A common theme in accounts of choosing mathematics is that of persistence in the face of troubles... more A common theme in accounts of choosing mathematics is that of persistence in the face of troubles or difficulties which are often associated with the structuring effects of gender, class, culture and ethnicity. Centring on an analysis of one woman's account of becoming a mathematician, we build on our understanding of multiple and developing identities with the aim of capturing the nature of individual challenge to structuring discourses and its implications for choice and participation in mathematics more generally. Inspecting how she talks about events in the past, present, and future, we expand on Leont'ev's (1978, 1981) notion of leading activity to explore how we organise and prioritise activities (and their related identities) within the context of Holland et al.'s (1998) theory of identity in practice, hybridity and world-making. We interrogate the part played by contradiction in creating a space for individual agency through its resolution in hybrid practices and its relation to social change, exploring how our informant narrates taking up mathematics " against the odds " as part of an ongoing process of " rewriting " herself into new imagined worlds. In providing an insight into how one individual envisages and enacts a different mathematics culture in which she can have a place, our analysis suggests ways forward in creating new, more inclusive, mathematics education.
The construction of positive mathematical identities (MIs) is a complex and central issue in scho... more The construction of positive mathematical identities (MIs) is a complex and central issue in school mathematics, where girls are usually “counted out” of the field. This study explores positive MIs (high achiever and positive relationship with mathematics) of 3 girls. We employed a nested model of identity based on a case study approach (i.e., female mathematics students nested within a cluster of students nested within a mathematics classroom). The results highlight diversity in how these girls experienced mathematics: They valued different forms of doing mathematics (independent and collaborative; wider and complex; and straightforward, procedure-oriented mathematics), showed different forms of engagement (detachment, protagonist and challenging, and compliant and support-seeker), and narrated different MIs (efficient, different, and responsible). The study also explores and discusses the roles of mathematical practice and belonging to different peer clusters in these different forms of identification.
International Journal of Mathematical Education in Science and Technology, 2014
ABSTRACT Mathematics has long been known to be problematic for university engineering students an... more ABSTRACT Mathematics has long been known to be problematic for university engineering students and their teachers, for example, Scanlan.[11. Scanlan JO. The role of mathematics in engineering education: an engineer's view. Int J Math Educ Sci Technol. 1985;16:445–451.[Taylor & Francis Online]View all references] This paper presents recent data gathered from interviews with engineering students who experienced problems with mathematics and their lecturers during their transition through the first year in different programme contexts. Our interviews with the students reveal how they understand the relation between engineering and mathematics and we draw on the concept of ‘use- and exchange-value’ to explore this relationship more fully. This paper challenges both the pedagogical practice of teaching non-contextualized mathematics and the lack of transparency regarding the significance of mathematics to engineering. We conclude that the value of mathematics in engineering remains a central problem, and argue that mathematics should be a fundamental concern in the design and practice of first-year engineering.
Recent years have seen many valid and important critiques of mathematics, mathematics education a... more Recent years have seen many valid and important critiques of mathematics, mathematics education and mathematics education research (M, ME & MER). However, we also discern in some of these critiques a tendency toward one-sidededness and passivity. Unrelenting stress on the negatives of M, ME and MER can lead to a dismissal of the possibility of improving ME and a dismissal of those who attempt to do so. The separation of critical theory from critical practice which follows is then in danger of rendering critique sterile, becoming a mere pseudo-radicalism. As an alternative, we explore here the mutual relation between critical pedagogy and critiques of society, and the relationship between reform and more radical change, in wider society and ME. We argue that this analysis encourages a stress on joint activity, between individuals and organisations with a wide range of perspectives on what change is needed, to tackle the problems a critical perspective raises.
