Teaching and Learning Research Programme - Widening Participation
Society for Research in Higher Education Conferemce, Liverpool, 9-11 Dec 2008
1409: The mediation of ideological values in students' journeys into higher education
(convenor Pauline Davis)
Towards a theory of value in education.
Julian Williams
The aim of this paper is to situate our understanding of the conceptions of "use" and "exchange" values of mathematics education within a theoretical framework. The original theory and methodology of choice in the project included Cultural-historical Activity Theory (CHAT) as a means to situate activity in classrooms within institutions and wider social structures and discourses, and hence situate learners? and teachers? subjectivities (for more on this see Williams et al., IJER special issue 2007). In summary and very briefly, CHAT provides a framework of concepts for understanding collective activity as structured by Activity systems, constellations of systems, and boundary objects and crossers that link systems (after Vygotsky, Leont?ev, Bakhtin, Engestrom and Cole, etc). It derives from Vygotskyan/Marxist materialist psychology and should by no means contradict a classic Marxist political-economic theory of value in education developed hereafter.
Renegotiating identities: mediation of troubling AS Level mathematics.
Wake, G.D. and Davis, P.
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.
University subject choice and discourses of parental influence: decision-making amongst AS Level mathematics students.
Davis, P. and Pampaka, M. University of Manchester
In this paper we draw on an analysis of the discourses of parental (family) expectations across ethnicity and social class. The vast majority of the 1700+ sample aspired to go on to a university degree and they stated through surveys that their interests were in a wide variety of subjects. Nearly half the sample intended a degree in a STEM subject (Science, Technology, Engineering and Medicine). Normative subject choices were typically gendered and classed. However, differences in the distribution of subject choice were especially notable between students when grouped according to their ethnicity, detected also in the inferential statistical analysis (Hutcheson et al, 2008). For example, Figure 1 shows that Asian or Asian British Indian heritage students were four times as likely as White British students to indicate a preference for “Business and Administrative Studies”. Alternatively, Black African students were about six times as likely as White British students to express a preference for “medicine or dentistry”, while Indian and Pakistani heritage students were five times as likely as White British students to express a preference for this same subject. Such trends are in line with existing literature (Ashworth & Evans, 2001; Bhattacharyya, Ison, & Blair, 2003; Siann & Gallaghan, 2001).
University subject choice and discourses of decision-making amongst AS Level mathematics students - powerpoint presentation
ISCAR 2008, San Diego
Symposium Title: Biographical, Classroom , Institutional, and Programme mediation of pedagogy: narrative and cultural -historical activity theory perspectives
Statistical versus personal narratives of the effect of pedagogy on learning
Pampaka, M., Williams, J. & Wake, G.
In this paper we reflect on the ‘effectiveness research’ that the project has conducted as regards ‘pedagogy’ we reconceptualise this work as a form of ‘narrative’: in itself, and contrast it with the narratives of our qualitative research, and with a reflective story of the research written for the purposes of this paper. For us ‘story-telling’ is an activity of reporting that, according to activity theory, has an object, but is mediated by instruments (genres) and rules (story-telling norms etc) that serve certain, sometimes inexplicit, purposes in regards to the outcomes subjectively sought. In this way we try to generate insights into our research, and hence perhaps research in general.
Pedagogy: the (mathematical) narrative in classroom practice
Wake, G.
Central to individual students? emerging identities as learners and users of mathematics is their experience of mathematics in classrooms. Therefore in seeking to understand how we might engage more students in mathematics we focus on mathematics lessons, making observations and analyses in the ethnographic tradition with video and audio recordings. One focus of analysis investigates how teachers mediate the mathematics (i) using a range of different "pedagogic practices", and (ii) by developing a lesson narrative interweaving mathematical with other, everyday narrative devices.
Immediately visible and apparently dominant in setting a "tone" for the classrooms of different teachers are their pedagogic practices e.g. the monological transmission of information; whole-class discussions; "modelling" an answer to an exam question; playing a "game" in pairs; group problem solving, etc. These practices appear to differentially support relational or instrumental understanding of students whilst also developing classroom communities that are more or less engaging for different students.
To bring the mathematics more sharply into focus we turn to the socio-cultural construct of narrative (Bruner, 1996). Thus we conceptualise the teacher as storyteller engaging learners with his/her personal construction of a mathematical narrative of a topic/concept. From our case studies we analyse how each teacher organises the total "story" of their lesson using the "social narrative thread" in an attempt to connect with their students "everyday" world and knowledge, running alongside, and at times interconnecting with, the "mathematical" world and "scientific knowledge" (in Vygotsky's sense of the everyday and scientific).
We explore how in, two lessons where teacher colleagues introduce "the same" mathematics, these two strands of narrative (mathematics and social) may be aligned to a lesser or greater extent. We see how these may support each other in a powerful way to (re-) define what it is to do mathematics, and how a CHAT analysis suggests that this realigns the object of the classroom activity system so that the community acts together to support the relational understanding of mathematics.
