I promised myself that I would get my head around some of the reading that we’ve got to do over this holiday. So far I have tackled Chapter of Primary Mathematics – Teaching for understanding by Patrick Barmby and others as well as a journal essay by John Mason ‘Structure of Attention in the Learning of Mathematics’
I have bought the book by Barmby and it is a very accessible text with lots of practical applications to maths teaching. Chapter 1 is all about how important it is for teachers to make connections for children. If maths learning is unconnected to what they already know then they will never develop real understanding. He talks about how important representations are in helping children to make these connections.
This builds on the Richard Skempe article about relational and instructional understanding. Here Barmby is explaining ways in which relational understanding can be achieved. The chapter struck several chords with me as it linked with previous inset we had in school about neural connections helping children to learn.
The John Mason essay was much harder to get to grips with and understand. Possibly because it wasn’t making any connections in my brain????????
He talks about how attention is structured at 5 different levels. At first sight these seem to be an order that your mind develops but then it appeared that all the levels are necessary for real understanding.
Points that I did manage to pull out were the ways in which learning builds upon prior knowledge, making further distinctions and the importance of not just using one method to teach. A task can be presented in many ways to suit specific students. This relates back to Barmby where he says that a variety of representations are necessary to enable pupils to fully develop their understanding of a concept.
I think that I shall have to revisit the Mason essay at some point in the future to see if I can make more sense of it.