A common theme in accounts of choosing mathematics is that of persistence in the face of troubles... more A common theme in accounts of choosing mathematics is that of persistence in the face of troubles or difficulties which are often associated with the structuring effects of gender, class, culture and ethnicity. Centring on an analysis of one woman's account of becoming a mathematician, we build on our understanding of multiple and developing identities with the aim of capturing the nature of individual challenge to structuring discourses, and its implications for choice and participation in mathematics more generally. Inspecting how she talks about events in past, present and future, we expand on notion of leading activity to explore how we organise and prioritise activities (and their related identities) within the context of Holland et al.'s (1998) theory of identity in practice, hybridity and worldmaking. We interrogate the part played by contradiction in creating space for individual agency through its resolution in hybrid practices and its relation to social change, exploring how our informant narrates taking up mathematics 'against the odds' as part of an ongoing process of 're-writing' herself into new imagined worlds. In providing an insight into how one individual envisages and enacts a different mathematics culture in which she can have a place, our analysis suggests ways forward in creating new, more inclusive, mathematics education.
Multiple Perspectives on Difficulties in Learning Literacy and Numeracy, 2010
No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form ... more No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.
In this paper we describe the validation of two scales constructed to measure pre-university stud... more In this paper we describe the validation of two scales constructed to measure pre-university students' changing disposition (i) to enter Higher Education (HE) and (ii) to further study mathematically-demanding subjects. Items were selected drawing on interview data, and on a model of disposition as socially- as well as self- attributed. Rasch analyses showed that the two scales each produce robust one-dimensional measures on what we call a 'strength of commitment to enter HE' and 'disposition to study mathematically-demanding subjects further' respectively. However, the former scale was initially found to suffer psychometrically from a ceiling effect, which we 'corrected' by adding some harder items at a later data point, and revised the scale according to our interpretation of subsequent results. We finally discuss the potential significance of the constructed measures of learning outcomes, as variables in monitoring or even explaining students' prog...
ABSTRACT Introduction This paper explores the "troubles" that some students mee... more ABSTRACT Introduction This paper explores the "troubles" that some students meet as they journey into, through and out of their study of AS mathematics on two different programmers (AS traditional Mathematics and AS Use of Mathematics) as we attempt to understand how this impacts on their developing identities in relation to their current and future studies and career aspirations. To set the scene we take the unusual step of immediately presenting some data in the form of the summary narrative accounts of two such students before detailing methodology, theoretical framework and analysis. David's Story David had a "troubled" relationship with mathematics during his AS studies the result of which being that he eventually opted out of following a trajectory into a mathematically demanding Higher Education course in science or engineering. At school he had always been in the top sets for mathematics, got good grades and enjoyed the subject. However, he felt that he could have been pushed more and ended up "only" achieving an A grade at GCSE rather than A*. He acknowledges that this was partly due to his not having done too well in producing coursework towards his GCSE, for which he got a relatively low mark, and that he had rather enjoyed socialising. His "troubles" continue when he arrived at college as after only a short time he "moved down" to the Use of Mathematics programme from the traditional AS Mathematics course and attributed the move to maths at college being very different and more difficult than maths at school, "at GCSE you could just blag a few good grades but college is a lot harder". At this stage David was also studying physics, accountancy and psychology and planned to study radiotherapy at university (combining maths and physics) and had a back-up plan of studying accountancy. At the time of a second interview, David talked about his positive experience of the Use of Maths course and how his confidence was increasing, so much so that he planned after successful completion of the AS to get back onto the traditional maths course and complete the whole A-level in one year. At this point his aspirations were to continue with physics and accountancy and after completing the maths to go to a high status redbrick university to study physics. He was determined to do this and talked of doing a foundation year if necessary at his first choice university if he didn"t get the required grades. His actions at this point, such as sitting on his own in maths lessons to avoid distractions and his talk of family support, including financial help so he could give up his part time job, all supported his talk of his determination. Family support and approval seemed important, with David telling of how his family recognised future potential job opportunities associated with physics and how he was happy at the idea of providing a role model for his siblings.
