Educ Stud Math (2014) 87:221–239DOI 10.1007/s10649-013-9468-4 Structural exclusion through school mathematics: using Bourdieu to understand mathematics as a social practice Robyn Jorgensen & Peter Gates & Vanessa Roper Published online: 7 February 2013 # Springer Science+Business Media Dordrecht 2013 Abstract In this paper, we explore a sociological approach to mathematics education and offer a theoretical lens through which we can come to understand mathematics education as part of a wider set of social practices. Many studies of children’s experiences in school show that a child’s academic success is a product of many factors, some of which are beyond the control and, sometimes, the knowledge of the classroom teacher. We draw on the sociological ideas of Pierre Bourdieu to frame our analysis of the environment in which the pupils learn and the ways in which the practices help to create parallel worlds which are structured quite differently inside and outside the classroom. Specifically, we use Bourdieu’s notions of habitus, field and capital. Using two cases, we highlight the subtle and coercive ways in which the practices of the field of mathematics education allow greater or lesser access to the hegemonic knowledge known as school mathematics depending on the cultural backgrounds and dispositions of the learners. We examine the children’s mathematical learning trajectories and reflect on how what they achieve in the future will, in all likelihood, be shaped by their social background and how compatible this is with the current educational climate. Keywords Bourdieu . Sociology . Equity . Habitus . Field . Capital 1 The marketization of education For some years now, there has been a belief within government circles around the world that there are problems within national systems of education and that the route to improving R. Jorgensen (*) Griffith University, Brisbane, Australia e-mail:
[email protected] P. Gates The University of Nottingham, Nottingham, UK V. Roper Nottinghamshire Local Authority, Nottingham, UK 222 R. Jorgensen et al. standards lies in applying the commercial concept of a “free market”, in which schools will improve by being in competition with each other for students. In such a free market system, schools are measured on various criteria, ranked into “league tables” and are encouraged to see themselves in competition for scarce resources and urged to raise themselves up these league tables. In both the UK and Australia, national testing has become the measure that defines the success of schools. In Australia, all students in years 3, 5, 7 and 9 are tested in literacy and numeracy. Scores for schools are then published on a national website (ACARA, 2010). At this stage, there are no formal rankings or interventions for underperforming schools which is in stark contrast to the UK where the effect of national testing has become so powerful. In spite of some recent and limited retrenchment, the results of testing in the UK can effectively move a school into a category requiring significant improvement—sometimes through the removal (or “resignation”) of the head teacher—or it may ultimately be closed. These “failing” schools are a product of the political system, and often, the reason they ‘fail’ is due not to bad teaching or leadership, but to the structures of the education system; rarely are ‘failing schools’ located in middle-to-affluent suburbs. Most frequently, they are located in poor, working-class and/or multicultural areas (Bell, 2003; Lupton, 2004). That is not to say that we can absolve leaders and teachers from responsibility for poor practices. Rather we seek to understand the systemic failure of disadvantaged students and communities which becomes reified in curriculum and through testing and management processes. By understanding how these practices are structured to marginalise particular social and cultural groups in ways that are coercive and invisible, we will be better able to change those practices. When the normalised practices within education are not challenged and the status quo is preserved, then the most disadvantaged groups suffer through symbolic violence (Bourdieu, 1972) whereby they take on board the value-laden processes of education and become victims of those approaches through which they are effectively excluded and marginalised. In writing this paper, we draw on our experiences in working-class and culturally diverse classrooms to illustrate the ways in which social practices work to marginalise particular students in their study of school mathematics while preserving the hegemony of the dominant classes; the same sort of pupils tend to succeed, and the same sort of pupils fail. The structuring of the field of education is a result of strategies engaged in by pupils and teachers within the specific field of school mathematics. The political rhetoric in favour of the current policy direction suggests that testing, accountability, league tables, etc. are strategies to “drive up standards”, and in this way, state education will be improved for all—with the high-profile “successful” schools “pulling up” those seen as “failing”. At the same time, however, there is also a policy discourse about the need for social justice with a consequent drive to support learners from less affluent