I’ve not been teaching (much) over the past 5 months. Instead I’ve been doing copious amounts of reading and a heck of a lot of thinking. In having the opportunity to step back and think deeply about we do, I’ve found myself questioning teaching and thinking more of the nature of mathematics. Or should I say I’m thinking about mathematics teaching? To teach, in a general sense, doesn’t quite capture what it means to teach mathematics. As mathematics teachers we need to have that intimate understanding of how our subject can be arranged to be learned. We need to take our own understanding and mental schema of this myriad of ideas and be able to transpose this into something which can be shared with pupils.
I've focused on these topics due to some of the work of Mark McCourt who has written an excellent sequence linking these topics using manipulatives and area models. However, If you want to see that you'll need to come along to one of our sessions!
For a question such as the following, I suggest that the dominant method pupils are taught is inordinate.
ired. No division needed. The division occludes understanding, rather than supporting it.