Upon thy distemper sprinkle cool patience…
I found very little to disagree with in either piece. Skemp’s argument for relational understanding and Meyer’s wanting maths to involve learners in setting and solving problems (rather than filling gaps with pre-packaged information) come together as a great manifesto for modern maths teaching.
But, what needs to be done to bring about a brave new world?
There is something about the tried and tested. I love a rule. I apply it and the right results comes out*. But it is a bit like modern Lego sets where – with detailed instruction – you build the Malibu power boat and it looks exactly like it should. But a few months later, with the instructions recycled and a few bits missing, it is impossible to recreate. Instead it goes into the breakers’ yard where, with the knowledge you’ve built up yourself, it becomes a castle, a playground, fighter space ships…..
So step one is moving beyond the tried and tested. I think ‘manipulatives’ (something that I was just introduced to at Hastings Academy) could be an important part of bringing about change . Using physical materials to develop understanding by trial and error and allow self-directed individual or group learning is, to my view, an incredibly powerful (and fun) way of teaching**.
What else needs to change?
Confidence to bring about such a change in teaching method. The idea of having more free-flow lessons where learning is not necessarily directed feels a bit scary. Questions that I am asking myself are: what would I do if it got out of hand? what would I do if it didn’t? how patient do I really need to be? how do I bring it all back together to make sense of all the learning ? But these barriers are surely ones in my gift to solve and – in truth – don’t feel that different to my general concerns about leading a class.
The other barrier is surely time. In my (short) experience I am amazed at how quickly an hour disappears and the pace at which a lesson has to move to fit into its time slot. I really cannot see how a teacher can introduce methods based on Skemp’s and Meyer’s thinking with such short and staccato bursts of learning. So is the solution longer lessons or – more feasibly – planning learning to span over a number of lessons? One to keep reflecting on.
*this is pretty much the way that I was taught maths and this world still seems to exist. As I struggle to re-remember lots of long forgotten mathematics, I am struck by resources that still tell the reader the rule. Pleasing at first but then I quickly feel as if I have lots of disconnected knowledge, insecure in my ability to explain it to others.
**At this point I’d like to mention how much I enjoyed Meyer’s on-line games. Dutifully following Task 2 instructions, I thought that I’d better give them a cursory glance. An hour or so later I was still trying to improve my tracking of the human cannon.