Wednesday, March 26, 2008

Allegories about Arid Mathematics Teaching

How is current mathematics teaching like teaching music without instruments or teaching art without using blank canvas? Find out by reading Paul Lockhart's Lament.

I found this on Vlorbik on Math Ed, where one of my posts was featured recently. You can also get a sense of how well it resonates with the Kitchen Table Math crowd. It also explains many of the challenges, including teacher content knowledge, that are being explored there.


David said...

I've just read part way through Paul Lockhart's Lament and I can't help wondering "Does anyone actually ever teach this way anymore?". (the bit about memorising the formula for the area of a triangle) Seriously, do they? And if so, where are they? I've never met any of them, fortunately, at least not to my knowledge. All the maths teachers I've met understand, nay, appreciate the wonder and beauty of mathematics and try very hard to communicate this to their students. You know, the other day I had to teach IB students to use the normal distribution, and simply giving them the formula was a weird experience. I don't do that. I had an almost physical reaction to this, it was so uncomfortable.

My classes are always about exploring things. No one is allowed to use anything unless they have some idea of where it comes from. I don't expect everyone to be able to prove everything (depends on their level, really) but they do have to have been able to follow through an argument and agree, at some point, that it makes sense.

I can't contemplate teaching any other way. The teaching mentioned in the Lament is mythical to me, like something out of olden times when Gods walked the Earth and people burned witches. Does this really still happen? Who teaches this way? How do they get away with it?

I'm sorry, I'm bemused. This feels to me like it's the perpetration of a myth, like some sort of urban legend.

Ross Isenegger said...

Hi David,

Thanks for your comment. Perhaps this kind of approach to Math teaching is a peculiarly North American phenomenon. In my experience, for many teachers, questions like "Why does it work?", "How is it related to other topics we have studied?" and "What are some other ways of doing it?" are not natural at all.

The area formula for rectangles, triangles and trapezoids are archetypal examples of this mindset. Area is length times width. End stop.

On this side of the pond, teaching is telling.