backgrounds. Research, however, does not support the claim that current policies are reducing social exclusion. Whitty argued these structural shifts are “policies that do nothing to challenge deeper social and cultural inequalities” (Whitty, 1997, p. 58). In fact, the shift towards a “free market” in education seems to have made little change at all to these inequalities (Power, Halpin & Fitz, 1994, p. 39). The education system continues to favour those whom it has always favoured—those of higher socioeconomic status and those who know how to work the system and have a “feel for the game” (Bourdieu, 1990, p.9). We would argue that this privileging does not happen through oversight or accident but is a result of some deliberate, though possibly covert, strategies. habits and preferences—their taken-for-granteds. Effectively. p. 127) making sure they fall in line with expected practices. this means that the embodied culture. it does not require or even desire change. 2000. This explains. it is a task of schools to align the individual habitus with the field. 2000. 1979. and this shapes the way they act in and interpret their worlds. For society more generally. learners engage in an activity (such as learning mathematics) with a habitus that has already been shaped by their early socialisation within the family. Mathematics acts as a marker of success in schools. this process aids success in school whereby those who are most likely to benefit are those from the groups whose class habitus aligns with the practices of the school.Structural exclusion through school mathematics 223 2 Using Bourdieu (1): introducing the habitus A socially critical stance sees that “more affluent parents are more likely to have the informal knowledge and skill… to be able to decode and use marketized forms to their own benefit” (Apple. (Apple. Bourdieu defines these dispositions as the “habitus” (Bourdieu. Consequently. mathematics is a useful context in which to explore the inequality apparent in the education system as a whole because it performs a role of social segregation. or in his terms “cultural capital”. Effectively. 250) This means that the children equipped with the right habitus are able to gain an advantage in school and can exchange their dispositions for other rewards—grades. p. These students are generally not those from the lower socio-economic classes. that can be exchanged for other goods within the economy of the school. 248). p. and informal and formal procedures by drawing on their own sets of dispositions. home and immediate environment. Although the habitus is to a large extent durable and stable. Consequently. p. Mathematics has been described as a “badge of eligibility for the privileges of society” (Atweh. 2001. as well as for many parents. those whose class habitus does not resonate or align with the practices of school mathematics are in need of a reconstruction of the familial habitus if they are to be successful in school. why the marketization of education has done little to change the traditional models in place. and it fails children from social and cultural backgrounds that are different from the majority of mathematics teachers. Bleicher. in part. if students are to be positioned as successful. it fails children from ethnic minorities. it fails children on the margins of society. But Bourdieu argues these are rather more than mere preferences as they are operationalised by class positions. certificates and so forth. the subject of mathematics is traditionally held as important—as a gatekeeper to travelling successfully through the educational system and as an inherent marker of intellect. 63) which itself begs the question of how this privileging works. or as Bourdieu prefers—the “habitus”—now becomes a form of capital. and therefore. usually leads to a successful conversion of economic and social capital into cultural capital. 1984)—a collection of informal skills and knowledge which participants have constructed over time. These dispositions then operate to construct the pupil as “like a fish in water” (Bourdieu & Wacquant. 7) . 1998. Conversely. p. it can be reshaped or transposed (Bourdieu. Such parents do what they can for their children through both explicit and implicit practices. The class with the habitus to take advantage of the market consists of those whose values are actually best reflected by the current system. (Gates. It has been observed that the habitus of more affluent parents often coincides with that expected in schools since … the match between the historically grounded habitus expected in school and in its actors and those of more affluent parents. combined with the material resources available to more affluent parents. bringing their dispositions in line with those of the ideal pupil. 