Tracy Part

On the way to Mathematical Wellbeing…

Adult learners do not just bring mathematical skills with them into the classroom; they bring values and beliefs about the purpose of mathematical knowledge/education and unconsciously formed expectations of teaching and learning. What mathematics comes to represent to each individual is the product of particular and shifting identities, which are continuously mediated through lived experiences, personal beliefs and first hand encounters of teaching and learning. Thus, when an adult learner returns to education, they do so with unconsciously (per)formed and durable learning habits, often framed by previous, painful, experiences of learning (Noyes, 2004) and habits and dispositions that can all too frequently become internalized as a natural (in)ability to learn mathematics (Boaler, 2002).

The following paper is my first attempt, as a PhD student, to wrestle with Bourdieu’s analytical toolkit of habitus and field with a sideways look at capitals. I intend to use the narrative of a learner participant, James, from my PhD inquiry into the possible constructions of mathematical wellbeing, to illuminate some of the ways in which his complex system of learning dispositions have come to produce mathematical practices that at times simultaneously act as a product of his social history and a producer of his future (Noyes, 2004).

I will provide a brief overview of the context of learning mathematics in the Lifelong Learning Sector, pre level 2, before making a sociological case for using mathematical habitus as an analogy to depict some of the ways in which James may have come to fit, or fall between the social spaces (Skeggs, 2004) of learning mathematics. I will then foreground insights from James’ stories of learning, to examine some of the possible constructions of his mathematical habitus before applying aspects of the notion of performativity, through the contextualized works of Mendick (2005, 2006, Mendick, Moreau, & and Hollingworth, 2008) to reach a more textured understanding of how James’ narratives of ‘doing’ mathematics may exhibit inherently gendered and classed practices and perceptions of ‘being’ a mathematician.

Mathematical context

Bourdieu uses the analogy of a game to introduce the interrelated notions of habitus (1977), field, and capitals (1992) and thus, I intend to first situate the game of learning mathematics in the field of the Lifelong Learning Sector, pre level 2. Whilst it is not possible to do the philosophy of mathematics justice within the confines of this paper, a brief overview of this complex

and fiercely contested debate (Ernest, 1991; Skovsmose & Valero, 2005: Burton, 2001) can provide a useful spectrum from which to position the individual learner in relation to epistemic assumptions within the field.

At one end of the spectrum the Absolutist view tends towards maintaining positivistic assumptions over the purpose of mathematical knowledge as an “objective, absolute, certain and incorrigible body of knowledge, which rests on the firm foundations of deductive logic” (Ernest, 1991, p. 4). Although there is of course a range of perspectives from within this paradigm, all stem from the belief that mathematics is a universal language of ‘truths’, comprised of structures that transcend the cultural, historical and political complexities of (hu)mankind. In contrast to Ernest’s (1991) focus on the Absolutist philosophy of mathematics, Dowling (1998) extends the debate within an educational context by coining the distinction between ‘public’ mathematics against the complex specialist esoteric mathematics of the intellectually able.

Traditional pedagogies of mathematics tend towards an epistemic assumption of truths existing within the esoteric domain, which requires teachers to demonstrate rules and procedures and to use specialist mathematical symbols, language, and codes. The teacher’s role is assumed to be one of eliminating learner mistakes and organising knowledge; the student in return is expected to demonstrate mastery of simple operations before progressing onto, and reproducing, prescribed routes of inquiry using general mathematical principles (Coben, 2000). Antagonists (Coben, 2000; Burton, 2004; Boaler, 2009; Ernest, 2009; FitzSimons, 2002; Skovsmose & Valero, 2005) argue that, within this traditional model, opportunities to progress are restricted to those who can (and are willing) to conform to (and perform) linear models of learning, and are willing (and able) to reproduce mathematical “truths” as prescribed by their educator(s).

