BACKGROUND In the summary of findings (Coles, 2000) from a one year teacher-research grant (award... more BACKGROUND In the summary of findings (Coles, 2000) from a one year teacher-research grant (awarded by the UK's Teacher Training Agency (TTA)) I identified teaching strategies that were effective in establishing a 'need for algebra'(Brown and Coles 1999) in a year 7 class (students aged 11-12 years) whom I taught. Evidence for students finding a 'need for algebra'was that they were able to ask their own questions about complex mathematical situations and structure their approach to working on these questions.
At Cambridge there was the third meeting of the re-formed Mathematics Education and the Analysis ... more At Cambridge there was the third meeting of the re-formed Mathematics Education and the Analysis of Language Working Group. In the first meeting (November 2011) we worked with conversation analysis and linguistic ethnography approaches to analyzing data. This was followed in March 2012 by a session that triangulated conversation analysis and a multi-modal approach (see Farsani 2012). The aims of the group are to share and develop approaches to the analysis of classroom talk.
Abstract What is story? How do we, two teacher educators, use 'storytelling'as a pedagogical tool... more Abstract What is story? How do we, two teacher educators, use 'storytelling'as a pedagogical tool with prospective teachers? There are two versions of what 'story'means to us that we want to explore in this paper. The first is from Bateson's book 'Mind and Nature','a story is a little knot or complex of that species of connectedness which we call relevance… the notion of context, of pattern through time.'(pp.
In this paper I explore some implications of taking a virtue theory approach to ethics within cla... more In this paper I explore some implications of taking a virtue theory approach to ethics within classroom-based research. I argue that an ethical dilemma arises around the gaining of informed consent at the very beginning of a relationship with a new class; to the extent that it is not ethical to engage in such research until a classroom culture is established. I argue, secondly, that ethical behaviour as a practitioner-researcher in the classroom is an issue pertinent to every decision, not just something to address at the start of a project.
Methods Over one academic year, September 1999 to July 2000 which is split into 3 terms, the proj... more Methods Over one academic year, September 1999 to July 2000 which is split into 3 terms, the project team (3 teachers, 1 teacher-researcher and 3 researchers) investigated the samenesses and differences in the developing algebraic activity in the four classroom cultures through:• working in a collaborative group, meeting once every half-term for a full day and corresponding through e-mail
This paper examines data from an ongoing study of classrooms and teacher-meetings in one secondar... more This paper examines data from an ongoing study of classrooms and teacher-meetings in one secondary mathematics department in the UK. The study draws on enactivist methodology and linguistic ethnography in its conception and practice. This report is focused around the notion of dialogue (Bakhtin 1981) and the development of patterns of dialogue.
The use of video recordings of lessons for teacher professional development is under-researched (... more The use of video recordings of lessons for teacher professional development is under-researched (Hall and Wright 2007, 9). There have been conflicting recommendations related to viewing videos of similar or different contexts (eg, Hall and Wright 2007, 11 and, Clarke and Hollingsworth 2000, 40). It has been reported that it can be hard or take time to establish norms for discussion of video (Van E's and Sherin 2008, Jaworski 1990).
In this paper, we report on our analysis of four transcripts of teacher meetings that took place ... more In this paper, we report on our analysis of four transcripts of teacher meetings that took place over the academic year 2011-12. These meetings took place in the context of a project looking into tackling underachievement in primary mathematics through a focus on creativity. We bring the idea of growth indicators (Jacobs, Lamb and Philipp 2010) within the framework of noticing (Mason 2002) in order to analyse shifts in teacher discourse.
In this paper I consider methodological aspects of Gattegno's (1987) conception of a Science of E... more In this paper I consider methodological aspects of Gattegno's (1987) conception of a Science of Education. His emphasis on the watchfulness of the teacher, and on personal transformation is close to ideas in Dewey (1934) and Mason (2002). In all three authors this foregrounding of the personal can at times read more like a description of aesthetic rather than scientific experience; and I have found it helpful to see these as two different perspectives or lightings on the complex whole that is education.
In this paper I review some recent reviews of mathematics education research, which seem at first... more In this paper I review some recent reviews of mathematics education research, which seem at first sight to confirm a judgement by Steen (1999) that it'is a field in disarray'. As a PhD student, looking at competing methodologies there can seem a bewildering complexity from which to choose. It appears that there are relatively few (three to five, depending on authors) theoretical perspectives or paradigms that guide the field, but a plethora of methodologies that can be used with them.
The data for this study is taken from a project [1] looking into the development in year 7 studen... more The data for this study is taken from a project [1] looking into the development in year 7 students (aged 11-12) of a'need for algebra'(Brown and Coles, 1999) in four teacher's classrooms in the UK. I introduce the notions of evaluative, interpretive and transformative listening,(adapted from Davis, 1996), to analyse three transcripts from lessons of one teacher on the project. The project design and case study were informed by ideas of enactivist research (Varela, 1999, Reid, 1996).