International Journal of Mathematical Education in Science and Technology, 2014
ABSTRACT Mathematics has long been known to be problematic for university engineering students an... more ABSTRACT Mathematics has long been known to be problematic for university engineering students and their teachers, for example, Scanlan.[11. Scanlan JO. The role of mathematics in engineering education: an engineer's view. Int J Math Educ Sci Technol. 1985;16:445–451.[Taylor & Francis Online]View all references] This paper presents recent data gathered from interviews with engineering students who experienced problems with mathematics and their lecturers during their transition through the first year in different programme contexts. Our interviews with the students reveal how they understand the relation between engineering and mathematics and we draw on the concept of ‘use- and exchange-value’ to explore this relationship more fully. This paper challenges both the pedagogical practice of teaching non-contextualized mathematics and the lack of transparency regarding the significance of mathematics to engineering. We conclude that the value of mathematics in engineering remains a central problem, and argue that mathematics should be a fundamental concern in the design and practice of first-year engineering.
Previous work on transition between institutions suggests transitional problems can be dangerous ... more Previous work on transition between institutions suggests transitional problems can be dangerous for individual learners‟ progress. Drawing on the literature, and on our CHAT perspective, we anticipated that transition points would be significant to students narrative construction of ...
A wide body of literature has highlighted how high achievement in mathematics in secondary school... more A wide body of literature has highlighted how high achievement in mathematics in secondary school does not necessarily motivate students to both choose and succeed on mathematically demanding programmes at post-compulsory level. The recent Enterprising Science project (Archer et al. (2015, J. Res. Sci. Teach., 52, 922–948)) and before that, the ASPIRES project (Archer et al. (2013, London: Kings College)), have both highlighted that access to science capital is perhaps more important than prior achievement in shaping students’ aspirations and their future trajectories in Science, Technology, Engineering and Mathematics. In this article, we critically analyse the notion of science capital and its role in mediating students’ choice of and experience of studying mathematically demanding degree programmes at university. Drawing on data from the TransMaths project, we present two cases—Stacey and Elton—who are both enrolled on the same ‘Mathematics for Physics’ course at university. We show that although both discuss access to science capital in narrating their choice of degree, they do so in different ways and this invariably interplays with different forms of identification with ‘Mathematics for Physics’. We conclude that there is a need to re-conceptualize science capital so that the dialectic relationship between its exchange and use value is theorized more fully. Whilst some students may access science capital as a means to accumulate capital (e.g. qualifications) for its own sake (exchange value), others appear to recognize the ‘use value’ of science learning and knowledge and this produces different forms of engagement with science (and mathematics). We therefore argue that authoring oneself in the name of a STEM identity is crucial in mediating how one perceives science capital. Finally, we argue that mathematics should be a central part of this framework since it significantly contributes to the exchange value of science as a form of capital (especially Physics), but it also offers use value in scientific labour (e.g. in modelling scientific problems).
In this chapter we make sense of our personal mathematical journeys as accounts of defended subje... more In this chapter we make sense of our personal mathematical journeys as accounts of defended subjects, while also exploring the role of discourses in our defences. Following Wendy Hollway and Tony Jefferson (2000, p.21), we argue that “subjects invest in discourses when these offer positions which provide protections against anxiety and therefore supports to identity”. Thus, we aim to understand our accounts as both psychic and social, without reducing one to the other. We begin by outlining the idea of the defended subject before turning to Jacques Nimier’s application of this to mathematics. Next we use these ideas to analyse the extracts above. We argue that a psychoanalytic approach can give us new understandings of the pain, power and pleasure of selection and assessment that provide a critique of current practices. Reference: Black, L., Mendick, Rodd, M. and Solomon, Y. with Brown, M. (2009) Pain, pleasure and power: selecting and assessing defended subjects. In: L. Black, H. Mendick and Y. Solomon (eds), Mathematical Relationships in Education: Identities and Participation.
We address the current concerns about teaching-to-the-test and its association with declining dis... more We address the current concerns about teaching-to-the-test and its association with declining dispositions towards further study of mathematics and the consequences for choice of STEM subjects at university. In particular, through a mixed study including a large survey sample of over 1000 students and their teachers, and focussed qualitative case studies, we explored the impact of 'transmissionist' pedagogic practices on learning outcomes. We report on the construction and validation of a scale to measure teachers' self-reported pedagogy. We then use this measure in combination with the students' survey data and through regression modelling we illustrate significant associations between the pedagogic measure and students' mathematics dispositions. Finally, we discuss the potential implications of these results for mathematics education and the STEM agenda.