Fallibilists polarise this Absolutist stance and contest the notion of timeless and flawless mathematical ‘truths’ (Ernest, 1991) and frame mathematical knowledge as a product of its social discourse (Skovsmose, 1994), a decision making construct whereby mathematical behaviours change in response to the community where the mathematics is situated (Burton, 2001). In consequence, general mathematical principles become contextualised to local settings, which arise from the cultural contexts of the students (Ernest, 2009), and where the language of mathematics tends to be viewed as a malleable tool to facilitate, rather than organize, mathematical thinking (Skovsmose, 1994). The role of the teacher is to become less visible, more instructional by tone, encouraging learners to make agentic decisions about the ways in which their mathematical world makes sense to them (FitzSimons, 2002). However, there is a sizeable minority of mathematics educators (Volmink, 1994; Coben, 2000; Burton, 2001) who contest the assumption that learners need to be protected from the abstract, non-contextualized, mathematical knowledge of the esoteric domain. Coben (2000), whilst favouring constructivist changes within the curriculum, stresses that learners should not be restricted to working within familiar contexts and advocates an everyday discursive approach thus taking the abstract out of the esoteric domain and maintaining the powerful nature of general mathematical principles central to the transfer of knowledge between familiar and unfamiliar contexts.

A Constructivist approach, irrespective of the position of abstract principles, demands that learners become engaged with open-ended dialogue and assumes agentic ability (and willingness) to co-construct mathematical ideas and to value their own mathematical knowledge (Swan, 2006). However, this approach to learning brings a new set of expectations into the field of learning mathematics, which can all too easily conflict with, and restrict, those learners working within mathematical trajectories more closely aligned with more traditional approaches to teaching and learning. Thus, whilst there may be varying degrees of autonomy at the level of delivering the curriculum in the classroom; the macro context and the broader social milieu where the learning takes place will intertwine in complex and multilayered ways generating particular logics of practice (Reay, 2004). These logics will structure the rules of the game and (re)position the individual in ways which are likely to legitimize, constrain and/or silence (Squire, Andrews, & Tamboukou, 2009) mathematical thinking and voice.

Mobilizing a Bourdieunan Landscape

Hillier & Rooksby (2002) position habitus as a generative machine that emphasizes the structuring forces of social, cultural and physical experiences and posit that it is through these multiple (and evolving) lenses that we come, as individuals, to know and position ourselves and through which others come to know, and position us. The classed nature of habitus is further expanded by Skeggs (1997), as the ways in which individuals inherit their understanding of the world through their social positions and positionings within discourse and in knowledge. Noyes, (2004) translates this theory into a mathematical context and suggests that the ways in which an individual comes to gain a feel for the game is subconsciously formed through the memories of previous social encounters. The products of these experiences is internalized by the individual as natural or normal learning behaviours, and thus generate learning dispositions which, according to Zevenbergen (1993), informs the ways in which expectations, perceptions, and behaviours are enacted in the classroom.

In theorizing habitus through the complex systems of dispositions (Wedege, 1999) generated in an unconscious form, it is important to emphasize that an individual’s habitus will remain highly adaptive and thus incline, not determine, the ways in which an individual is likely to interact in the classroom. Whilst the analogy of habitus holds both durable and stable characteristics, changes within behaviours are possible, although relational to the repressions and pressures of the macro, meso and micro fields of learning (Hillier & Rooksby, 2002). Bourdieu writes that ‘when habitus encounters a social world of which it is the product, it finds itself “as a fish in water”, it does not feel the weight of the world and takes the world about it for granted’ (Bourdieu & Wacquant, 1992, p. 127). Those in the social milieu (including teachers) with the greatest volume of the valued capitals (most often cultural) are most likely to feel like ‘fish in water’ and are likely to participate in ways that will perpetuate the rules to promote their social positioning. Essential to the pedagogic expectations through a social

constructivist lens, those with a lesser amount of capitals are likely to position themselves (and be positioned by others) less favourably, are less likely to value their participation and are thus more likely to devalue their mathematical contributions.

The shape and form of mathematical habitus remains relatively under-researched, but the ways in which individuals may come to be (further) positioned and disadvantaged through the pedagogic practices that structure classroom mathematics have been worked through by Zevenbergen (1993, Grootenboer & Zevenbergen, 2009) and contributed to by Noyes (2004, 2009), Boaler (2002, 2009), and contextualized into adult learning by Wedege (1999, Wedege & Evans, 2006).

