start my day with a run to settle myself out a bit.  As I was running though a soccer field I noticed that the crossbar of the goal was reinforced with a triangular support. 

Within seconds a classroom inquiry-based lesson on linear relations and quadratic functions had formed in my mind. 

We often complain that our students are blind to the obvious in our lessons, often giving us bizarre answers that have no foundation in reality.  Their understanding of mathematics does not extend beyond the calculator results, the textbook examples or the walls of the classroom.  Yet we teachers are similarly plagued.  Our mathematical thinking is also confined in the pages of a textbook or the limits of a classroom activity.  If we can turn our backs on the so-called safety of our sanitized material, we can begin to see mathematics which surrounds us. 

We sometimes hear about how a song somewhat inexplicably came to an artist in a moment of brilliant clarity. I once heard that Gordon Lightfoot wrote the haunting Bitter Green during a London cab ride.  I believe that music is a very different experience to a composer than it is to me.  I enjoy listening to music – consuming it somewhat passively.  A composer defines the world through music and they hear it in places that I tend to be oblivious to.  Yet there was a time in my life I did make up my own songs.  I had no car radio and it was a 2 hour drive from school to home.

If we want to hear and see mathematics, we have to start turning off our usually feeds and start listening and looking for it. Once you stop being a consumer of ideas, you can begin to create your own ideas.  That is true for teachers and it is true for students.  Given the chance, students will see and create mathematics to explain the world around us.  We owe it to our students to stop feeding them with our ides and allow them the struggle and bliss of formulating their own ideas.  We owe it to ourselves.

Where do my ideas from? They come from anywhere and everywhere.  I just need to open myself up to it.  Later in my run I ran across an overpass and glanced down at the railway tracks that converged toward a vanishing point.  I immediately had a lesson on ratio and proportion.