The aim of this paper is to describe and validate the development of two measures constructed to ... more The aim of this paper is to describe and validate the development of two measures constructed to measure AS students disposition (i) to enter HE and (ii) to further study mathematically-demanding subjects, which we regard as potentially significant variables in monitoring or even ...
The construct of identity has been used widely in mathematics education in order to understand ho... more The construct of identity has been used widely in mathematics education in order to understand how students (and teachers) relate to and engage with the subject (Kaasila, 2007; Sfard & Prusak, 2005; Boaler, 2002). Drawing on cultural historical activity theory (CHAT), this paper adopts Leont’ev’s notion of leading activity in order to explore the key ‘significant’ activities that are implicated in the development of students’ reflexive understanding of self and how this may offer differing relations with mathematics. According to Leont’ev (1981), leading activities are those which are significant to the development of the individual’s psyche through the emergence of new motives for engagement. We suggest that alongside new motives for engagement comes a new understanding of self—a leading identity—which reflects a hierarchy of our motives. Narrative analysis of interviews with two students (aged 16–17 years old) in post-compulsory education, Mary and Lee, are presented. Mary holds a stable ‘vocational’ leading identity throughout her narrative and, thus, her motive for studying mathematics is defined by its ‘use value’ in terms of pursuing this vocation. In contrast, Lee develops a leading identity which is focused on the activity of studying and becoming a university student. As such, his motive for study is framed in terms of the exchange value of the qualifications he hopes to obtain. We argue that this empirical grounding of leading activity and leading identity offers new insights into students’ identity development.
We address the current concerns about teaching-to-the-test and its association with declining dis... more We address the current concerns about teaching-to-the-test and its association with declining dispositions towards further study of mathematics and the consequences for choice of STEM subjects at university. In particular, through a mixed study including a large survey sample of over 1000 students and their teachers, and focussed qualitative case studies, we explored the impact of ‘transmissionist’ pedagogic practices on learning outcomes. We report on the construction and validation of a scale to measure teachers’ self-reported pedagogy. We then use this measure in combination with the students’ survey data and through regression modelling we illustrate significant associations between the pedagogic measure and students’ mathematics dispositions. Finally, we discuss the potential implications of these results for mathematics education and the STEM agenda.
A common theme in accounts of choosing mathematics is that of persistence in the face of troubles... more A common theme in accounts of choosing mathematics is that of persistence in the face of troubles or difficulties which are often associated with the structuring effects of gender, class, culture and ethnicity. Centring on an analysis of one woman's account of becoming a mathematician, we build on our understanding of multiple and developing identities with the aim of capturing the nature of individual challenge to structuring discourses and its implications for choice and participation in mathematics more generally. Inspecting how she talks about events in the past, present, and future, we expand on Leont'ev's (1978, 1981) notion of leading activity to explore how we organise and prioritise activities (and their related identities) within the context of Holland et al.'s (1998) theory of identity in practice, hybridity and world-making. We interrogate the part played by contradiction in creating a space for individual agency through its resolution in hybrid practices and its relation to social change, exploring how our informant narrates taking up mathematics " against the odds " as part of an ongoing process of " rewriting " herself into new imagined worlds. In providing an insight into how one individual envisages and enacts a different mathematics culture in which she can have a place, our analysis suggests ways forward in creating new, more inclusive, mathematics education.
The construction of positive mathematical identities (MIs) is a complex and central issue in scho... more The construction of positive mathematical identities (MIs) is a complex and central issue in school mathematics, where girls are usually “counted out” of the field. This study explores positive MIs (high achiever and positive relationship with mathematics) of 3 girls. We employed a nested model of identity based on a case study approach (i.e., female mathematics students nested within a cluster of students nested within a mathematics classroom). The results highlight diversity in how these girls experienced mathematics: They valued different forms of doing mathematics (independent and collaborative; wider and complex; and straightforward, procedure-oriented mathematics), showed different forms of engagement (detachment, protagonist and challenging, and compliant and support-seeker), and narrated different MIs (efficient, different, and responsible). The study also explores and discusses the roles of mathematical practice and belonging to different peer clusters in these different forms of identification.