Interweaving narratives with CHAT: the institutional culture and ‘voice’
Williams, Pampaka, et al
We can consider pedagogy to be mediated by the institutional culture, the student community and the teachers' professional identity. In this paper we focus on the institutional component. We suggest that the College "institution" adds its own, particular "voice" to the heteroglossia that constitutes pedaogogy. Whilst often sotto vocé, the voice of the institution, we shall illustrate, can nevertheless have a significantly different role in different institutional contexts. We illustrate with regards to two institutions in the UK with somewhat different market positions, whose Principal's have different narratives with regard to "widening participation" and pedagogy, and which constrain pedagogies in their different ways. There are clear implications for professional development and even curriculum development. In terms of the theoretical development, we conclude that the "voice" of the institution comes into being historically as a function of the institutions sociocultural, geographic and economic positioning in the market place.
The influence of students’ life narratives on identification with learning mathematics
Pauline Davis et al
In order to capture pre-university students' subjectivities about learning mathematics, we draw on interviews focusing on students' experiences of learning mathematics in different pedagogic/curriculum cultures, and on their imagined futures about their education and careers. These seek to capture students? decision-making about learning mathematics, within the context of their motivations and professional goals. We are especially interested in cultural models (Holland, Lachicotte, Skinner, & Cain, 1998), which students use as discursive tools during the interview events in order to position themselves in certain kinds of ways as certain kinds of people, and how their beliefs about learning mathematics fits into this. The paper addresses the question, How does students’ mathematical positions/disposition appear in their identity and career decision-making?
We found that usually students' identification with mathematics was not critical to their identities (for this sample of 44 students. Talk about learning and decision-making was dominated by a cultural model of performativity and this was tied up with where their saw themselves heading in their careers and who they wanted to become over the next few years. Mathematics fitted into their stories primarily as something that gave status as a tool that could make them look good and in this way they could be said to identify with mathematics. However, students seldom identified themselves as having a love of mathematical ways of thinking.
Implications for pedagogy are that dispositions towards learning mathematics can be resistant to change and that if it is to make a difference to students' lives in the longer-term then pedagogy will need to connect better with identity. However, this isn't the case in the current system, where (for our sample) students, learning mathematics is only rarely rapped up with a sense of who they are and who they want to become, so that they mostly cannot be said to have a mathematical identity. For the purposes of this paper, we highlight students' accounts of their decision-making about future careers that they said influenced their subjectivities about learning mathematics and their views of themselves as young people transitioning into higher education, getting nearer to embarking on their professional careers. The students selected are amongst those for whom mathematics might be expected to have some relevance given their choice of degree subjects, accountancy, vetinary science and computer science. For the purposes of this paper they were amongst those who revealed about their positioning with mathematics in non-trivial ways.
Symposium Title: ###
The Cultural Historical Mediation of a Professional Identity
This paper will trace the cultural historical mediation of professional identities of mathematics teachers and relations to their distinct professional and pedagogical practices. The cultural-historical data is drawn from narrative accounts of (sometimes co-constructed dialogically from interviews with) teachers, whereas the 'consequences' for pedagogical practice are drawn from observational and case study work in their classrooms. While it is known that pedagogical practice is mediated by many 'systemic' factors, there nevertheless remains grounds for believing that the personal history of the individual teacher's 'professional identity' is a significant 'instrument' that the teacher can draw on in their practice. In this sense we argue that even in strictly controlled teaching-learning systems, pedagogical practice can allow agency and provide some space for professional self-authoring.
Research Briefing
4-page Research Briefing on the project.
Working Papers
Aspirations, subject choice and drop out: decision-making amongst AS Level mathematics students
Davis, P., Pampaka, M., Williams, J., Hutcheson, G., Hernandez, P., Kleanthous, I, Black, L., Nicholson, S & Wake, G.
This paper draws on surveys of up to 1700 students and interviews with 31 students collected during the ESRC- TLRP funded project, “Opening doors to mathematically-demanding programmes in further and higher education (FHE)”. The students were taking Level 3 (preuniversity qualifications, usually, over a period of two years), and as part of their general education A Level programme had opted to take an AS Mathematics or Use of Mathematics course.
The paper begins with a summary description of trends in university degree subject choices and considers how these are influenced by gender, ethnicity and social class (using the survey data). This analysis motivates an exploration of ideological values that mediate social identities, such as those shaped by gender, ethnicity and class. Specifically, we analyse students’ cultural models and situated identities (Gee, 1999) regarding university and career choices in terms of the ways they challenge and/or reinforce ideologies that maintain the status quo across particular social group identifications. We draw on van Dijk’s (1998) notion of social identity and ideology to link our analysis of cultural models to the investigation of social phenomena from a critical theoretical perspective.
