Alf Coles

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Re-thinking ‘Concrete to Abstract’ in Mathematics Education: Towards the Use of Symbolically Structured Environments

Alf Coles, Nathalie Sinclair

Canadian Journal of Science, Mathematics and Technology Education > 2019 > 19 > 4 > 465-480

In this article, we question the prevalent assumption that teaching and learning mathematics should always entail movement from the concrete to the abstract. Such a view leads to reported difficulties in students moving from manipulatives and models to more symbolic work, moves that many students never make, with all the implications this has for life chances. We propose working in ‘symbolically structured...

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Facilitating the use of video with teachers of mathematics: learning from staying with the detail

Alf Coles

International Journal of STEM Education > 2019 > 6 > 1 > 1-13

Background This article is focused on the role of the facilitator in the professional development of mathematics teachers. It is a feature of several frameworks for using video that teachers are invited to comment on the detail of what they saw and heard, and base comments on evidence from the video. It is also a common finding that it is hard to establish ‘speaking evidentially’ as a way of working...

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Ritualisation in early number work

Alf Coles, Nathalie Sinclair

Educational Studies in Mathematics > 2019 > 101 > 2 > 177-194

In this paper, we propose a way of thinking about ritual that is new to mathematics education research and that challenges the more common approaches to ritual that dichotomise thinking and acting. We argue for a material, monist conceptualisation of ritual, which we refer to as ritualisation. In the context of early number work, we show that ritualisation can be seen as meaningful—and not simply...

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Mathematical tasks and the student: navigating “tensions of intentions” between designers, teachers, and students

Heather Lynn Johnson, Alf Coles, David Clarke

ZDM > 2017 > 49 > 6 > 813-822

We articulate a student perspective on task design in mathematics education, foregrounding a dynamic relationship between intentions of task designers, teachers, and students. First, we characterize a student perspective on task design. Second, we provide theoretical perspectives that we use as tools to account for different facets of task design from a student perspective. Third, we elaborate on...

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Resisting the desire for the unambiguous: productive gaps in researcher, teacher and student interpretations of a number story task

Mellony Graven, Alf Coles

ZDM > 2017 > 49 > 6 > 881-893

This article offers reflections on task design in the context of a Grade R (reception year) in-service numeracy project in South Africa. The research explores under what conditions, and for what learning purpose, a task designed by someone else may be recast and how varying given task specifications may support or inhibit learning, as a result of that recasting. This question is situated within a...

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Task design for ways of working: making distinctions in teaching and learning mathematics

Alf Coles, Laurinda Brown

Journal of Mathematics Teacher Education > 2016 > 19 > 2-3 > 149-168

A problem identified in the literature around task design is the persistence of a gap between teacher intention and student activity. We show how principles designed around the making of distinctions and having an explicit language of mathematical thinking can eliminate the “gap” by guiding teacher planning, teacher actions in the classroom and student activity in the classroom. We show how our task...

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On enactivism and language: towards a methodology for studying talk in mathematics classrooms

Alf Coles

ZDM > 2015 > 47 > 2 > 235-246

This article is an early step in the development of a methodological approach to the study of language deriving from an enactivist theoretical stance. Language is seen as a co-ordination of co-ordinations of action. Meaning and intention cannot easily be interpreted from the actions and words of others; instead, careful attention can be placed in not going beyond what is observable within the text...

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Mathematics teachers learning with video: the role, for the didactician, of a heightened listening

Alf Coles

ZDM > 2014 > 46 > 2 > 267-278

This article addresses two main questions, how do mathematics teachers learn from using video? and, what is the role of the didactician? A common problem is reported in the difficulty of keeping teacher discussion of video away from judgment and evaluation. A review of mathematics education literature revealed four existing models for the use of video with teachers. Drawing on enactivist ideas (Rosch,...

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Using video for professional development: the role of the discussion facilitator

Alf Coles

Journal of Mathematics Teacher Education > 2013 > 16 > 3 > 165-184

Past research into the use of video for professional development has failed to problematise or theorise sufficiently the role of the discussion facilitator. It has been reported consistently that it can be hard or take time to establish norms for discussion of video but little has been said about reasons why, or the role of the discussion facilitator. As a starting point in this area, I suggest fives...

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

Laurinda Brown, Alf Coles

Educational Studies in Mathematics > 2012 > 80 > 1-2 > 217-231

We illustrate and exemplify how the idea of reflection is framed by the enactive concept of “deliberate analysis”. In keeping with this frame, we do not attempt to define reflection but rather work on the question of “how do we do reflecting?” within such a frame. We set out our enactivist theoretical stance, in particular pointing to implications for how we can learn from experience and showing the...

article

Developing expertise: how enactivism re-frames mathematics teacher development

Laurinda Brown, Alf Coles

ZDM > 2011 > 43 > 6-7 > 861-873

In this article, we present a re-framing of teacher development that derives from our convictions regarding the enactive approach to cognition and the biological basis of being. We firstly set out our enactivist stance and then distinguish our approach to teacher development from others in the mathematics education literature. We show how a way of working that develops expertise runs through all mathematics...

article

Mathematics teacher and mathematics teacher educator change—insight through theoretical perspectives

Laurinda Brown, Alf Coles

Journal of Mathematics Teacher Education > 2010 > 13 > 5 > 375-382

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Search results for: Alf Coles

Re-thinking ‘Concrete to Abstract’ in Mathematics Education: Towards the Use of Symbolically Structured Environments

Facilitating the use of video with teachers of mathematics: learning from staying with the detail

Ritualisation in early number work

Mathematical tasks and the student: navigating “tensions of intentions” between designers, teachers, and students

Resisting the desire for the unambiguous: productive gaps in researcher, teacher and student interpretations of a number story task

Task design for ways of working: making distinctions in teaching and learning mathematics

On enactivism and language: towards a methodology for studying talk in mathematics classrooms

Mathematics teachers learning with video: the role, for the didactician, of a heightened listening

Using video for professional development: the role of the discussion facilitator

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

Developing expertise: how enactivism re-frames mathematics teacher development

Mathematics teacher and mathematics teacher educator change—insight through theoretical perspectives

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