Mathematical Habitus

Mathematical habitus is woven from the life that an individual has been able to live (Zevenbergen, 2001), thus learning histor(ies) (Coben, 2000) in conjunction with the wider habitus generate a repertoire of possible mathematical dispositions (Kenway & McLeod, 2004) which simultaneously enable and restrict mathematical thinking and voice. Whilst an individual’s mathematical habitus cannot determine how they will approach their mathematics in the classroom on any given day, strategies tend to be instinctively rooted in habitual behaviors, which are, more often than not, fixed around the reproduction of authorised mathematical ‘truths’ (Wedege, 1999).

Arguably, one of the most crucial features of habitus is that it is not theoretically restricted to a matrix comprised of mental attitudes, actions and perceptions but is the product of the embodiment of social structures (Bourdieu & Wacquant, 1992) summarized by Holt (2010), as the ways in which the social world exists within the body.

“People carry their experiences into the classroom in their bodily hexis, their taken for granted assumptions, their sense of what is right and natural, it relates back to their family, the broader social milieu and the educational experience associated with their background (Noyes, 2004, p. 246).”

Noyes (2004) captures the importance of the embodiment, where bodily hexis refers to the ways in which social and cultural norms become imprinted, enacted, and reproduced through the ways in which we use our bodies (Youdell, 2006). It is through our expressions, postures, speech styles etc, that our body language communicates our particular ways of being (Youdell, 2006) and many adults marginalized by their experiences of learning mathematics have come to internalize negative self-images of their abilities to grapple with the mysterious and complex language of mathematics.

Mathematics has a long history of a high status academic discipline, which in part, has been derived from its perceived efficiency to be able to exercise and discipline the academic mind (Boaler, 2009). Thus, those engaged with mathematics tend

to be held within a privileged space, an assumption that has served to naturalise the use of mathematics as an appropriate tool to judge, sort, label and track students (Boaler, 2009; Noyes, 2007; Bourdieu, 1998; Volmink, 1994). Whilst this high status has undoubtedly empowered a sizeable minority to succeed well beyond school years (Wolf, 2002), ‘success’ of the oft-privileged few has come at a heavy price for the many.

“People are generally not neutral in their affective commitment to mathematics, but feel extremely alienated from, if not actively hostile to it. In fact it has almost become a status symbol to display one’s disdain or disinterest in mathematics (Volmink, 1994, p. 52).”

Skovsmose (1994) argues that it is the accumulation of the invisible structuring practices of mathematics, which has embedded the notion of a “mathematical gene” firmly within the psyche of the individual. Thus, it is through survival strategies that individuals come to (re)produce a mathematical habitus that is likely to distance themselves from the discipline of mathematic (Skovsmose & Valero, 2005; Volmink, 1994) and the pedagogic discourse of social constructivism.

The Data

James is one participant from a small scale, qualitative study for a PhD inquiry into the ‘usefulness’ of the capabilities framework as a means to encourage adult learners to identify and reflexively consider the ways in which they approach the learning of mathematics. ”Narrative about the most “personal” difficulties… frequently articulates the deepest structures of the social world and their contradictions” (Bourdieu, 1999, p. 511) and so starting with an open narrative approach to collecting life stories, the epistemic assumption that underlies my methodological approach, holds that experience is socially, historically and culturally situated and expressed through spaces of time, location and social contexts, that are particular to the interview. Thus any insights gained into the possible constructions of mathematical habitus from James, can only be considered as one possible interpretation from many possible stories of learning.

The aim of the narrative approach is to provide a Bourdieuian landscape from which to situate what mathematical knowledge may mean to the individual. This is of course, an abstract question almost impossible to visualise let alone answer and so to enquire in a meaningful way, required the use of a second data gathering tool; a non participatiory observation of the participant ‘being’ a mathematician and ‘doing’ mathematical problems in the classroom. These observations were then used to stimulate further discussions for the second and final, semi-structured interview to illuminate more textured insights into how the participants made sense and perceived ‘being’ a mathematician and ‘doing’ mathematics.

The learner participants were drawn from a small sample of experienced and specialist mathematical teachers who, to a varying degree, interweave mathematical discourse into their practices of learning mathematics. The initial learner-participant sample was constructed of 4 tutors, however a month after initial data collection, the sample base was revisited to identify and address research gaps, both in terms of learning context and participant demographic. From this point, another 3 tutors agreed to provide access to their learners and from this pool of 7 tutors, 11 participant learners were recruited. For more details of the demographic spread and learning context of the participant sample, please refer to appendix A.