We find that students taking AS maths and other A level or equivalent level three qualifications indicated high expectations of university entry, and we describe trends in University subject choice, which are broadly in line with the literature and government statistics. We found that most students had already decided upon a degree subject area and sometimes also a career by the beginning of their AS Level courses, but that early intentions were subject to change.
We found that in articulating their intentions about degree and career choices that students draw on a number of ideological values and cultural models, e.g. as a son, a daughter, a wife, a future worker and/or a successful person, and that these were used in the construction of nuanced gendered, ethnic and classed narratives. We found that students drew on values and other cultural models to do with performance, but that while White British students tended to narrate themselves as individuals in a ‘system’, minority ethnic heritage students tended to emphasise their families and communities.
We found a difference in the articulation of White and Asian students with regard to university subject choice; while Asian students tended to draw on identifications to do with the family, and to articulate family cultural social rules that they often recognised as mediating their decisions, White British students tended to present themselves as in the position of power, with regard to their university subject choice. We found White British students tended say little about the cultural social rules mediating their decision-making. We suggested this “absence” of talk occurred precisely because they position themselves as agentive decision-makers, and that this then closes or reduces a discursive space, rendering discussion of family or community social rules as contradictory or unnecessary. We suggest that this can sometimes act to mask social differences, as might exist, within the White British category, for instance different sets of social rules that might be situated in different classed “White communities. This suggests we may need to find ways to probe more deeply to learn about less visible social rules.
Towards a political economic theory of value in education
In this paper I explore theoretical conceptions of ‘use’ and ‘exchange’ values of mathematics in education within a CHAT perspective. I draw on Lave & McDermott’s study of ‘estranged learning’, and from Marx’s Capital. From the former, one deduces the source of learners’ alienation from learning in the exchange value of mathematics education. However, I turn to Marx’s Capital to find the correct meaning of use-value, and conclude that the use-value of mathematics education derives from (i) its value to learners in consumption, and (ii) its value in enhancing (mental) labour power.
Students' perceptions of mathematics' coursework in first year of College
Hernandez-Martinez, P., Black, L., Davis, P., Hutcheson, G., Nicholson, S., Pampaka, M., Wake, G., & Williams, J.S.
Students taking AS Use of Mathematics course perceived coursework as a different learning, teaching and assessment experience from that of regular lessons and examinations. For many students, coursework provided a resource for conceptual understanding in a different, less stressful environment than that of time-pressured exams, something which in turn could enhance their grades and eventually help them to succeed in mathematics. Coursework was also seen by students, particularly those in vocational courses, as a means to gain practical knowledge, something that suited their interests. Many students (although not all) considered these aspects of coursework enjoyable and beneficial to them. The few comments on coursework (mainly from their GCSE experience) of students taking a traditional AS course agreed in general with those of their Use of Maths peers. These results point to the need of rethinking the policies that have abandoned coursework as a way of learning, teaching and assessing, especially if we want to increase participation in mathematics.
Renegotiating identities: mediation of troubling AS Level mathematics
Davis, P., Williams, J., Hernandez, P., Nicholson, S., Pampaka, M., Black, L.,Wake, G., Hutcheson, G. & Kleanthous, I.
This paper examines serial interviews with 44 students from five 6th form/Further Education institutions in England. The students were taking Level 3 (pre-university qualifications, usually taken over a period of two years), and as part of their programme had opted to take an AS Mathematics or Use of Mathematics course.
According to Geertz narratives are the stories we tell ourselves and others about ourselves and are central aspects of culture. Narratives are also the lenses through which we understand and organise our world as individuals and collectively. Bruner suggests that narrative is a means for explaining the exceptional and forming a bridge to the ordinary (Rosenwald and Ochberg, 1992) and suggests that people’s troubles provide a means with which to understand changes of direction in narratives. Thus, a classification of troubles in narratives may provide a lens with which to see the salient values in the students’ lives that implicate their degree choices.
Holistic "synoptic" accounts intended to capture the essence of students' trajectories were compared in order to identify students with similar trajectories. Drawing on Bruner's account of narrative inquiry we focused on the influence of "troubles" in students' accounts as means of classification. These categories (canonical story schematic outlines) were classified as (a) "steady as they go –no significant troubles articulated", (b)"trouble comes ambitions adjust", and (c)"troubles come I persist in my plans”.
We found that when confronted with a trouble (for our students example troubles were experiencing “maths as too hard”, “feeling a need to maximise grades”, concerns about ways to gain a lucrative, outwardly successful career in future times, or troubles occurring in other aspects of their lives and usually associated with family life) students' renegotiation of identity, could be recognised in the interview text by means of changes or shifts in positioning towards or away from certain values (cultural models) that mediated their decision making. We found that in the face of troubles how students (re)negotiated their identities was mediated (i) by various cultural models about making one’s way in the world into adulthood and (ii) by the quality of emerging professional identification with specific intended careers. Students’ who articulated a view of their projected professional selves, which showed an intrinsic valuing of the “chosen” professions were in the category of students who persisted with their goals in the face of troubles, whereas students in the category that adjusted their intended career in the face of troubles, showed a strong identification with values of performativity and status, which came above those to do with the intrinsic worth of their abandoned originally intended careers.