The use of video recordings of lessons for teacher professional development is underresearched (H... more The use of video recordings of lessons for teacher professional development is underresearched (Hall and Wright 2007, 9). There have been conflicting recommendations related to viewing videos of similar or different contexts (eg, Hall and Wright 2007, 11 and, Clarke and Hollingsworth 2000, 40). It has been reported that it can be hard or take time to establish norms for discussion of video (Van E's and Sherin 2008, Jaworski 1990).
This case study draws on data collected in one secondary mathematics department in the UK in the ... more This case study draws on data collected in one secondary mathematics department in the UK in the academic year 2007-8. I took six video recordings of Teacher A working with her year 7 class. In line with the enactivist methodology that informed the research, in this paper I look at the final recording of the year and trace the patterns that can be observed back through the rest of the data.
In this paper I report on the outcomes of a'Mathematics Knowledge Network'(MKN) project, aimed at... more In this paper I report on the outcomes of a'Mathematics Knowledge Network'(MKN) project, aimed at developing rich tasks in the primary curriculum. The work was funded by the National Council for Excellence in Teaching Mathematics (NCETM) and carried out in collaboration with the Arts based charity" 5x5x5= Creativity". The approach to the project was informed by Gattegno's ideas on the'powers of the mind'.
METHODS We look at the detail of our practice, what we do, using the strategy of giving 'accounts... more METHODS We look at the detail of our practice, what we do, using the strategy of giving 'accounts-of'(Mason, 2002, p. 268) significant incidents for us, often recognised through dissonance (Festinger, 1957; Brown and Dobson, 1996) and reflecting on, or accounting for those incidents to probe our motivations and implicit beliefs and theories (Claxton, 1996).
DEVELOPING ALGEBRA-A CASE STUDY OF THE FIRST LESSONS FROM THE BEGINNING OF YEAR 7 Alf Coles and L... more DEVELOPING ALGEBRA-A CASE STUDY OF THE FIRST LESSONS FROM THE BEGINNING OF YEAR 7 Alf Coles and Laurinda Brown Kingsfield School and University of Bristol Graduate School of Education This is a case study from the start of a project, funded by the Teacher Training Agency (ITA), looking at one mixed ability year 7 class in a Bristol comprehensive, investigating what algebra is taught and what algebra is learnt over the period of their first term at secondary school.
This paper briefly tells the story, through four critical stages, of the developing complexity of... more This paper briefly tells the story, through four critical stages, of the developing complexity of our theories-in-action (SchOn, 1991) as teacher-researchers over a period of 18 months. These theories-in-action are related to the ways in which teacher and student purposes (Brown and Coles, 1996) act as organisingfoci through which intuitive ways of knowing (Bruner 1974, Fischbein 1982, Gattegno 1987) are accessed.
BACKGROUND In the summary of findings (Coles, 2000) from a one year teacher-research grant (award... more BACKGROUND In the summary of findings (Coles, 2000) from a one year teacher-research grant (awarded by the UK's Teacher Training Agency (TTA)) I identified teaching strategies that were effective in establishing a 'need for algebra'(Brown and Coles 1999) in a year 7 class (students aged 11-12 years) whom I taught. Evidence for students finding a 'need for algebra'was that they were able to ask their own questions about complex mathematical situations and structure their approach to working on these questions.
At Cambridge there was the third meeting of the re-formed Mathematics Education and the Analysis ... more At Cambridge there was the third meeting of the re-formed Mathematics Education and the Analysis of Language Working Group. In the first meeting (November 2011) we worked with conversation analysis and linguistic ethnography approaches to analyzing data. This was followed in March 2012 by a session that triangulated conversation analysis and a multi-modal approach (see Farsani 2012). The aims of the group are to share and develop approaches to the analysis of classroom talk.
Abstract What is story? How do we, two teacher educators, use 'storytelling'as a pedagogical tool... more Abstract What is story? How do we, two teacher educators, use 'storytelling'as a pedagogical tool with prospective teachers? There are two versions of what 'story'means to us that we want to explore in this paper. The first is from Bateson's book 'Mind and Nature','a story is a little knot or complex of that species of connectedness which we call relevance… the notion of context, of pattern through time.'(pp.
In this paper I explore some implications of taking a virtue theory approach to ethics within cla... more In this paper I explore some implications of taking a virtue theory approach to ethics within classroom-based research. I argue that an ethical dilemma arises around the gaining of informed consent at the very beginning of a relationship with a new class; to the extent that it is not ethical to engage in such research until a classroom culture is established. I argue, secondly, that ethical behaviour as a practitioner-researcher in the classroom is an issue pertinent to every decision, not just something to address at the start of a project.
Methods Over one academic year, September 1999 to July 2000 which is split into 3 terms, the proj... more Methods Over one academic year, September 1999 to July 2000 which is split into 3 terms, the project team (3 teachers, 1 teacher-researcher and 3 researchers) investigated the samenesses and differences in the developing algebraic activity in the four classroom cultures through:• working in a collaborative group, meeting once every half-term for a full day and corresponding through e-mail
This paper examines data from an ongoing study of classrooms and teacher-meetings in one secondar... more This paper examines data from an ongoing study of classrooms and teacher-meetings in one secondary mathematics department in the UK. The study draws on enactivist methodology and linguistic ethnography in its conception and practice. This report is focused around the notion of dialogue (Bakhtin 1981) and the development of patterns of dialogue.