Introducing James

James is in his mid-twenties and at the time of the interview, was studying on an Access to Higher Education course, with the eventual aim of teaching Computers, Design and Technology (CDT) in an inner city secondary school. He had, on his fourth attempt, gained a C grade at GCSE level 2, mathematics1. James has one brother and described his family background as coming from a “single parent family, like typical working class London”. He told a story of both his mother and father leaving school at 13 or 14, with no qualifications explaining: “they are intelligent people, but they just didn’t fit, or just didn’t manage to survive the school”. He described his mother as a ‘typical working class, working mum” explaining that she had worked at the same biscuit factory for the past 45 years. He also added that after a difficult experience of school, his brother had recently trained as a plasterer. James frequently talked of his father’s family (but without any further reference to his father) and in particular of his aunt, a university lecturer.

On describing his motivation to turn to higher education, James spoke of moving through “… various crap jobs in retail and things” until he found a job in youth work, where he realized he was “good with the kids”. James emphasized his desire to get more involved in his work, but described feelings of frustration as he hit an “invisible ceiling” in earnings. He talked with passion of conversations with his aunt that had led him to the decision to leave youth work and take a lesser paid job as a Learning School Assistant (LSA) in anticipation of ‘learning the rules of the game’ before training to become a qualified secondary school teacher. These stories were retold through the third person, an indicator of his processes of becoming (Mendick, 2006) and were often contrasted to the now, retold in the first person.

“… then the teaching thing kind of happened and you need to have a degree to do what you love, and what you are passionate about. That’s the only reason why I’m back in education, because I would be a lot better off a lot richer for starters. So now I am looking at it as taking the plunge: be broke, but you’ll be way better off in the long term.”

1 The qualification taken at 16 by most students in the UK.

During the interview, James used a language of resistance to the institutional demand to re-engage with learning mathematics, “God I just have to get through this”, and after a term of taught sessions, opted to complete the mathematical portfolio under his own steam, a decision not taken in conjunction with the access team. However, James’ story is not just an account of institutional failure to accredit prior learning but a fascinating journey through the ways in which the cognitive and social processes of learning can come to be intertwined through the affective domain (FitzSimons, 2002).

Thus in this second section, I intend to gather insights to illuminate aspects of James’ wider habitus, and then return to his discourses of mathematics, for a relational discussion to glance at possible constructions of his mathematical habitus. However, in having set out the theoretical conditions in the opening part of the paper, an inquiry which attempts to “determine the unthinkable and the inexpressible is likely to reproduce a (mathematical) habitus that replicates the theoretical leanings of the author (Reay, 2004). In response, I intend to supplement the possible constructions of James’ mathematical habitus through Mendicks’ (2005, 2006, Mendick, Moreau, & and Hollingworth, 2008) applications of performativity, to glance at the gendered and classed ways in which he ‘others’ himself from mathematics.

Being Working Class and Being Clever James grew up in a single parent household, with his brother, and describes his mother as a “typical London working class, working mum”. In a vein similar to the findings of Leathwood & O’Connell (2003), James’ stories of his journey towards higher education can be broadly categorised as a narrative of struggle; his emerging, powerful identity as a potential university student is discursively situated as different, often superior, to his brother, mother and his working class roots.

“My dad’s side are really switched on, they are really clever people and, well, one’s a uni lecturer and she was the one who put me onto wanting to be a teacher … and my mum’s side is kind of completely different. My mum’s clever, but her sisters … it’s like God, I can’t believe we are related. I mean they are nice, but they are simple straightforward people … education’s valued, but only as much as you do what you can … but people don’t really look up to academical achievement and erm, it was even a point when my aunt (from his mother’s side of the family) was just thinking that I was wrong, because I wanted to be intelligent.”

James has undoubtedly reflected on his reasons for returning to higher education and has weighed up some considerable costs against some possible long-term gains. However, he tended to navigate his stories through a pre-reflexive narrative, which seems to emulate many of the assumptions of a neo-liberal discourse of a classless educational system (Skeggs, 2009) where learners are constructed as being ‘able’ to resist all influences and choose strategically for themselves (Mendick, Moreau, & and Hollingworth, 2008). James identifies through his working class roots, but through a deficit lens (Skeggs, 1997) driven by

an unconscious class bound struggle to leave his past, to escape the monotony of his mother’s life and to seize the opportunity to become respected by those he respects through engaging with work that he can feel passionate about.