We found that students’ explanations/accounts of decision-making are nuanced by a myriad of socio-cultural circumstances, to do with class, gender and ethnicity, but is also very much about their imagined futures. Therefore simplistic, policies that fail to take account of this by touching the valued concerns of students’ lives are less likely to have sustained impact. On the other hand, arguably policies for education that can touch students’ identities may have a greater chance of success. In the case of widening participation in mathematics we have a complex case because students take mathematics for a wide range of reasons often to do with its perceived exchange value rather than use (see Davis et al, working paper c).
ASTrad and UoM courses: factors influencing enrolment
Hutcheson, G.D., Black, L., Davis, P., Hernandez, P., Nicholson, S., Pampaka, M., Wake, G., Williams, J.S. (2008a).
The aim of this paper is to describe the students who have enrolled on the ASTrad and UoM courses and the factors that might have influenced this enrolment. The modelling process is used to identify the underlying factors that might affect course selection and also to select a subset of variables that can be used for a predictive model of course selection.
It can be hypothesised that a number of “underlying” factors might be influencing course enrolment. For example, course enrolment might be associated with the socio-economic status of the student and previous examination grades. One can also hypothesise other “factors” that may also be associated with course such as the family history of University attendance, disposition to continue to higher education and other variables such as ethnicity and gender. These factors are represented in the data set by single and multiple variables and the factors also interact with each other (for example, the two distinct factors “ethnicity” and “socio-economic indicators” are associated with each other).
The following analysis attempts to identify the important influences on course choice and include these in a predictive model to assess their relative importance. The models are then compared to see which are the best-fitting and also the most useful for descriptive and practical purposes. The aim is to select a final model that is not only good-fitting, but also interpretable with regards to the underlying factors that the variables represent.
Dispositions towards studying Mathematically-Demanding subjects in HE
Hutcheson, G.D. (2008b)
The aim of this working paper is to model (and hence illustrate the modelling approach/heuristics in the project) student disposition to study mathematically-demanding subjects in HE (MHEdisp) over three time points (represented as MHEdisp1, MHEdisp2 and MHEdisp3, which broadly corresponds to the start of AS, the end of AS and during A2). This paper will describe dispositions at each time point and also investigate which variables are associated with these. Using ordinary least square (OLS) regression models we can obtain a prediction of MHEdisp at any point in time. For example, given information about the course a student is enrolled on, their language use and TierGrade, one can make a prediction of MHEdisp at time point 1 using the OLS regression model:
MHEdisp1 = Course + Language + TierGrade
These models will help us to answer questions such as: “Is the course a student enrols on associated with their MHEdisp score at time 1?”, or “Is disposition associated with TierGrade, even after taking into account the effect of course and language use?”. Such regression models will determine the existence of associations in the data, which may give indications of causal relationships. In addition to these analyses, it is also useful to investigate the changes in MHEdisp over time. For example, the change in MHEdisp between time points 1 and 2 may be modelled using an OLS regression
(MHEdisp2 – MHEdisp1) ~ Course + TierGrade + Pedagogy
These models will help to answer questions such as “does having a teacher with a high pedagogy score affect changes in MHEdisp over time?” and “are changes in disposition associated with tiergrade and course enrolled on?”. The data include a large number of interacting variables that may influence dispositions. It is also the case that disposition scores are highly variable over time and may also be subject to considerable random variation, or at least variation due to variables that have not been recorded. In these circumstances, there may be a large number of similarly-fitting models that can be applied. A major challenge for this analysis is therefore to select appropriate models to represent the relationships in the data.
Participating differently in mathematics: the value of mathematics, learner approach and Programme context
Davis P., Pampaka, M., Williams, J.S., Wake, G., Nicholson, S., Hutcheson, G., Hernandez-Martinez, P., Black, L. and Kleanthous, I. (2008c).
A cluster analysis of students discourses by codes applied to their interview responses leads to (i) categories of 'maths values' (exchange-orientated; use-orientated, and 'mixed' orientation'), (ii) categories of 'learning approach' ('surface' and ' not surface'), and hence to hypotheses about the relations between these two constructs. We find that there is a weak relation between ‘surface’ and ‘exchange’, and 'mixed' and 'other', but that ‘use-oriented’ and ‘not surface’ are related. However, these relationships are complicated when Programme (BTEC vocational-'AS uses of maths' and 'AS maths) are taken into account. Finally, we interpret these findings as patterns in discourse in their pedagogic and curriculum contexts. We suggest that when students are in dialogue with a ‘uses of mathematics’ Programme/ course narrative a space is created that some students may take up to become a different kind of mathematics learner – a mathematical modeller.