International Journal of Mathematical Education in Science and Technology, 2014
ABSTRACT Mathematics has long been known to be problematic for university engineering students an... more ABSTRACT Mathematics has long been known to be problematic for university engineering students and their teachers, for example, Scanlan.[11. Scanlan JO. The role of mathematics in engineering education: an engineer's view. Int J Math Educ Sci Technol. 1985;16:445–451.[Taylor & Francis Online]View all references] This paper presents recent data gathered from interviews with engineering students who experienced problems with mathematics and their lecturers during their transition through the first year in different programme contexts. Our interviews with the students reveal how they understand the relation between engineering and mathematics and we draw on the concept of ‘use- and exchange-value’ to explore this relationship more fully. This paper challenges both the pedagogical practice of teaching non-contextualized mathematics and the lack of transparency regarding the significance of mathematics to engineering. We conclude that the value of mathematics in engineering remains a central problem, and argue that mathematics should be a fundamental concern in the design and practice of first-year engineering.
Recent years have seen many valid and important critiques of mathematics, mathematics education a... more Recent years have seen many valid and important critiques of mathematics, mathematics education and mathematics education research (M, ME & MER). However, we also discern in some of these critiques a tendency toward one-sidededness and passivity. Unrelenting stress on the negatives of M, ME and MER can lead to a dismissal of the possibility of improving ME and a dismissal of those who attempt to do so. The separation of critical theory from critical practice which follows is then in danger of rendering critique sterile, becoming a mere pseudo-radicalism. As an alternative, we explore here the mutual relation between critical pedagogy and critiques of society, and the relationship between reform and more radical change, in wider society and ME. We argue that this analysis encourages a stress on joint activity, between individuals and organisations with a wide range of perspectives on what change is needed, to tackle the problems a critical perspective raises.
A common theme in accounts of choosing mathematics is that of persistence in the face of troubles... more A common theme in accounts of choosing mathematics is that of persistence in the face of troubles or difficulties which are often associated with the structuring effects of gender, class, culture and ethnicity. Centring on an analysis of one woman's account of becoming a mathematician, we build on our understanding of multiple and developing identities with the aim of capturing the nature of individual challenge to structuring discourses, and its implications for choice and participation in mathematics more generally. Inspecting how she talks about events in past, present and future, we expand on notion of leading activity to explore how we organise and prioritise activities (and their related identities) within the context of Holland et al.'s (1998) theory of identity in practice, hybridity and worldmaking. We interrogate the part played by contradiction in creating space for individual agency through its resolution in hybrid practices and its relation to social change, exploring how our informant narrates taking up mathematics 'against the odds' as part of an ongoing process of 're-writing' herself into new imagined worlds. In providing an insight into how one individual envisages and enacts a different mathematics culture in which she can have a place, our analysis suggests ways forward in creating new, more inclusive, mathematics education.
Multiple Perspectives on Difficulties in Learning Literacy and Numeracy, 2010
No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form ... more No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.
In this paper we describe the validation of two scales constructed to measure pre-university stud... more In this paper we describe the validation of two scales constructed to measure pre-university students' changing disposition (i) to enter Higher Education (HE) and (ii) to further study mathematically-demanding subjects. Items were selected drawing on interview data, and on a model of disposition as socially- as well as self- attributed. Rasch analyses showed that the two scales each produce robust one-dimensional measures on what we call a 'strength of commitment to enter HE' and 'disposition to study mathematically-demanding subjects further' respectively. However, the former scale was initially found to suffer psychometrically from a ceiling effect, which we 'corrected' by adding some harder items at a later data point, and revised the scale according to our interpretation of subsequent results. We finally discuss the potential significance of the constructed measures of learning outcomes, as variables in monitoring or even explaining students' prog...