Skeggs (2004) summarizes habitus as the “metaphoric model of social space where embodiment is the product of the volumes and compositions of different capitals and the fit between the habitus (disposition organising mechanism) and the field (p.421)”. James’ stories illuminate his class-based struggles to internally weigh up the attributes that he values, at the expense of those he feels need to be forgotten (Hillier & Rooksby, 2002). Consequently, his habitus appears to fall somewhere between the social fields occupied by his complicated and conflicting family roots. The physicality and endurance of his working class brother “well I would say he’s a bit more of the brawn and I am the brains” is situated against his cleverness and self-governance (Skeggs, 2004), and the simple lifestyle of his mother’s family is inferred as an internal justification to return to education; “the degree you need to have, if you want to do something that you love and are passionate about.”

In line with Ingram’s (2011, p. 290) theorising of a habitus tug, “where the individual can at times feel pulled in different directions… where conflicting dispositions struggle for supremacy”, James reproduced stories that were generally humorous but at times hinted at internal divisions and feelings of shame. In using a Bourdieuian framework, the dispositions, and practices that James may have acquired through his early life experiences have become internalised as constraints against the dispositions, perceptions and expectations generated by his new life experiences (Ingram, 2011). James’ story appears representational of Ingram’s (2011) paper, not only of a struggle for legitimacy to go to university, but also of legitimizing his immersion into the social structures more aligned with his middle class self. A struggle that he seems to reconcile through imagining his ‘fit’ as a professional, existing at the margins of the secondary school educational system. Interestingly, James does not paint himself as a teacher in the embodied form and it is useful to refer back to Skeggs (2004), to theorise the processes of entitlement to an embodied space. She suggests processes become structured through hierarchical relations of difference and to this extent, James only hints at teaching qualities that he values through the binary oppositions of ‘us and them’ in a relational account of a favoured previous schoolteacher.

“There was a cockney Lovejoy … and I said, ‘Wow, you come from where I come from … just brilliant.’ Unorthodox, I mean break all the rules, just to get it in your head and to see what is going on. So, you can still be part of them. If you work it well and do it properly, you can be one of them and make it work.”

Possible Constructions of James’ Mathematical Habitus This next section does not attempt to paint a picture of James’ mathematical habitus, as identifications with mathematics are fragmented, contradictory, and fluid (Mendick, 2005) and therefore it is only appropriate to hint at possible constructions. However, theorised as a product of his wider habitus, his mathematical habitus is also presented through the tension of his

social positioning and thus cannot be reduced to an over simplified polarization of positive or negative attitudes towards learning (Wedege, 1999).

James hinted at a mathematical habitus produced through an expectation, a need, to be judged by his mathematical performance. His stories will be discussed in detail later, but his discourse terrain appears at times, to be a caricature of a battlefield; James ‘happily’ fighting a gallant battle to ‘destroy’ mathematical questions and ‘willing’ to reproduce, on demand, the mathematical art forms of the esoteric domain. Thus, although he appears fairly confident with reproducing mathematics on demand, his learning dispositions polarize a social constructivist account of mathematics; that is of a useful, living, and protean body of knowledge.

“There’s one more maths related hurdle … you have to do some kind of test (to get qualified as a secondary school teacher)… I mean just to see if you are average. So I know that’s coming and I am really not looking forward to it. The plan is to get through the level 2 maths… and then knuckle down the weeks before this test, and make sure that I have got my times table in my head back to front ”

James is as proud of his brother’s recent mathematical achievement, as he is of his own GCSE success. However, there are interesting differences that are in line with research findings (Lerman, 1999; Noyes, 2009; Cooper & Dunne, 2000). James differentiates his success from his brother, despite the equivalency of the qualification, through a relational account of their school-based expectations. James holds a paternal pride for his brother, but this success is framed by a poor performance in school, which through a class based discourse of vocational training (Mendick, Moreau, & and Hollingworth, 2008), situates his brother’s kind of mathematics firmly within the public domain (Dowling, 1998).