Transition into post-compulsory (mathematics) education
Julian Williams, Paul Hernandez-Martinez, Laura Black, Pauline Davis, Maria Pampaka and Geoff Wake (2008).
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 their (mathematical) subjectivity/identity, i.e. that they would offer troubling moments. In this working paper we draw on and analyse cross-sectionally the interviews of project students regarding their (post hoc) experience of transition into 6th form or FE College programmes (and some teachers data form case study interviews and observations). We find that for many students transition is recalled as a key moment, when trouble with the 'step up' in demand was experienced at the same time as social, intellectual and emotional challenges were being posed (by the need to re-construct a peer group, be the increased autonomy of the expected work, and by demands to be 'grown up'). However, we draw attention to significant positive features of students? accounts: most students tell of this as being an important learning and growing experience. Even in their learning of mathematics, a significant number of students tell of the new experience as being an improvement on secondary school: they tend to say they understand more and that the work is better. Thus the „transition? is widely seen as a growth point rather than a problem (at least after the event). We discuss some general implications for conceptualising 'transition' and identity.
Publications (Journals and Edited books)
Measuring pedagogic practice for widening participation in mathematics
under review in Assessment in Education: Principles, Policy & Practice,
Maria Pampaka*, Julian Williams, Graeme Hutcheson, Pauline Davis, and Geoff Wake
A new self-report instrument was constructed to measure the „pedagogy? of mathematics teachers for pre-university programmes in the UK. Data from 110 cases of pedagogy are employed to validate this measure using the Rating Scale Rasch model. We report on the outcomes of this analysis that resulted in a one-dimensional measure of what we call „teacher-centrism? (ranging from „teacher- centred? to „learner- centred?). The validation process is also enriched with case study data from teachers and results of a parallel student survey. The paper concludes with the methodological and educational significance of the study.
Imagined futures: mediation of the mathematical biography
Laura Black
This paper presents data drawn from biographical interviews with students (ages 17-18) conducted as part of a research project on widening participation in mathematics education. The students were asked about their educational background, their experiences of learning maths and their disposition towards future study.
We view the stories students tell us in these interviews as narratives of identity – narratives in which students draw on troubles, obstacles and resources as they map the trajectory of their imagined lifestory (Bruner 1996). Thus, we are interested in the ways in which students identify with mathematics and how this connects with the trajectories they construct within the interviews. The paper asks: how do students connect their identity as a learner of mathematics with their other salient identities within the interview narrative?
The paper focuses on three students (Gemma, Mary and Lee) drawn from our wider sample of 50. These have been selected because of their contrasting positions towards learning maths. However, all three cases exemplify the kind of positionings which were evident in students’ narratives across the dataset. All interviews were analysed as biographical narratives focusing on how students’ self identity statements fitted with the overall story they were attempting to construct. We are particularly interested in self-identity statements regarding students’ career plans (e.g. ‘I want to be an engineer’), their decision to enter HE and their relationship with mathematics.
The stories told by these three students illustrate various modes of positioning with or against mathematics and highlight how one might narrate oneself as some kind of ‘maths person’ or ‘anti-maths person’. For instance, Lee, finds himself marginalised from mathematics due to his insititutional position as a ‘struggling’ student and consequently draws on the notion that ‘maths is irrelevant’ to his career trajectory in order to reconcile a sense of ‘not belonging’. The notion of a ‘leading identity’ in the student’s narrative appears to be pertinent for some – this is the imagined ‘identity’ of the future which appears signficant in ‘leading’ the individual’s development (derived from the concept of leading activity from Stetsenko & Arievitch 2004, Leontev 1981). For example, Gemma, a ‘low grade’ student, who in another college would have been prevented from taking AS maths, constructs her narrative with the view that ‘mathematics is hard and challenging’ which provides positive energy for her imagined future identity as a marine biologist.
We conclude that some students may narrate a ‘leading identity’ in their account at ‘critical moments’ in time (e.g. on completion of the UCAS form or having watched a particular film). Once this emerges it then permeates the narrative throughout. Sensitivity to the use or non-use of ‘leading identity’ in our analysis enables us to see the degree to which student’s identity as a learner of maths plays a part in the students imagined future.
Academic Papers and Presentations
Listed below are some of the papers and presentations from the project in Microsoft Word/Powerpoint or Adobe Acrobat PDF formats, with the latest listed at the top of the page.
2008
Narratives, Cultural Models and Identity
Williams, J.S., Black, L., Hernandez-Martinez, P., Davis, P., Pampaka, M., and Wake, G., (accepted).
in M. César and K. Kumpulainen (Eds.) Social Interactions in Multicultural Settings, Sense. Publishers: Rotterdam.
