Working with teachers, engaging in mathematics

: an enactivist perspective

Abstract

The aim of this dissertation is to develop awarenesses of new possibilities for how a mathematics teacher educator, or professional development facilitator, might engage in mathematics with teachers. In particular, possibilities for ways of working with teachers which might help those teachers to recognise when and in what ways to engage in mathematics themselves, with a view to effective action in their classrooms.
An enactivist perspective informs all of: a methodology for conducting the research; a methodology for working with teachers; and a framework for interpreting teachers’ learning. Knowing and doing are considered equivalent, and the assessment of actions as “effective” is dependent upon observer. Notions of “deliberate analysis” and “purposes” are discussed, in the context of teacher education. It is suggested that teachers may be prompted to engage in mathematics as a mechanism to account for their experiences of teaching, in an ongoing practice of deliberate analysis.
A review of existing literature is presented, concerning teachers engaging in mathematics. From this review, a collection of ways of engaging in mathematics is distilled, summarised by the label multiplicity and invariance. These ways of engaging in mathematics share similarities with practices associated with “variation theory”.
Empirical research is driven by the research question: When engaging in mathematics with teachers, prompted by teachers’ own experiences, how does multiplicity and invariance occasion subsequent learning for those teachers? The analysis of data collected from collaborative meetings and individual interviews with four teachers leads to a response to the research question: multiplicity and invariance involved the teachers comparing multiple solutions to a problem; a pattern of pedagogical talk, when comparing solutions, revealed variations in the teachers’ interpretations of effective action; and those variations seemed to play a part in occasioning learning for the teachers. Further research is suggested regarding the role of a mathematics teacher educator/professional development facilitator in establishing productive discussion norms, relating to pedagogical talk, when engaging in mathematics with teachers.

Date of Award	21 Nov 2024
Original language	English
Awarding Institution	University of Bristol
Supervisor	Alf T Coles (Supervisor)