The use of video recordings of lessons for teacher professional development is under-researched (... more The use of video recordings of lessons for teacher professional development is under-researched (Hall and Wright 2007, 9). There have been conflicting recommendations related to viewing videos of similar or different contexts (eg, Hall and Wright 2007, 11 and, Clarke and Hollingsworth 2000, 40). It has been reported that it can be hard or take time to establish norms for discussion of video (Van E's and Sherin 2008, Jaworski 1990).
In this paper, we report on our analysis of four transcripts of teacher meetings that took place ... more In this paper, we report on our analysis of four transcripts of teacher meetings that took place over the academic year 2011-12. These meetings took place in the context of a project looking into tackling underachievement in primary mathematics through a focus on creativity. We bring the idea of growth indicators (Jacobs, Lamb and Philipp 2010) within the framework of noticing (Mason 2002) in order to analyse shifts in teacher discourse.
In this paper I consider methodological aspects of Gattegno's (1987) conception of a Science of E... more In this paper I consider methodological aspects of Gattegno's (1987) conception of a Science of Education. His emphasis on the watchfulness of the teacher, and on personal transformation is close to ideas in Dewey (1934) and Mason (2002). In all three authors this foregrounding of the personal can at times read more like a description of aesthetic rather than scientific experience; and I have found it helpful to see these as two different perspectives or lightings on the complex whole that is education.
In this paper I review some recent reviews of mathematics education research, which seem at first... more In this paper I review some recent reviews of mathematics education research, which seem at first sight to confirm a judgement by Steen (1999) that it'is a field in disarray'. As a PhD student, looking at competing methodologies there can seem a bewildering complexity from which to choose. It appears that there are relatively few (three to five, depending on authors) theoretical perspectives or paradigms that guide the field, but a plethora of methodologies that can be used with them.
The data for this study is taken from a project [1] looking into the development in year 7 studen... more The data for this study is taken from a project [1] looking into the development in year 7 students (aged 11-12) of a'need for algebra'(Brown and Coles, 1999) in four teacher's classrooms in the UK. I introduce the notions of evaluative, interpretive and transformative listening,(adapted from Davis, 1996), to analyse three transcripts from lessons of one teacher on the project. The project design and case study were informed by ideas of enactivist research (Varela, 1999, Reid, 1996).
The use of video recordings of lessons for teacher professional development is underresearched (H... more The use of video recordings of lessons for teacher professional development is underresearched (Hall and Wright 2007, 9). There have been conflicting recommendations related to viewing videos of similar or different contexts (eg, Hall and Wright 2007, 11 and, Clarke and Hollingsworth 2000, 40). It has been reported that it can be hard or take time to establish norms for discussion of video (Van E's and Sherin 2008, Jaworski 1990).
This case study draws on data collected in one secondary mathematics department in the UK in the ... more This case study draws on data collected in one secondary mathematics department in the UK in the academic year 2007-8. I took six video recordings of Teacher A working with her year 7 class. In line with the enactivist methodology that informed the research, in this paper I look at the final recording of the year and trace the patterns that can be observed back through the rest of the data.
In this paper I report on the outcomes of a'Mathematics Knowledge Network'(MKN) project, aimed at... more In this paper I report on the outcomes of a'Mathematics Knowledge Network'(MKN) project, aimed at developing rich tasks in the primary curriculum. The work was funded by the National Council for Excellence in Teaching Mathematics (NCETM) and carried out in collaboration with the Arts based charity" 5x5x5= Creativity". The approach to the project was informed by Gattegno's ideas on the'powers of the mind'.
METHODS We look at the detail of our practice, what we do, using the strategy of giving 'accounts... more METHODS We look at the detail of our practice, what we do, using the strategy of giving 'accounts-of'(Mason, 2002, p. 268) significant incidents for us, often recognised through dissonance (Festinger, 1957; Brown and Dobson, 1996) and reflecting on, or accounting for those incidents to probe our motivations and implicit beliefs and theories (Claxton, 1996).
DEVELOPING ALGEBRA-A CASE STUDY OF THE FIRST LESSONS FROM THE BEGINNING OF YEAR 7 Alf Coles and L... more DEVELOPING ALGEBRA-A CASE STUDY OF THE FIRST LESSONS FROM THE BEGINNING OF YEAR 7 Alf Coles and Laurinda Brown Kingsfield School and University of Bristol Graduate School of Education This is a case study from the start of a project, funded by the Teacher Training Agency (ITA), looking at one mixed ability year 7 class in a Bristol comprehensive, investigating what algebra is taught and what algebra is learnt over the period of their first term at secondary school.
This paper briefly tells the story, through four critical stages, of the developing complexity of... more This paper briefly tells the story, through four critical stages, of the developing complexity of our theories-in-action (SchOn, 1991) as teacher-researchers over a period of 18 months. These theories-in-action are related to the ways in which teacher and student purposes (Brown and Coles, 1996) act as organisingfoci through which intuitive ways of knowing (Bruner 1974, Fischbein 1982, Gattegno 1987) are accessed.
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