In this chapter we will draw on work from our project, Opening doors to mathematically-demanding programmes in Higher Education and in particular on four of the project’s recent papers (Black, Davis, Hernandez-Martinez, Pampaka, Wake, & Williams, under review; Hernandez-Martinez, Black, Williams, Davis, Pampaka, & Wake, 2008; Williams, 2007; Williams, Black, Hernandez-Martinez, Davis, Hutcheson, Nicholson, & Wake, 2007) to demonstrate three distinct methodological frameworks, based on ‘discursive psychology’, a narrative approach to identity, and cultural-historical activity theory (CHAT) respectively. The first two of these papers analysed interview data to gain insight into how different students formulate different aspirations and identities in regard to mathematics. The latter two increasingly draw on a broader set of case study data that includes observations of classrooms and interviews of observed students and their teachers, and indeed managers and principals in the colleges where the learners were studying.
In addition to grounding these three methodological approaches in the project’s data, we aim to evaluate the adequacy of these approaches to understanding and explaining how identity is produced in practice. Although the substance of our results are of interest to mathematics educators, our main aim in this paper is to illustrate the different theoretical and methodological approaches and what they can offer researchers interested in identity. We finally will argue the need for discursive and narrative methodologies to be complemented by ethnographic-style case studies of social practice in order to produce ‘explanations’ of trajectories of identity. In particular, we argue that this requires a ‘boundary’ concept between the activity of doing mathematics (the mathematical practice) and the activity of storying one’s self (narrating a biography) and accounting for one’s aspirations. We show how we use ‘cultural models’ in this regard: indeed we show how cultural models arising from classroom mathematical practice can be instrumental in students’ accounting for their aspirations and in their narrative identity work.
Mathematics students' aspirations for higher education: class, ethnicity, gender and interpretative repertoire styles
Paul Hernandez-Martinez*, Laura Black, Julian Williams, Pauline Davis, Maria Pampaka and Geoff Wake
This paper reports how students talk about their aspirations in regard to higher education (HE) and their mathematics, what ‘repertoires’ they use to mediate this discourse, and how students’ predominant ‘repertoire style’ relates to their cultural background. Our analyses draw on an interview sample (n=40) of students selected because they are ‘on the cusp’ of participation or non-participation in mathematically demanding programmes in further and higher education. The interviews explored the students’ aspirations for their future in general and HE in particular, influences on these choices, and the place of mathematics in these. Thematic analysis revealed four interpretative repertoires commonly in use, which we call ‘becoming successful’, ‘personal satisfaction’, ‘vocational’, and ‘idealist’ repertoires. Most of the sample was found to use a single, predominant repertoire, which we call their repertoire ‘style’: what is more, this style is found to be strongly related to background factors independently obtained. The implications for policy and practice are discussed.
The central role of the teacher – even in student centred pedagogies
Geoff Wake & Maria Pampaka, presented at PME 32, Morelia, Mexico
We describe a case study of an unusually ‘student-centred’ mathematics teacher whose students construct unusual – and positive – mathematical dispositions and identities. We draw on a self-report ‘teacher-centred pedagogic practices’ scale, interview and classroom lesson analyses to identify her pedagogic practice and her reflections on these. Our analysis distinguishes ‘mathematical’ and ‘social’ strands in her narrative within lessons which ensure that whilst her practices are found to be engaging and ensure agency and choice she maintains firm control over the ‘mathematical narrative’. In this sense her practice appears contradictory: Activity Theory suggests this as an objective contradiction between the learners’ knowledge and the mathematical reformulation of it that the teacher mediates.
2007
Hybridity of maths and peer talk: crazy maths.
Davis, P. and Williams, J. (2007)
In Black, L; Mendick, H and Solomon, Y. Mathematical Relationships in Education: Identities and Participation. London: Routledge.
In this chapter we show how students’ collaboration regarding their work in class can sometimes facilitate a sociable 'community influenced' classroom mathematics talk. The social affordances of collaboration and indeed mathematics as a human, social activity have been examined by many others, although sometimes under the guise of equitable mathematics or inclusive mathematics pedagogy (Boaler, 2000, Boaler and Greeno, 2000, Nasir and Cobb, 2002, and many others) and earlier in the area of 'cooperative' classrooms. Such research has consistently pointed to the value of encouraging student-student interaction as a means to foster more positive identifications with mathematics, often for those who might be described as struggling learners (for example Boaler, ibid).
Annual Conference of the British Educational Research Association (BERA)
5th-8th September 2007, Institute of Education, University of London
Symposium entitled: ESRC-TLRP Research in Widening Participation Opening doors to mathematically-demanding programmes in Higher Education 1
Laura BlackThis paper presents data drawn from biographical interviews with students (ages 17-18) conducted as part of a research project on widening participation in mathematics education. The students were asked about their educational background, their experiences of learning maths and their disposition towards future study.