1992. and consequently. & Cooper. p. Mathematics education fails too many children. vii) by practices and sets of rules and expectations. and it is this process we explore in this paper. Mathematics holds a privileged place in the school curriculum. As another example. the field is a key organiser. Cooper and Dunne (2000) and Dowling (1998). and these encounters produce the accepted social practices that typify the field (Griller. p. its teaching is heavily structured and it can be represented as a set of hierarchically organised skills usually divorced from applicability. but who share a related set of dispositions. In a social field. when taken together. the mathematics curriculum is structured in a particular way that privileges certain forms of thinking (Walkerdine. literacy educators often see the practice of reading a numeracy problem as a literacy event. However. define the practices we see in classrooms and relations between the learner and teacher. it draws on specific language patterns. and for a Bourdieuian analysis. interpret and respond to the literacy event per se. 2001). the home and school contexts and between government and schools. mathematics has an almost unique place in the school curriculum of all countries. p. the habitus does not operate in isolation. We feel comfortable locating our analysis within what we argue is a field of mathematics education because the practices within mathematics education are often unique to this field. The accepted and common practices within mathematics education will differentially acknowledge what is seen as valued within that field. 1996. expectations become organised around visions of different futures. behaviours are shaped around the image of the ideal pupil. However.. The way in which the social practices then become organised and reified is defined by the balance between these points and among the distributed social capital that groups of individuals have (Mahar et al. Bourdieu’s stance is that because our dispositions are historically and socially constructed and sustained. For example. relationships with parents place teachers in very specific positions of authority and so on. it operates within a set of socially organised rules through which power and control are dissipated and legitimised. Not only does the student need to read. 8). defining learners as “can do” or “can’t do”. 3 Using Bourdieu (2): introducing the field We have already outlined the significance of the habitus as a key construct in understanding learning of mathematics. With this in mind. in the field of mathematics education. All of which.224 R. the field of mathematics education can provide us with a critical lens to observe the day-to-day processes that lead to social segregation. Jorgensen et al. pedagogy is structured to distinguish between different learners. Why are we being asked the question? Who wants to know the answer? What will you do with the answer? What assumptions are behind the givens? The role of language in shaping mathematical understanding for diverse groups has been extensively studied by Cooper (2001). various individuals interact. For example. but he/she also is required further cognitive work that goes beyond literacy. which extends the literacy event in ways that are beyond a typical reading. the numeracy aspect requires significant mathematical interpretation of the task in order to be able to solve it. Social fields are described as the system or set of objective social relations of power between those holding different positions within the field. 1990. 1988. the field of mathematics education is a particularly appropriate unifying field because it encompasses and defines a clear set of rules that hold the discipline together. This set of rules defines what Bourdieu calls the field of power. The field will have particular practices that value and convey status on particular dispositions and learning. Apple. 1979). In our case. 6). Unlike literacy. and ability in mathematics is highly prized and valued. and the field . it is much more. such as mathematics education. The reader/student needs to have a very specific interpretation of the world which the field accepts as legitimate (Cooper. Bourdieu sees that cultural capital exists in three forms: the embodied state. the reification of social disadvantage—social. By using Bourdieu’s framing. machines. 1991. Within the field of mathematics education. knowledge systems.. Consider the middle-class families who. it confers entirely original properties on the cultural capital which it is presumed to guarantee (Bourdieu. The field values particular dispositions over others. books. By analysing practices within school mathematics. 2000. therefore. Bourdieu is able to describe how capital is realised within a field because “the kinds of capital. in the form of long lasting dispositions of the mind and body. like trumps in a game of cards. Through this game analogy. a form of objectification which must be set apart because. 231). as in the institutionalised state. Bourdieu relies on the games metaphor which enables us to offer a theorisation of how the practices within the teaching of mathematics give some students greater access to mathematical knowledge while excluding others. as Brice-Heath (1983) showed. etc. p. who then enters the school with these attributes embodied as their cultural background—their habitus. dictionaries. dispositions. p. cultural or linguistic— can be challenged because we can see it as an arbitrary set of responses by individuals with power rather than a natural state of how things just are. as will be seen in the case of educational qualifications.) Using Bourdieu’s framework. etc. The practices within the familial context. the students who are able to enter the field with a habitus that has been shaped by familial interactions that are valued within the field will have those displays of language sanctified within the field. These students are better able to engage with the interactional style found in school than their working-class peers whose familial habitus is one where parents engage in declarative interactions.Structural exclusion through school mathematics 225 will organise itself by imposing an objective structuring upon pupils and teachers through curriculum. However. 