ABSTRACT Introduction This paper explores the "troubles" that some students mee... more ABSTRACT Introduction This paper explores the "troubles" that some students meet as they journey into, through and out of their study of AS mathematics on two different programmers (AS traditional Mathematics and AS Use of Mathematics) as we attempt to understand how this impacts on their developing identities in relation to their current and future studies and career aspirations. To set the scene we take the unusual step of immediately presenting some data in the form of the summary narrative accounts of two such students before detailing methodology, theoretical framework and analysis. David's Story David had a "troubled" relationship with mathematics during his AS studies the result of which being that he eventually opted out of following a trajectory into a mathematically demanding Higher Education course in science or engineering. At school he had always been in the top sets for mathematics, got good grades and enjoyed the subject. However, he felt that he could have been pushed more and ended up "only" achieving an A grade at GCSE rather than A*. He acknowledges that this was partly due to his not having done too well in producing coursework towards his GCSE, for which he got a relatively low mark, and that he had rather enjoyed socialising. His "troubles" continue when he arrived at college as after only a short time he "moved down" to the Use of Mathematics programme from the traditional AS Mathematics course and attributed the move to maths at college being very different and more difficult than maths at school, "at GCSE you could just blag a few good grades but college is a lot harder". At this stage David was also studying physics, accountancy and psychology and planned to study radiotherapy at university (combining maths and physics) and had a back-up plan of studying accountancy. At the time of a second interview, David talked about his positive experience of the Use of Maths course and how his confidence was increasing, so much so that he planned after successful completion of the AS to get back onto the traditional maths course and complete the whole A-level in one year. At this point his aspirations were to continue with physics and accountancy and after completing the maths to go to a high status redbrick university to study physics. He was determined to do this and talked of doing a foundation year if necessary at his first choice university if he didn"t get the required grades. His actions at this point, such as sitting on his own in maths lessons to avoid distractions and his talk of family support, including financial help so he could give up his part time job, all supported his talk of his determination. Family support and approval seemed important, with David telling of how his family recognised future potential job opportunities associated with physics and how he was happy at the idea of providing a role model for his siblings.
International Journal of Mathematical Education in Science and Technology, 2014
ABSTRACT Mathematics has long been known to be problematic for university engineering students an... more ABSTRACT Mathematics has long been known to be problematic for university engineering students and their teachers, for example, Scanlan.[11. Scanlan JO. The role of mathematics in engineering education: an engineer's view. Int J Math Educ Sci Technol. 1985;16:445–451.[Taylor & Francis Online]View all references] This paper presents recent data gathered from interviews with engineering students who experienced problems with mathematics and their lecturers during their transition through the first year in different programme contexts. Our interviews with the students reveal how they understand the relation between engineering and mathematics and we draw on the concept of ‘use- and exchange-value’ to explore this relationship more fully. This paper challenges both the pedagogical practice of teaching non-contextualized mathematics and the lack of transparency regarding the significance of mathematics to engineering. We conclude that the value of mathematics in engineering remains a central problem, and argue that mathematics should be a fundamental concern in the design and practice of first-year engineering.
Previous work on transition between institutions suggests transitional problems can be dangerous ... more Previous work on transition between institutions suggests transitional problems can be dangerous for individual learners‟ progress. Drawing on the literature, and on our CHAT perspective, we anticipated that transition points would be significant to students narrative construction of ...