Pauline DavisThe paper is based on the ESRC TLRP research project in widening-participation in HE, `keeping open the door to mathematically-demanding F&HE programmes', which aims to understand how cultures of learning and teaching can support learners in ways that help widen and extend participation in mathematically demanding courses in F&HE. In this paper we address the following questions: how do some students talk about their mathematics social practice? And (conceptually) how can different pedagogies mediate mathematical identity?
Paul Hernandez-MartinezThis paper is part of an ongoing ESRC-TLRP project which aims to understand the reasons implicated in young people’s decisions to go into Higher Education (HE) and particularly into mathematically demanding courses.
As part of the project, we are doing a series of longitudinal interviews with students about their family and educational backgrounds, their experiences and views about mathematics and their dispositions and aspirations towards future study and particularly, if these are related to mathematics or not. In this paper we report on interviews made at the time when the majority of these students were beginning their first year at College, and were taking at least one course in mathematics. We were interested in analysing the impact that social class and ethnicity have in these students’ aspirations and how this relates to their mathematical disposition.
The research literature shows that students who come from lower social class backgrounds are especially vulnerable to marginalisation by the education system (Ball et al, 2002a), particularly in relation to mathematics (Cooper & Dunne, 2000), and also how social class position affects students’ access to, and participation in HE (Lynch & O’Riordan, 1998). The literature also shows how ethnic minorities’ choices of HE are limited by the education system, highlighting class and racial differences and inequalities (Reay et al, 2001). Therefore, in this paper we will address the following question: How are students’ aspirations and dispositions towards entering HE (especially mathematically demanding subjects) influenced by social class and ethnicity?
Symposium entitled: ESRC-TLRP Research in Widening Participation Opening doors to mathematically-demanding programmes in Higher Education 2
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 explaining students progress in to different studies in HE. The items for the scale were constructed on the basis of interview data, and drew on a model of disposition as socially- as well as self- attributed. Drawing on Rasch analyses of pilot and ‘main’ data sets, we find that the two scales each produce healthy one-dimensional fits on what we take to be a ‘strength of commitment to enter HE’ and ‘disposition to study mathematically-demanding subjects further’ respectively. However, as a measurement scale for this sample in this context the former scale suffers from a ceiling effect: our sample are overwhelmingly committed to entering HE (at the early stages of AS level mathematics course anyway). To ‘correct’ for this, we added some harder items to the analysis at a later data point, and found (i) an item that improved separability of the instrument for the higher scorers, and (ii) a massively misfitting, hard item that is worthy of future research.
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 mathematics) on value added to some ‘learning outcomes’ (measures of disposition), and how background variables such as gender, proxies of class, etc. influence these. The data set comprises of disposition measures at two data points early and late in the AS year, and does not yet include measures of grades or UCAS decisions that will follow later in the project. We focus on students disposition to ‘further study mathematically-demanding subjects’ and their ‘mathematics self-efficacy’ in this paper, and find some statistically significant but uninterpretable process effects related to Programme, pedagogy and EMA grant support.
Geoff WakeAs you set out to read this paper you may wonder about the story it will tell. Already as authors we are manipulating your engagement as a (potential) reader. Hopefully, our choice of title appeals suggesting that our focus will be AS mathematics lessons and that we will be viewing these by taking account of the practices that teachers employ within their teaching and the different stories that are involved. The narrative device of speaking to you directly is perhaps unusual in an academic paper: you may be wondering how else we will attempt to maintain your interest and engagement and how we will sequence events to ensure that the points we wish to make potentially have maximum impact. We raise these issues at the outset, as narrators ourselves, to help us suggest that mathematics teachers in their design and implementation of lessons make similar choices: they narrate a story, or stories, for their students where the development of mathematics is in the main central, but may not always be so. However, their medium, the lesson, has much more potential than the page available to us here. They consequently have other choices to make about how to engage the audience, their class, in their unfolding narrative(s): what pedagogic practices will they use to maximise impact, entertain, and so on? In this way teachers, therefore, might be considered as directors of a performance art production, who may at times decide to incorporate the audience to a greater or lesser extent, in the story they tell.
American Educational Research Association (AERA)
April 2007, Chicago
Multi-dimensional structure of a (use of) Mathematics self efficacy instrument
Pampaka, M., Black, L., Davis, P., Hernandez-Martinez, P., Hutcheson, G., Nicholson, S., Wake, G., & Williams, J.
An instrument was built to measure self-efficacy (s.e.) of 16-17 year old students in relation to their use of mathematics, a ‘soft’ learning outcome measure that is expected to provide important information when contrasting subgroups following a ‘mathematics’ and a ‘use of mathematics’ programme. Analysis revealed significant DIF between the two subgroups. Further, multi-dimensional analysis suggests that ‘pure (P)’ and ‘applied (A)’ scores might better be reported separately (in addition to the overall ‘maths (M)’ s.e. score). Furthermore the subgroup score means P and A are significantly different in the expected direction (i.e. the use of maths group is significantly more confident on the Applied dimension and vice versa), while the relation of M (A, P) is nearly invariant across subgroups.