243.e. become internalised by the child. are powers which define the chances of profit in a given field” (Bourdieu. 1983. in the form of cultural goods (pictures.. problematic. engage in the standard classroom triadic dialogue—initiation–response–feedback—commonly used by teachers of mathematics. instruments. we are taking a move away from deficit and individualised thinking to a more encompassing and systemic approach. 230). 2001). we see that learners enter the field of mathematics education—some of whom will be very aware of how the game is played in that field. in the objectified state. while others have little . the students who enter formal schooling with a linguistic repertoire (or linguistic habitus) that has a middle-class register are more likely to experience success (Zevenbergen. and these become entrenched into part of the habitus that can be exchanged for forms of capital. Using this metaphor. To explain how power is enacted in a field. which include language. How well one succeeds in the game (or field) is determined by the “overall volume of the capital… and the composition of that capital” (ibid. we are in a better position to understand the systemic failure of students from marginalised backgrounds rather than looking at the problem as a result of individual deficiencies on the part of particular pupils and parents.) which are the trace or realization of theories or critiques of these theories. p. i. 4 Using Bourdieu (3): integrating habitus and field The habitus becomes a form of culture that is now exchanged for capital which is reified through practices (such as assessments) which effectively impose structure upon those participating in the field. pedagogy and the organisation of learners. For example. Jorgensen et al. Bourdieu (1984) argued that those players with the most resources are able to exert the most force over how the game is played. in defining how interactions are played out. In doing so. the teachers and students are able to exert and display what is seen as valued mathematical knowledge and ways of being in the classroom that ensure that the field. This example illustrates some of Bourdieu’s key concepts that are integral to analysing the systemic exclusion of some social and cultural groups in their learning of school mathematics. For students coming in from middle-class families. teachers rely considerably on the use of the signifiers “more” and “less” to develop many mathematical concepts—which number is 2 more than 3. Bourdieu also argued. These experiences are likely to have been embodied by the children as part of their culture or as part of their habitus. These children. “…it is often the state of relations of force between the players that defines the structure of the field” (Bourdieu & Wacquant.226 R. or what is seen as desired in activities or responses. and so on. One only has to consider the power of the teacher. they are able to engage with the substantive learning as well as perform on test items that reflect this language. thus positioning them as somewhat more “knowing” than peers who have not had such experiences. 99). but is a relationship that . These experiences position them well when they encounter the mathematics classroom. This discursive positioning enables middle-class students to enter the field of mathematics education with a linguistic habitus that is more closely aligned to the practices within the field than their working-class peers. and a sense of odd and even numbers. with its inherent practices. Walkerdine and Lucey’s (1989) work has shown how the mother–child interactions of working-class and middle-class families resonate less or more with the discursive practices of schooling. the informal teaching games that the parents or caregiver have used to immerse the student in these number experiences are likely to resonate with the pedagogical practices the teacher will use in the classrooms. Already these students come to school with knowledge of number and teaching episodes. what number is less. Where early learners have access to this discourse. are more likely to be able to participate in the pedagogical practices of school and to display knowledge valued by the teacher. but some sense of what bigger numbers mean and perhaps an intuitive sense of place value. these experiences rest well with the curriculum they will go on to experience. Considering early childhood settings. Not only do they have knowledge about numbers. For example. 1992. Collectively. 3 or 5. Language is not merely a form of communication. 