This is what I have been doing and what we should all be doing according to my ‘extensive’ reading anyway.
One of the first texts we had to read for MaST was chapter 1 of Primary Maths, Teaching for Understanding by Barmby et al. The thing that struck me most was the stress on how important it is for connections to be made with what children already know. It seems obvious but I wonder how many teachers really take that on board, especially bearing in mind the conversations that I have had with secondary colleagues in the past!
The idea of making connections for children to really understand what is being taught comes up again and again in my reading. Earlier this year in Derek Haylock and again this week when I read Mike Askew’s article on effective teachers of numeracy. He makes the point that the most effective maths teachers are often those who make connections explicit for children.
This seems to me to tie with Skemp’s work on instrumental v relational understanding. If there are no connections with what the children already know then the learning can only be instrumental, or rules learned by rote.
As I said earlier, it seems obvious but how many of us really make all the connections that we can? And are the connections that we make the ones that the children need? Thinking about this emphasis on connections reminded me of something else that I had read and I had to spend half an hour tracking it down.
In her book The elephant in the classroom, Jo Boaler looks at the differences between more and less able pupils (or the pupils that have been labelled as more and less able). In Chapter 7 she looks at ways of working by different groups of pupils when solving problems. The different strategies used by less able compared to the more able is startling. None of the less able were able to solve calculations by using derived facts. None of them could use known facts to derive others that might help them to perform their calculations.
This seems to link directly with the emphasis on making connections when we teach. If we don’t teach those children to make connections with the number facts that they already know and to help them to be able to manipulate those facts, then we are leaving them to struggle unneccessarily. Boaler makes the point that the maths the lower ability children are doing is actually a more difficult subject than the one done by the higher achievers. And so the cycle gets reinforced that maths is a hard subject and can only be done by clever children!
We need to make sure that we always start with what the children already know. However sometimes that place is not always where we think it is.