Output details

Developing "deliberate analysis" for learning mathematics and for mathematics teacher education: how the enactive approach to cognition frames reflection

This output was developed into a journal paper from a contribution to the invitation only Mathematics Education and Contemporary Theory conference, to which I was invited because of my enactivist framework. Enactivism has been referred to as a paradigm-shifting worldview. This paper forms part of a collection of papers, developed by Laurinda Brown and Alf Coles out of a longitudinal collaboration since 1995, that look at how concepts are seen and enacted through this worldview. The paper advances theory by taking a critical look at reflection from the other side of a paradigm shift.

Research questions

From an enactive approach to cognition, we work on the question “how do we do reflecting?”

Methodology

Linking theory and practice is at the heart of enactivist thinking since all learning is seen as doing. We look at the practice of teacher education and individual teachers who have developed as teachers through this practice. We work with student teachers and teachers so that they stay with the detail of their experience. We use transcripts, writing from the teachers about issues in their teaching and field-notes.

Analysis

We analyse the data through the framework of Varela’s concept of “deliberate analysis”. Given the enactivist stance, integrity, coherence and consistency are evidenced through the braiding of first and third-person accounts.

Means of dissemination

Responding to invitations to work with staff and students at the University of Agder, Norway (October 2012) and Monash University, Australia (August, 2012) on enactivist ideas in relation to the teaching and learning of mathematics. There is an entry in the on-line Springer Encyclopedia of Mathematics Education entitled Enactivist Theories. In this writing, my work is identified as being influential, including reference to this ESM paper. Mainly, though, our dissemination is through our developing practice with pre- and in-service teachers of mathematics.