Thoughts on Teaching Math via Computer Programming

Friday was the first ever common pro-d day for all ISABC schools.  Teachers from different (and sometimes competing) Independent Schools in British Columbia all met at two different venues for an exciting day of learning and sharing.  Twitter was leveraged as a back channel tool, and notes and resources were shared via public Google Docs.  It was a good day.

I spent the morning in a session with David Wees that made me thinks differently about some of the assumptions I have been making as a math teacher.  The session title was Teaching Math via Computer Programming.  David’s basic premise  was influenced by the the work of Conrad Wolfram who claims that cranking numbers doesn’t do anything at all, but that programming teaches understanding.

We started by looking at algorithmic thinking and did an activity many computer science students have done before.  We drew a shape and then tried to write instructions so that someone else could re-draw the shape.  This process really showed the assumptions involved in giving or describing instructions.  I found myself thinking that this would be a good way to get my Math 7 students to reflect on how they communicate their work.  In my class I find that my students fall into two camps when it comes to showing work: they either don’t want to show much of their thinking at all, or they spend too much time writing long descriptive paragraphs and run out of time to do the math.  I suspect that part of the problem is that they don’t fully understand why they have to communicate their work, and how to do it in a logical way, and that a focus on algorithmic thinking activities at the start of the year might help.

We programmed Logo the Turtle to draw different geometric shapes.  I loved this activity.  Instead of ‘teaching’ students the properties of different shapes, the process of writing a simple program to draw them forces students to explore and experiment with these properties.  I might try this activity later this year.

We also struggled to figure out what function had been X’d out in the simple program below:

While I probably wouldn’t give this one to my Math 7 students I did appreciate the way it forced me to use a lot of different problem solving methods and really think about numbers.  As David said (quoting Dr. Gordon Hamilton) “the heart of mathematics is problem solving”.

My big take away from this session was the result of a discussion at the end of the workshop.  It was a discussion I have heard many times before but this time a few things became more clear in my head.  The gyst of the discussion was the tension between using technology to do calculations and the need to students to do the calculations themselves in order to really understand them.  Currently I am a teacher that only lets students use calculators sparingly.  I find that as soon as I let my students use calculators they stop thinking for themselves as much, and are reluctant to question the answer the calculator spits out.  So my approach has always been to stick with paper and pencil and ‘showing your work’ so that if the answer is wrong I can help students unpack the thinking that led them there.

What I realised during the discussion, however, was that I am assuming that the process of doing math calculations by hand is the best way to instill number sense into my students.  The honest truth is that a lot of them are tempted to learn a paper based algorithm for finding the right answer and then try to replicate the algorithm without actually thinking about what they are doing.  They have to do a lot more thinking when I ask them to estimate an answer, because there is no one right way to estimate and they have to think and apply their knowledge in order to do it.  I do teach estimation, and in my class we do a lot of modeling and problem solving, and I have had a certain amount of success improving my student’s number sense.  However, I always do this in a context that assumes being able to do hand calculations trumps all.  Now I am wondering what my classroom mught look like if I let students use calculators for the basic calculations and really focused on estimation, modelling and problem solving the rest of the time.  As David said “Using technology to do the calculations lets us use more of our brain to do the Big Math.