Mathematical Reasoning

I saw this TED talk by a math teacher linked to today and I really liked what he had to say, especially about Two and a Half Men.  Well, that and how we spend way too much time focused on mathematical computation instead of mathematical reasoning.

I hated math in most of school.  However, when I taught math it was so much fun.  We used a lot of brain teasers and group problem solving.  I was especially into Louis Sachar’s Sideways Arithmetic from Wayside School because it presented logic problems and algebra in an unexpected (not to mention funny) way.  I felt like it made my students think much more than anything in the textbook.

With my kids now, we’ve been using a number of books by Mitsumasa Anno, including Anno’s Math Games and Anno’s Hat Tricks.  The problems Anno presents usually start out deceptively simple.  However, by the end, they’ve usually made me think too.  Like this section of Anno’s Math Games II, where the little elves have made a machine that changes things.  Sometimes, you can send things back through the machine.  But sometimes you can’t, and the text asks you why not.

The magic machine changes things. Sometimes, they can go back through the machine (from the right page to the left), but not this time.

I enjoy puzzles and games so I think I’ve been thinking about mathematical reasoning mostly in those terms.  The kids do lots of sudoku, we play games like SET, and do puzzles like tangrams.  I do think that can be a big piece of it.  However, I love the idea that Dan Meyer presents in the TED talk about using more real world examples.  We’ve done a lot of real world math that relates to the computational side of math, such as counting things or identifying shapes.  They’re too young for the sort of thing he talked about in the video, but now, I’m soaking up the idea of looking for more of those connections.