‘Maths Talk’ project now underway
Our first meeting of the ‘Maths Talk’ project took place two weeks ago at some very posh meeting rooms in Richmond. Teachers from 32 schools in the London boroughs of Wandsworth and Merton are taking part and we had a full house at this first meeting and a very positive response. Excellent catering too.
I am not a mathematician. I have never found maths easy but I have always been interested in why I didn’t find it easy. And, as a research project, it is making me think very hard about learning and conceptual development – the unfamiliarity of the mathematics is, I think, helping me achieve that. And as research, it has raised three interesting problems that we shared with the participating teachers.
Problem 1. There is little evidence of an association between teachers’ ‘subject knowledge’ and pupil outcomes. The only subject and phase for which some good evidence exists is secondary mathematics where the better qualified in maths you are the better your pupils seem to do. This is a finding from research that analyses hundreds of other studies, studies that have to meet the criteria of a controlled experiment. There is some evidence from the same sort of research (meta-analyses) that, in the early years of the primary school, the pupils of teachers with advanced degrees in mathematics do less well than teachers with fewer maths qualifications. So for the teachers we are working with, if they don’t have advanced degrees in maths (which most don’t) this should be reassuring. But it is also problematic for us as our project has been funded by the Mayor of London and Michael Gove who both have unambiguous faith in absolute correlations between advanced degrees and better pupil outcomes.
Problem 2. There is more than forty years of evidence of better pupil outcomes in classrooms where exploratory talk, dialogue, inter-thinking, oracy, etc., is a high priority. From early studies of classroom interactions by people like Flanders, Sinclair and Coulthard, Barnes, and then recent intervention studies from people like Mercer, we know that when pupils have the chance to work out and work through ideas in meaningful, purposeful talk, they tend to learn more and do better in tests and exams. Very often this line of research is referenced to Vygotsky and, because Vygotsky was first translated and his work first mediated by cognitive psychologists, a particularly rational mode of dialogic interaction is often privileged. It is a kind of classroom interaction that is characterised by tentative hypotheses, qualification and modification, if-/then- constructions, subjunctification, etc. My feeling is that this kind of talk is a difficult ideal for adults to achieve never mind Key Stage 1 children.
So we have turned to some fantastic work from nearly 30 years ago that emphasises the importance of symbolic play in young children’s conceptual development, the importance of narrative, research that questions simple dichotomies of abstract and concrete and suggested instead mobility between discursive practices. The first set of ideas are from Valerie Walkderdine and the second from Carol Fox. From Walkerdine, we’ve taken the view that, especially for young children, concepts like quantity are strongly located in the material and discursive resources of the child and their family. For one child, the contrastive pair ‘more/less’ may be part of the material and discursive resources of the home; for another, the contrastive pair may be ‘more/no more’. These relations are profoundly different but no less conceptual and arise from different discourses. So rather than thinking of mathematics as a universal language of abstraction, it is still always socially and culturally tied.
From Carol Fox’s work, we take the idea that narrative is not a lesser form of discourse, somehow less conceptual than rational modes of argument, but that it is just as capable of representing and developing concepts and, for young children, perhaps more so. Fox’s study was of young children’s oral storytelling and from her data she was able to show how the pre-school kids were doing maths in their spontaneous stories in ways that were probably beyond them in a school classroom. ‘Josh’ was able to do addition and show understanding of place value in his stories of vampires and imaginary house sales in ways that were conceptual (or on their way to being conceptual) even if they weren’t being argued per se.
Problem 3. The third problem is how we put these first two problems together to help the teachers from the 32 schools make a difference. How can we confront the evidence that there is not a simple relationship between ‘more maths for teachers’ and better pupil outcomes? And how can we promote spoken language activities in Key Stage 1 classrooms that do not privilege decontextualised, rational modes of abstract argument but that can recognise that narrative and the kind of symbolic play it makes possible is just as (or more) likely to lead to small people doing better at maths? And how can we plan for the next two years’ work with the teachers that takes the same principles to their own CPD? Answers on a postcard …..