5 Language and social class—social heritage and the linguistic habitus In this section. and use of language is a key aspect of that background. when playing the game of schooling. In this case. idea and must learn the game if they are to be constructed as successful learners. remains intact. The converse is the case for students who do not have this linguistic repertoire when they enter schooling. they found that middle-class mothers were more likely to use both “more” and “less” in their interactions with their children whereas working-class mothers were more likely to use only the signifier “more”. which group has more. in comparison with the young students working in a classroom. students are effectively included or excluded on the basis of their backgrounds. Furthermore. their exposure to particular language practices provides them with better/more trump cards than their working-class peers. Consider young preschool children whose parents have walked down streets talking about the numbers on houses. p. we draw on these concepts to explore how significant practices are allowed to operate—the ways in which language and the linguistic habitus are differentially acknowledged and rewarded in mathematics. Language. Without substantial reconstruction of their familial habitus. which means those who are struggling with familiarising themselves with a new linguistic structure may get lost and hence fall behind before they have had a chance find their feet. making access to mathematics and success difficult to achieve. p. 220) The need to fully understand the broader meaning behind mathematics tasks has serious repercussions for working-class children who are placed in higher-ability sets. not only conveys particular concepts but also provides a medium through which those concepts are conveyed. Language is an integral part of the social heritage that is brought into school mathematics and becomes reified through various objective structuring practices. effective participation in the mathematics classroom is transitory and intangible. working-class children encounter forms of language in the home environment different from that which they encounter in the school. etc. 1966). Cooper. Forms of spoken language in the process of their learning initiate. 1998). each carry specific nuanced calls for type of mathematical thinking and behaviour. 2001. Yet. it is not simply what is being said but the structure of how it is said that constitutes linguistic competence (Bourdieu & Wacquant. “show”. the forms of the habitus and the acquisition of social capital. one needs to know how to “read” mathematical questions as real or imaginary contexts (Cooper. Here. It is therefore important to consider not only the concepts that are being considered but also the medium of instruction. Such competence is a form of capital that can be exchanged for success in the classroom. in very broad terms. Forms of language drawing on elaborated codes have a sentence structure that draws on more complex forms. and by extension. understanding what is expected in school mathematics is a much larger issue than just understanding test questions—the problems of interpreting language within test questions is symptomatic of a difficulty with understanding the language used within the school mathematics. The subsequent success (or failure) of . To working-class children. 43) Hence.Structural exclusion through school mathematics 227 determines certain behaviours between individuals and groups. “prove”. (Zevenbergen. 2000. This has also been theorised by Bernstein’s ideas of linguistic competence and restricted codes. and thus defines power structures that in turn define the shape of the field. often using unusual words and phrases. Dowling. one needs to learn to interpret examination questions to be successful at certification. For example. the structure is much more confusing. 1971. Boaler found that the lessons taught to higher-ability children proceed at a fast pace (Boaler. (Bernstein. 1997a). (Zevenbergen. and one sees that the cultural capital a child possesses must impact heavily on their success within school. Zevenbergen argues The rich language of middle-class parents prepares children for the language they will encounter in school mathematics. the children’s social and linguistic capital serves as a filter. 1992). p. “find”. Language acts in numerous ways to define the forms of practices acceptable. & Dunne. This orientation to meaning is most obvious in the moves towards abstraction and generalisation which is in contrast to meanings that are bounded by context specificity. p.76) The idea of a restricted code is a less formal form of talk. structured on shorter phrases often with tags such as “you know” and “know what I mean”. but also in the orientations to meaning (Bernstein. generalize and reinforce special types of relationship with the environment and thus create for the individual particular forms of significance. 2001. Conversely. 2000. “hence”. Middle-class children find the structure of classroom interactions familiar—they already have a large amount of linguistic capital from home. not only conveys particular concepts but also provides a medium through which those concepts are conveyed. We do not subscribe to this view of innate ability. we extend this work to explicitly address issues of social class looking across two national cultures. Passeron. While his focus was on social class. It is therefore important to consider not only the concepts but also the medium of instruction. (Bourdieu. He argued that: To fully understand how students from different social backgrounds relate to the world of culture. School mathematics represents a particular and powerful example of how social heritage converts to academic success. 