“My brother did quite a lot worse than me at school … he did level 2 maths to be a plasterer … and it was good to see him come home and say you know, ‘I know this, I’ve got this’.”

School appears to have been more monotonous, a story of missed potential, than a struggle for James, where he spent much of his time ‘ducking and diving’ and ‘dodging’, perhaps tricking the teachers. Resultantly, he is more qualified about his own achievement and carefully frames his success through a discourse of overcoming poor teaching, financial constraint, and struggling with a difficult although ‘beautiful’ body of knowledge (Mendick, 2005). Like most in the UK (Mendick, Moreau, & and Hollingworth, 2008), James distances himself from a ‘real’ mathematician, although unlike many (Swain, 2005) is confident in his ability to ‘knuckle down’ and succeed thereby foregrounding his poor attitude over his ‘natural’ ability to ‘do’ mathematics.

“I don’t know, it’s easy to blame the teachers … but either they didn’t like us, or had had enough of … our stinky attitude, or maybe they didn’t believe in what they were teaching … but I think it was a case that I didn’t want to learn … (the teacher was) showing me fractions, I mean simple fractions and … I think literally, it was just because I didn’t want to know … I don’t think I could have been that stubborn that I was just going dunno, dunno, but it might have been … but I went back and got the maths. I just forced myself, I mean forced myself and …. I was in the right frame of mind and it was ridiculously easy and I was thinking what was I doing. Seriously and erm I got a C … total top marks for the lower foundation paper. Then I put it way behind me, and I thought ‘I never want to see it again. It’s done, go away, burn it!’ But then I joined this course and it’s like, no you are doing it again!”

Skeggs (1997) posits that knowledge plays a central role in the reproduction of power and legitimacy, and for James, mathematical knowledge takes a central position in his quest for respectability. James holds a majority view, of mathematics as a gatekeeper, “an objective judge, to decide who in society ‘can’ and who ‘cannot’ … a priori, who will move ahead and who will stay behind (Volmink, 1994, p. 51)”. However, his concluding remarks, framed by the starkest signifier of Dowling’s (1998) esoteric domain, a specialised body of mathematics, is the most indicative of his mathematical habitus.

“Don’t get me wrong, … it’s like satisfying ... It’s incredibly fun if you go through the long formulas like trigonometry, or like what the algebra stuff is. It’s really satisfying if you get it right, I mean if you go through the steps ‘oh I remember I have to use this, I remember I have to do that’ and then you get the answer and you double check it, and ‘oh yes’ its right ... I mean if I could plug in a USB and have all of the formulas … I would be well happy, I would just be away … I would love maths.”

Boaler (2002) posits that people are positioned as powerful or powerless according to their personal histories and James, by positioning himself within the esoteric domain, is staking a claim of intellectual ability. However, as Skeggs (1997) explains, the strongest elements of habitus occur during early childhood, where the logic of practice tends to be structured through the differences between the social fields. It is worth then, taking a moment to reflect on James’ early experiences of schoolroom mathematics. To wrestle with the changes as James relays his experiences of learning, particularly of how his stories of “ducking and diving” change from one of hiding within the classroom milieu, to an agentic discourse of a strategic and successful learner.

James’ memories of primary school were generally comprised of amusing but angry anecdotes of ‘smile mathematics’ a body of mathematics set within the everyday domain, which in line with Mendick, Moreau, & and Hollingworth, (2008) were not consumed as legitimate forms of mathematical knowledge, instead they were too easy, common sense.

“I remember, we just sat on the computers doing the Tea shop which was just stupid … and you had to guess the number of customers you could get … it just wasn’t maths … like really gamey. Like too much fun and … we should have been knuckling down with the serious stuff … but when we got to fractions and the books, and you were on your own, it was like ‘oh God’ … you know, I kind of developed strategies to kill time and just duck and dive until lunch.”

James suggested a self-image of being able ‘to do’ mathematics in his early school years, but did not perceive this as mathematics and is another indicator of his resistance to the public domain, and which conjured up images of ducking and diving, that surfaced as he talked of his initial struggles with the specialist mathematics of the esoteric domain. In his secondary school years, James relayed a self-image of an able scientist and generally able, if ‘lazy’, student, but it was at this stage he built a picture of frustration, with himself, of not being able to ‘destroy’ the maths questions that presented as a general discomfort within the mathematics classroom.

