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.  

Big Al Overwijk

Starting a blog is a rather daunting task.  It feels a bit like stepping off a cliff.   A fool's endeavor? April 1st seems like a perfect start date.  

This week I received a nomination for Ottawa's Capital Educators Awards.  I am flattered by the nomination and wish to thank my principal, a woman who writes a mean reference letter.  But what delighted me the most was the fact that two of my colleagues were also nominated.  The first is a former student of mine who teaches in an alternative school.  There is nothing better as a teacher than knowing that your students are making a difference and that you might have had a small part in their success.  

Another nomination was for my partner-in-crime Al Overwijk.  'Big Al' is a gifted teacher and I am happy to say that I had a part in his latest path (as he did mine).  When the present math department head (me) asked the former department head (Al) to teach the grade 10 applied math course, Al agreed.  The course is considered by many teachers as one of the most challenging assignments.  Al is an experienced, dynamic teacher so I gave him the task.  After teaching the course three times Al was exasperated and was ready to hand the course off to someone else.  It was the end of first semester.  We opened a second section of the course.  I took the new section and convinced Al to stay on to revamp the course together.  With nothing to lose, we took a very different approach.  We often met at lunch time and figured out things as we moved forward.  We stopped thinking about teaching and emphasized learning - learning by activities - activities that spiraled deeper and deeper into the curriculum.  No more units.  The activities were not limited to any particular curriculum strand.  We had some activities that touched half the curriculum expectations.

The results have been remarkable as suggested by our board-wide exam results and with reduced discipline problems.  Over a number of semesters Al has honed his grade 10 applied course and has begun to transform academic math courses in this style.  He has done workshops to share his materials and success with other teachers.  Unable to respond to all the email requests, he is blogging - encouraging me to do likewise.

Last May I was sitting in a workshop at the OAME annual conference.  Queen's University Math Professor Peter Taylor was explaining the virtues of teaching Calculus though problem solving.  A colleague, who was sitting at the same table with me, asked "Doesn't Al teach like this?"  "Yes", I answered.  A moment or two passed and a second colleague said, "Don't you teach like this too, Bruce?".  Feeling cheeky, I responded with, "I am Dr. Frankenstein, Al is the Monster." 

You can read more at Al's blog http://slamdunkmath.blogspot.ca/

P.S. I hope to use this space for professional reflection as a high school math teacher.  I will post ideas and materials that I have used that worked or didn't work.  I hope to learn by sharing my thoughts and experiences and share my learning.