2003. in very broad terms.228 R. and constrains their access to. To better understand the processes by which the home habitus of working-class students clashes with. 2005) has shown how the objective and subjective structuring practices of ability grouping make for stratified learning. Language is an integral part of the social heritage that children bring into school mathematics and is part of their “virtual school bag” (Thomson. In many disadvantaged communities. the work of Bourdieu can be useful to theorise the symbolic violations that occur when the clash between school and learners is foregrounded. we draw on two illustrative cases which are drawn from a larger study and are used here to exemplify the concepts within Bourdieu’s theory and how it can be applied to mathematics education. 6 Social class and ability grouping as social filters One particularly pertinent issue within mathematics education is that of the dominant practice of ability grouping. Using a Bourdieuian framework. & de Saint Martin. 53) The notion of social heritage thus becomes a central variable in coming to understand the differential successes in school mathematics. What we describe later in this paper are the detailed ways in which this process works at a micro level and how it acts as one element of a larger set of social practices. In this paper. school mathematics. This becomes reified to be seen as an innate ability. but it is an entrenched and naïve belief within the field. we need to recapture the logic through which the conversion of social heritage into scholastic heritage operates in different class situations. and more precisely. it is a product of institutionalised practices of which participants may be totally ignorant. to the institution of schooling. 1994. success in coming to learn the disciplinary knowledge within the field of school mathematics. Using Bourdieu’s framework to understand the implications of ability grouping (Zevenbergen. The larger study looked in detail at a group of learners in a school and in particular at how social demographic patterns are linked with . or not. the clash between the culture of school and the culture of learners contributes significantly to the failure to experience success of many learners. 2002). Jorgensen et al. p. The ways in which failure and success are organised become an entrenched and naïve belief within the field and one that is exposed through Bourdieu’s framework. The language. 7 Applying Bourdieu’s theory In the remainder of the paper. Bourdieu explains that educators need to understand the processes around the conversion of social and cultural backgrounds into school success. students is most frequently interpreted as an innate ability that facilitates. and this is a significant part of the structuring capability of school mathematics. the lack of success for some social groups becomes a non-random event. forms of representation. We use some demographic data but largely draw on interview data with pupils and parents to enable the application of Bourdieu’s model to understand the positioning of the students through the practices to which they were exposed as part of their school mathematics experiences. As part of this larger. The analysis that we now undertake highlights the power of a social theory to critically appraise a taken-for-granted practice in school mathematics. Our intent is to explicitly disrupt the use of such a term that reifies social characteristics as being somehow innately related to achievement or “ability”. The school population is diverse. a boy (Cory) and a girl (Caitlin). Particular care was taken over the power relationships in data collection. this being the highest possible level she could have achieved. enable a serious challenge to one of the most hegemonic discourses in school mathematics—that of ability. much more so than in Australian schools or indeed other countries where the practice is outlawed. Mathematics lessons were observed. “Ability grouping” is standard practice in UK schools. We particularly draw on Bourdieu’s constructs to illustrate the application of his theory to better understand the marginalisation and reification of students in and through school mathematics. come from the same school in the UK. Pupils were interviewed and talked to informally. we just focus on two pupils who are in starkly differing social and school positions. The third author was a teacher of mathematics at the school and obtained approval from the head teacher and head of department to undertake the study. as is made possible through Bourdieuian lenses. due to its alignment with the hegemonic discourses of innate ability. participants were invited to take part and all names are pseudonyms. a range of data collection methods were employed. It is our intent to focus on the social demographics of the students as these were the basis for the selection of these illustrative cases. for this paper. In our analysis. This already gives Caitlin an advantage through the “dividend” of being in a top set. The correlations between ability grouping and social background. While we are opposed to the use of the term