A wide body of literature has highlighted how high achievement in mathematics in secondary school... more A wide body of literature has highlighted how high achievement in mathematics in secondary school does not necessarily motivate students to both choose and succeed on mathematically demanding programmes at post-compulsory level. The recent Enterprising Science project (Archer et al. (2015, J. Res. Sci. Teach., 52, 922–948)) and before that, the ASPIRES project (Archer et al. (2013, London: Kings College)), have both highlighted that access to science capital is perhaps more important than prior achievement in shaping students’ aspirations and their future trajectories in Science, Technology, Engineering and Mathematics. In this article, we critically analyse the notion of science capital and its role in mediating students’ choice of and experience of studying mathematically demanding degree programmes at university. Drawing on data from the TransMaths project, we present two cases—Stacey and Elton—who are both enrolled on the same ‘Mathematics for Physics’ course at university. We show that although both discuss access to science capital in narrating their choice of degree, they do so in different ways and this invariably interplays with different forms of identification with ‘Mathematics for Physics’. We conclude that there is a need to re-conceptualize science capital so that the dialectic relationship between its exchange and use value is theorized more fully. Whilst some students may access science capital as a means to accumulate capital (e.g. qualifications) for its own sake (exchange value), others appear to recognize the ‘use value’ of science learning and knowledge and this produces different forms of engagement with science (and mathematics). We therefore argue that authoring oneself in the name of a STEM identity is crucial in mediating how one perceives science capital. Finally, we argue that mathematics should be a central part of this framework since it significantly contributes to the exchange value of science as a form of capital (especially Physics), but it also offers use value in scientific labour (e.g. in modelling scientific problems).
In this chapter we make sense of our personal mathematical journeys as accounts of defended subje... more In this chapter we make sense of our personal mathematical journeys as accounts of defended subjects, while also exploring the role of discourses in our defences. Following Wendy Hollway and Tony Jefferson (2000, p.21), we argue that “subjects invest in discourses when these offer positions which provide protections against anxiety and therefore supports to identity”. Thus, we aim to understand our accounts as both psychic and social, without reducing one to the other. We begin by outlining the idea of the defended subject before turning to Jacques Nimier’s application of this to mathematics. Next we use these ideas to analyse the extracts above. We argue that a psychoanalytic approach can give us new understandings of the pain, power and pleasure of selection and assessment that provide a critique of current practices. Reference: Black, L., Mendick, Rodd, M. and Solomon, Y. with Brown, M. (2009) Pain, pleasure and power: selecting and assessing defended subjects. In: L. Black, H. Mendick and Y. Solomon (eds), Mathematical Relationships in Education: Identities and Participation.
We address the current concerns about teaching-to-the-test and its association with declining dis... more We address the current concerns about teaching-to-the-test and its association with declining dispositions towards further study of mathematics and the consequences for choice of STEM subjects at university. In particular, through a mixed study including a large survey sample of over 1000 students and their teachers, and focussed qualitative case studies, we explored the impact of 'transmissionist' pedagogic practices on learning outcomes. We report on the construction and validation of a scale to measure teachers' self-reported pedagogy. We then use this measure in combination with the students' survey data and through regression modelling we illustrate significant associations between the pedagogic measure and students' mathematics dispositions. Finally, we discuss the potential implications of these results for mathematics education and the STEM agenda.
The aim of this paper is to describe and validate the development of two measures constructed to ... more The aim of this paper is to describe and validate the development of two measures constructed to measure AS students disposition (i) to enter HE and (ii) to further study mathematically-demanding subjects, which we regard as potentially significant variables in monitoring or even ...
The construct of identity has been used widely in mathematics education in order to understand ho... more The construct of identity has been used widely in mathematics education in order to understand how students (and teachers) relate to and engage with the subject (Kaasila, 2007; Sfard & Prusak, 2005; Boaler, 2002). Drawing on cultural historical activity theory (CHAT), this paper adopts Leont’ev’s notion of leading activity in order to explore the key ‘significant’ activities that are implicated in the development of students’ reflexive understanding of self and how this may offer differing relations with mathematics. According to Leont’ev (1981), leading activities are those which are significant to the development of the individual’s psyche through the emergence of new motives for engagement. We suggest that alongside new motives for engagement comes a new understanding of self—a leading identity—which reflects a hierarchy of our motives. Narrative analysis of interviews with two students (aged 16–17 years old) in post-compulsory education, Mary and Lee, are presented. Mary holds a stable ‘vocational’ leading identity throughout her narrative and, thus, her motive for studying mathematics is defined by its ‘use value’ in terms of pursuing this vocation. In contrast, Lee develops a leading identity which is focused on the activity of studying and becoming a university student. As such, his motive for study is framed in terms of the exchange value of the qualifications he hopes to obtain. We argue that this empirical grounding of leading activity and leading identity offers new insights into students’ identity development.