“I would duck and dive and I dodged all the other teachers through secondary. It was easy as long as you behaved, they would let you do what you liked, but he (the maths teacher) would … pick you out ... So it was just an exercise of embarrassment, every maths lesson … he was good, but I thought this was really bad.”

However, in line with Boaler’s theorising (2002), James’ final and successful story of learning is narrated by James ‘the professional’; working as an LSA in a special needs school, upskilling to meet the demands of his job and meeting the requirements of entrance into university. In this story, James’ discourse of ducking and diving incorporates elements of his middle-class self and is presented through an agentic, authoritative and strategic voice not present during his descriptors of learning in primary and secondary school.

“I skipped a couple of classes, didn’t do any homework, the bare minimum to get through it and I reckon I could have got a B or an A because it was fun, but it was like 6:30 – 9:30 after work and I was like a zombie … but once I did practice some past papers, err, there are ways they want to see, and I was not doing that and then once I realized … I was not losing the marks.”

By concluding with just a glance at the language of performativity, I am limiting the scope of the lens, but it is worth taking a moment to refocus on James’ language patterns (Mendick, 2005), to illuminate how he locates himself through a series of gendered binary oppositions, in aligning his identity as a (non) mathematician but good enough.

Heroic Maths

“For me (doing mathematics) it’s kind of like jumping off a building and thinking am I going to land and have I got it right … if something’s gone wrong then it’s back, back and there’s the mistake.”

There is something seriously powerful for James, about ‘doing’ mathematics and it is through his ability to (re)produce hard mathematical facts that he measures his natural intelligence. In line with Heather Mendick’s theorizing on the middle classness of the masculinities of mathematics (2006), in telling his stories, James relies on a heroic discourse of gendered oppositions to position his own mathematical practices. The USB of technical formulas versus the negotiation of meaning, the genius verses the ordinary, the right or wrongness and the heroic effort of all, or nothing (Mendick, 2005). James’ patterns of language repeatedly fall into a peformance of ‘effortless achievement’ of the ‘naturally able’ (Mendick, 2005), all the whilst distancing himself from being a genius. In ‘othering’ the mathematician as a genius, James negotiates an identity towards that of an idealized adventurer (Mendick, 2005) of jumping off buildings, whilst maintaining a distance from the nerd like mathematical practices of a frenzied mathematician (Mendick, 2005). However through his discourse of ducking and diving, James falls somewhere between the traditional gap of being good or bad at mathematics. He continually negotiates his own balancing spaces of ‘averageness’ through carefully weaving stories of working hard, particularly at past exam papers, through a more general discourse of skipping classes and not doing the homework.

Conclusions

“… Me personally, I would only really truly feel like I was a mathematician if I was in higher education studying maths … at the front (of the profession) messing around (with numbers) and trying to get it to work”

James sees mathematics as a critical filter to other occupational and educational fields and through his habitus lens, positions himself as holding average skills but not as a mathematician. However after a positive experience of learning, his mathematical habitus has transformed, like his broader habitus, into a state of inclusion albeit within the fringes of academia. His habitual learning dispositions remain tightly bound to notions of reproducing Absolutist mathematical ‘truths’ within the esoteric domain and thus remain tied to idealized and clichéd masculine images of mathematics. He is ‘willing’ to prove his intelligence through battling and destroying mathematical questions, but is resistant to the notion of expanding his repertoire of mathematical dispositions and of building his mathematical reasoning and voice. James, like many adults returning to learning mathematics, needs to reflexively consider how the structuring factors (of class, of gender and of race) of

mathematics have (re)positioned him as a (non)mathematician within the esoteric domain in order that he can transform his mathematical habitus in ways that value the Social Constructivist approach of negotiating mathematical meaning within the public domain. At the conference, I will use insights from James’ stories of learning to provide textured understandings of how his lived experiences and first hand encounters of ‘being’ a mathematician and ‘doing’ mathematics have reproduce mathematical expectations, perceptions, and behaviours that are inherently classed and gendered. Working from within a ‘capabilities approach’ (Nussbaum, 1997, 2000; Sen, 1992, 1993, 1999), I will argue for a curriculum space that is shaped by a discursive terrain that encourages learners to engage with the freedom and opportunities dimensions of learning (Walker, 2008) through a critical understanding of their social arrangements of learning.

