Analysing Teachers’ Use of Representations in School Maths: The Semantic Wave
Dr Andy Ash
Analysing classroom teaching is an important dimension of teacher education that supports student teacher learning. Using the tools provided by Legitimation Code Theory (Maton, 2014) helps to link analysis of teaching in a particular lesson, to organising principles for effective teaching. In particular the knowledge practices of the teacher can be revealed, and this helps student teachers to carry their learning forward and apply it in future teaching. In my doctoral research I investigated how the multi-dimensional subject domain of mathematics is recontextualised into what can be referred to as ‘school maths’ (Bernstein, 2000; Boaler, 2016). I focused on how teachers use representations to support students’ understanding of mathematical knowledge objects (Sfard, 2000; Carbonneau, Marley & Selig, 2013), but the approach to analysis can also be usefully applied in different curriculum subjects. I generated data by capturing video of lessons and then conducting video stimulated recall interviews with the teacher (Lyle, 2003). It was then possible to use the concepts of semantic gravity and semantic density to analyse the use of representations in a temporal way, by tracing the ‘semantic wave’ of the lesson (Matruglio, Maton & Martin, 2013). This workshop will introduce the use of Legitimation Code Theory to analysis of classroom teaching and propose its more widespread application within teacher education practice.
References
Bernstein, B. B. (2000). Pedagogy, symbolic control and identity: Theory, research, critique. Revised edition. Oxford: Rowman and Littlefield.
Boaler, J. (2016) Mathematical Mindsets: Unleashing students’ potential through creative math, inspiring messages and innovative teaching. San Francisco: Jossey-Bass.
Carbonneau, K. J., Marley, S. and Selig, J. P. (2013) ‘A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives’. Journal of Educational Psychology, 105(2), pp. 380 – 400.
Lyle, J. (2003) ‘Stimulated Recall: a report on its use in naturalistic research’. British Educational Research Journal, 29(6), pp. 861 – 878.
Maton, K. (2014) Knowledge and Knowers. Oxon: Routledge.
Matruglio, E., Maton, K. and Martin, J. R. (2013) ‘Time travel: The role of temporality in enabling semantic waves in secondary school teaching’. Linguistics and Education, 24, pp. 38 – 49.
Sfard, A. (2000) ‘Symbolizing Mathematical Reality into Being – Or how mathematical discourse and mathematical objects create each other’ in: P. Cobb, E. Yackel and K. McClain (eds) Symbolizing and Communicating in Mathematics Classrooms: Perspectives on Discourse, Tools, and Instructional Design. (pp. 37-98). Mahwah: Erlbaum.
Andy Ash
Cheshire and Wirral Maths Hub
Andy Ash has recently completed his Doctorate at Cumbria University, where he focussed upon better understanding how teachers use representations in the primary school maths classroom. Andy runs a ‘Maths Hub’, which is a regional government funded organisation in England that provides professional development for teachers across Cheshire and Wirral. Most of his work involves looking at how teachers can best be supported to ensure that student experience of the school maths curriculum is positive, and truly reflects the multi-dimensional nature of mathematics.
Teacher Education Advancement Network (TEAN) 