We address the current concerns about teaching-to-the-test and its association with declining dis... more We address the current concerns about teaching-to-the-test and its association with declining dispositions towards further study of mathematics and the consequences for choice of STEM subjects at university. In particular, through a mixed study including a large survey sample of over 1000 students and their teachers, and focussed qualitative case studies, we explored the impact of ‘transmissionist’ pedagogic practices on learning outcomes. We report on the construction and validation of a scale to measure teachers’ self-reported pedagogy. We then use this measure in combination with the students’ survey data and through regression modelling we illustrate significant associations between the pedagogic measure and students’ mathematics dispositions. Finally, we discuss the potential implications of these results for mathematics education and the STEM agenda.
The aim of this paper is to report our work in progress on the measurement methodology and some p... more The aim of this paper is to report our work in progress on the measurement methodology and some preliminary results of our analysis on an incomplete data set. We report on the analysis of the effect of some specific 'process variables' (pedagogy and Programme in AS level ...
This paper reports on a ‘photo-and-talk’ activity we conducted with 5-6 year olds to explore how ... more This paper reports on a ‘photo-and-talk’ activity we conducted with 5-6 year olds to explore how they might connect home/community activity with mathematics This activity was part of a larger project which aimed to understand young children’s mathematical identities, particularly children from poor communities. It builds on our previous work which addressed how school mathematics often alienates learners, resulting in their dis-engagement (Williams 2012). This project considers the origins of such alienation in the first year of formal schooling. Drawing on the ‘funds of knowledge’ approach (Moll et al, 1992), we developed this ‘photo-and- talk’ activity in order to capture the mathematical knowledge/practice young children engage with in their out of school activities. We worked with families and children to create an awareness of every day/home mathematics, in contexts outside of school. We did this by providing each child (and family) with a camera and asking them to take photographs of anything they thought was mathematical in their homes/community. This was subsequently followed up by interviews with the child and their parents (and sometimes siblings), most often in the home, where the child was asked to explain why each photo was considered mathematical and how it connected to their lives. Elsewhere (Black et al, in prep) we have argued that this photo-and-talk activity has potential as a hybrid home-school activity since it brings home/community activity and school mathematics into dialogue, and potentially into hybrid everyday-and-scientific mathematics. In this paper, we explore the nature of this ‘hybridity’ of mathematics further.
We build on previous work relating to Funds of Knowledge and our own work on mathematical identit... more We build on previous work relating to Funds of Knowledge and our own work on mathematical identities in a project seeking curriculum development potential using a photo-elicitation methodology. We theorise the combined unit of (i) a photo of ‘home maths’ plus (ii) the child’s commentary on it, as an act/ performance of mathematical ‘identification’ within the communicative ‘activity system’ constituted by the whole home-school research context. Drawing on two cases, we show how these identifications can ‘align’ with or ‘contradict’ mathematical identifications elicited in school-mathematical activity. We argue the contradictions may be most obviously interesting for development of practice and therefore for research. We discuss the social (classed/gendered) contexts of home and school responsible for such contradictions.
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Drawing on the ‘funds of knowledge’ approach (Moll et al, 1992), we developed this ‘photo-and- talk’ activity in order to capture the mathematical knowledge/practice young children engage with in their out of school activities. We worked with families and children to create an awareness of every day/home mathematics, in contexts outside of school. We did this by providing each child (and family) with a camera and asking them to take photographs of anything they thought was mathematical in their homes/community. This was subsequently followed up by interviews with the child and their parents (and sometimes siblings), most often in the home, where the child was asked to explain why each photo was considered mathematical and how it connected to their lives. Elsewhere (Black et al, in prep) we have argued that this photo-and-talk activity has potential as a hybrid home-school activity since it brings home/community activity and school mathematics into dialogue, and potentially into hybrid everyday-and-scientific mathematics. In this paper, we explore the nature of this ‘hybridity’ of mathematics further.