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Appendix 1

Name Learning context Position/course Highest qualification Gender Age Parental status

Ethnicity Class origin

Tutor Sarah Initial tutor sample

Further Education College

Senior practitioner

MA units

F 50 - 59 Child free White British Working class

Learner Alexandru 3 interviews & observation

Full time Embedded2 Foundation Learning Tier3

IT ESOL Level 1 Functional skills4

High school diploma (Romania)

M 22 Child free White Romanian

Working class (rural)

Learner Jalal 2 interviews & observation

Full time Embedded Foundation Learning Tier5

IT ESOL Entry level Functional skills

BA Hons Morocco Human Rights NARIC6 BA Hons UK

M 32 Child free Moroccan Asian

Working class (rural)

Tutor Elizabeth

Further Education College

Head of school Mathematics Teacher trainer Practitioner

MA Education Mathematics degree

M 40- 49 Child free White British Middle class

Learner James 2 interviews

Full time Embedded Access to Higher Education

Access to Teaching (secondary) Level 2 GCSE equivalent7

GCSE maths No other details offered

M 24 Child free White British

Working class

Learner Full time Access to Teaching GCSE maths M 21 Child free British Asian Middle class

2 Where the mathematics is taught as part of a wider, usually vocational, learning program

3 Introduced in 2011 and removed from qualification framework, the Foundation Learning Tier (FLT) includes entry-level and level 1 qualifications

4 Functional Skills Mathematics assessments consist of problem solving and decision making tasks within the public domain

5 Introduced in 2011 and removed from qualification framework, the Foundation Learning Tier (FLT) includes entry-level and level 1 qualifications

6 National Agency responsible for providing information on vocational, academic, and professional skills and qualifications from over 180 countries worldwide.

7 GCSE equivalent assessment is an internally marked and externally moderated portfolio consisting of problem solving and decision making tasks within the public domain

Abdul 1 interview

Embedded Access to Higher Education

(primary) Level 2 GCSE equivalent

No other details offered

Name Learning context Position/course Highest qualification Gender Age Parental status

Ethnicity Class origin

Tutor Jane Initial tutor sample

Further Education College Worked based learning 8 (classroom assistant)

Senior practitioner

Mathematics degree F 50-59 One child British Asian Middle class

Learner Karigaila 2 interviews & observation

Part time Discrete9

Level 2 GCSE

Teaching degree (Lithuanian) NARIC level 3 UK

F 50 - 59 Two children

White Lithuanian

Working class

Learner Kath 1 interview & observation

Part time Discrete

Level 2 GCSE

Details not given F 20-29 Child free White British Working class

Tutor Kate

Further Education College

Practitioner Teacher trainer

MA in education

F 40-49 Child free White British Middle class

Learner Suzie 2 interviews & observation

Full time Embedded Foundation Learning Tier

IT/Business Level 1 Functional skills

6 GCSE grade A-C F 19 Child free Black British Working class

8 Courses taken by employed staff as part of a professional development program

9 Mathematics is the only subject of study

Tutor Simon Initial tutor sample

Family Learning in a primary school

Practitioner

Level 5 DTLLS10 M 50 -59 Three children

White British Working class

Learner Fatima 2 interviews & observation

Part time Discrete

Entry Level Functional skills

None F 20-29 One child British Asian Working class

Name Learning context Position/course Highest qualification Gender Age Parental status

Ethnicity Class origin

Tutor Paul Initial tutor sample

Residential Women’s College

Practitioner Teacher trainer

MA Mathematics degree

M 50 – 59 Child free White British Middle class

Learner Julia 2 interviews

Part time Discrete

Entry level Non accredited

None F 60-69 Three children

White British Middle class

Tutor Ayo

Community Adult Education College

Practitioner

Level 5 DTLLS M 40 -49 Two children

Black African Working class

Learner Tony 1 interview

Part time Discrete

Level 2 Functional skills

Teaching degree (Nigerian) NARIC level 3 UK

M 50-59 Two children

Black African Working class

10

Initial Teacher Training Qualification, Diploma of Teaching in the Lifelong Learning Sector