Describing Mathematics Teaching


My PhD research is about the problems we have with describing mathematics teaching.

Working with PGCE Maths student teachers I became interested in how they learn from experienced teachers and this interest has evolved into a more general interest in how we communicate about our practices. Adler et al. (2005) found that case studies were helping to reveal the complexity of teacher development and called for further research into a number of areas including how teachers learn from experience. The importance of reflection on practice in initial teacher education is well documented (for example, Chapman, 2008, Brown and Coles, 2012) but there is surprisingly little research investigating the processes of reflection and learning of experienced and capable mathematics teachers.

The study

There is research revealing the complexity of teachers’ conceptualisations (Potari et al., 2010, Wake and Pepin, 2010, Morgan and Xu, 2011); and there are examples of studies paying close attention to language and terminology (Houssart, 2000, Penn, 2002, Burton, 2004, Morgan, 2011). My study will contribute to these lines of enquiry with in-depth analysis of mathematics teachers’ descriptions of their own teaching.


In seeking descriptions of teaching, if I use particular words or ask about particular things, descriptions tend to be steered in particular directions. To avoid the risk of leading the descriptions, I use video to aid recall with a small number of open questions. I am investigating teachers’ descriptions of their own teaching so I am not looking for particular things at the stage of the observation and interview. The interview starts with a focus chosen by the participating teacher with the aim of facilitating articulation of their knowledge of teaching. So the first question of the interview is entirely predictable and can be stated before we start, “With reference to the lesson, what shall we focus on that will facilitate articulation of your knowledge of teaching?” Ideally, teachers will position themselves as experts in their own teaching.


In my analysis, I will aim to characterise the knowledge of teaching articulated. Ideally, I will present this in a paper to the participating teacher and will welcome feedback on its validity. To minimise the risk of the teacher’s descriptions being steered by consciousness of a future audience, it is important that the teacher has control of this paper. I am not expecting the paper to be a risk for the teacher to share but nevertheless I would not want participants to be concerned about future audiences at the time of the interview. I will only provide the paper to the participant.

Please contact me below if you would like to participate in this research.


ADLER, J., BALL, D., KRAINER, K., LIN, F.-L. & NOVOTNA, J. 2005. Reflections on an Emerging Field: Researching Mathematics Teacher Education. Educational Studies in Mathematics, 60, 359-381.

BROWN, L. & COLES, A. 2012. Developing “deliberate analysis” for learning mathematics and for mathematics teacher education: how the enactive approach to cognition frames reflection. Educational Studies in Mathematics, 80, 217-231.

BURTON, L. 2004. Confidence is Everything” – Perspectives of Teachers and Students on Learning Mathematics. Journal of Mathematics Teacher Education, 7, 357-381.

CHAPMAN, O. 2008. Narratives in Mathematics Teacher Education. In: TIROSH, D. & WOOD, T. (eds.) The International Handbook of mathematics teacher education: Tools and processes in mathematics teacher education. Rotterdam: Sense.

HOUSSART, J. 2000. Perceptions of Mathematical Pattern amongst Primary Teachers. Educational Studies, 26, 489-502.

MORGAN, C. 2011. Making Sense of Curriculum Innovation and Mathematics Teacher Identity. In: KANES, C. (ed.) Elaborating Professionalism. Springer Netherlands.

MORGAN, C. & XU, G. 2011. Reconceptualising ‘obstacles’ to teacher implementation of curriculum reform: beyond beliefs. Mathematics Education and Contemporary Theory Conference. Manchester Metropolitan University, UK.

PENN, H. 2002. ‘Maintains a Good Pace to Lessons’: Inconsistencies and Contextual Factors Affecting OFSTED Inspections of Nursery Schools. British Educational Research Journal, 28, 879-888.

POTARI, D., SAKONIDIS, H., CHATZIGOULA, R. & MANARIDIS, A. 2010. Teachers’ and researchers’ collaboration in analysing mathematics teaching: A context for professional reflection and development. Journal of Mathematics Teacher Education, 13, 473-485.

WAKE, G. & PEPIN, B. Year. Conceptualising the mediation of mathematics in classrooms as textured narratives. In: JOUBERT, M. & ANDREWS, P., eds. Proceedings of the British Congress for Mathematics Education, 2010 Manchester. BSRLM, 223-229.