Conference for European Research in Mathematics Education (CERME5)
February 2007, Cyprus
Storying mathematical identities with cultural models
Julian Williams, Laura Black, Paul Hernandez-Martinez, Paulin Davis, Graeme Hutcheson, Su Nicholson, Maria Pampaka, Geoff Wake
presented at Working Group 10 (Mathematics education in multicultural settings), p.1607-1616 in the Proceedings
When we build our narratives of identity in interviews, we make use of “cultural models”, culturally normative rules, schemas, ways of describing people, activities and ways of being. In this study we identify cultural models used by two mathematics learners in the stories they told us about their lives, including their experiences of learning mathematics and their disposition to study mathematics in the future. Each model provides a tool for identifying or dis-identifying with mathematics. While some models might be thought more „positive?, and others more „negative?, students positioned with strong imagined life stories or ambitions can turn these models to their own purposes. Thus maths is „hard? can sometimes be storied as „challenging and fun? rather than „too hard and boring?. The significance of the educational culture is discussed.
Measuring perceived self-efficacy in applying mathematics
Geoff D. Wake, Maria Pampaka
presented at Working group 13 (Applications and Modelling), p.2210-2219 in the Proceedings
In England a new course of post-compulsory study has been developed based on the premise that developing confidence and ability in applying and modelling with mathematics will better prepare students to elect to study courses that require relatively high levels of mathematics in their future studies in Further and Higher Education. In investigating this we have designed an instrument to measure perceived self-efficacy beliefs in applying mathematics. Here we report principles of construction of the instrument together with initial analysis which suggests that it does allow measure of perceived self-efficacy beliefs in mathematics generally and in pure and applied mathematics separately with early evidence suggesting that the new course is successfully developing students’ confidence in applying mathematics.
2006
TLRP Annual Meeting (TLRP)
20th-22nd November 2006, Glasgow
Symposium entitled: ESRC-TLRP Research in Widening Participation "Opening doors to mathematically-demanding programmes in Higher Education"
Perceived self-efficacy in applying mathematics: implications for widening participation
Geoff WakeIn England a new course of post-compulsory study has been developed based on the premise that developing confidence and ability in applying and modelling with mathematics will better prepare students to elect to study courses that require relatively high levels of mathematics in their future studies in Further and Higher Education. In investigating this we have designed an instrument to measure perceived self-efficacy beliefs in applying mathematics. Here we report principles of construction of the instrument.
Maria PampakaAn instrument was built to measure self-efficacy (s.e.) of 16-17 year old students in relation to their use of mathematics, a ‘soft’ learning outcome measure that is expected to provide important information when contrasting subgroups following a ‘mathematics’ and a ‘use of mathematics’ programme. Analysis revealed significant DIF between the two subgroups. Further, multi-dimensional analysis suggests that ‘pure (P)’ and ‘applied (A)’ scores might better be reported separately (in addition to the overall ‘maths (M)’ s.e. score). Subgroup score means will also be reported.
Laura BlackNarrative inquiry has recently emerged as a constructive tool in the analysis of mathematical identity (Kaasila 2007). This paper presents the stories of two AS level students (aged 16-17 years), Mary and Lee, who were interviewed as part of a larger project on widening participation in mathematics education. The stories told by these students illustrate various modes of positioning with or against mathematics and highlight how one might narrate oneself as some kind of ‘maths person’ or ‘anti-maths person’. For instance, Lee, finds himself marginalised from mathematics due to his institutional position as a ‘struggling’ student and consequently draws on the notion that ‘maths is irrelevant’ to his career trajectory in order to reconcile a sense of ‘not belonging’. We argue that the notion of a ‘leading identity’ in the student’s narrative appears to be pertinent for some – this is the imagined ‘identity’ of the future which appears significant in ‘leading’ the individual’s development (derived from the concept of leading activity from Stetsenko & Arievitch 2004, Leontev 1981). Whilst some students have a clear sense of a leading identity from an early age, others are ‘living in the moment’ and may only narrow their possible futures at certain critical moments (e.g. in completing their UCAS form). We conclude that pedagogic and institutional practices can be crucial to sustaining or hindering a particular ‘leading identity’ – they may resource possible futures or narrow them depending on the positionings they offer students as learners of mathematics.
Pauline DavisThis short briefing paper addresses the research question ‘in what ways can classroom pedagogic culture mediate students’ relation with mathematics, (their mathematics learner identities)?
ESRC Seminar on Mathematical Relationship: Identities and Participation
8th November 2006, University of Manchester
Annual Conference of the British Educational Research Association (BERA)
6th-9th September 2006, Warwick University
2005
TLRP Annual Conference (TLRP)
May 2005, Warwick
Presentation: Keeping open the door to mathematically demanding Courses