ability grouping. so the cases serve to illustrate the manifestation of practices within the field and how they can position students as learners of mathematics. . The two pupils we focus on. we looked into patterns of language. and pupils were followed in other subjects.Structural exclusion through school mathematics 229 achievement. as well as understandings of self and others. we use the term here as it is one that is adopted by teachers and educationalists. Demographic data were obtained on where pupils lived. and parents were contacted at parent consultation evenings and followed up through interviews in the home. the study was approved through the procedures of the university. Caitlin Cory Gender Girl Boy SES/class status Middle/affluent Working/disadvantaged Maths group High-ability group Low-ability group 8 Case study 1: Caitlin Caitlin was placed in the highest-ability group in year7—the first year of secondary education in the UK. Ethically. more comprehensive study of the students. Whilst this larger study focussed on how pupils were organised and distributed through the structure of teaching groups. She was put into this group on the basis of achieving a 5a in her UK National Standard Assessment Test taken in the final year of primary school (year6). the key is to be successful and to trust in the system to bring that success. although. My Dad tells me a lot of stuff. Having just completed the end-of-year mathematics examinations. she cannot quite explain why it will be useful and just expresses a belief that it will important for her to have an all-round education. Echoing the importance Caitlin attached to mathematics. she identifies not only future financial rewards but also the personal satisfaction her mother has gained. She explains that they have had money troubles because her mother has been completing this but that it is worth it. Caitlin sees education as an important part of life. & Hurley. Interestingly. The most recent such visit consisted of going to “a small music festival” and seeing all her “friends and family from dad’s side”. Caitlin is an only child who lives with her mother. beyond numeracy and computers. and this seems to sum up Caitlin’s attitude towards school. The benefit of being in a top set rather than a low set was particularly strong in mathematics. (Ireson. she describes mathematics as: One of the most essential and basic requirements of education. Hallam. she made the following comments: It is frustrating because I know I could have achieved a 6a. Jorgensen et al. Caitlin’s mother is very pleased that her daughter is achieving highly in mathematics. Caitlin’s mother has just completed a PhD and is taking up a teaching post in university. She regularly visits her estranged father. Caitlin’s father is clearly keen on mathematics as a subject. Her year6 teacher described her as “precocious”. Both Caitlin’s mother and her father influence Caitlin’s positive attitude towards mathematics. Caitlin does have a healthy desire to achieve highly. Caitlin professes both to enjoy mathematics and to believe that it will be important in the future. Sometimes he will mention something and I’m like ‘I’ve never seen that before’ and he will explain it to me. Functionality and utilitarianism here do not matter. It was just because I didn’t pay attention to the units. I needed two more marks.230 R. p. Caitlin says. and her year7 form tutor described her as a “very prominent member of the form” who was elected by her peers as the class representative on the School Council. she believes learning can provide personal fulfilment as well as professional goals but feels no pressure to quantify these goals. particularly in a meritocracy. “It means I can do better next time”. . swimming and visiting different places”. Caitlin’s mother identifies “happiness and her goals” as being what she hopes Caitlin achieves at school. I have a head start in maths because he is very good at it and likes to talk to me about it. She was not worried by making mistakes but was keen to talk about her errors and explained that she found working out why she made mistakes interesting and added. In spite of a relaxed attitude towards school. where on average the top set dividend was just under one grade at GCSE. 2005. 455) Caitlin came over in class as an articulate and confident girl with a high degree of mathematical skill and in general achieved well on tests and other markers within the school context. She is involved in many extra-curricular activities in school including playing for a netball team and performing in school productions. In spite of describing mathematics as “not my strong point”. Caitlin talks about this with a lot of pride. She is clearly very close to her mother and spends time with her out of school doing a range of activities—“shopping. She was described by her teachers as a student of “high intelligence”. 9). This linguistic competence and confidence is part of Caitlin’s habitus. No. thus positioning Caitlin as a successful learner in the context of school. Caitlin’s parents were creating opportunities for her to engage in the game of school mathematics in ways that were enabling. they were creating the possibilities of a mathematical habitus whereby Caitlin could engage with and experience the game in productive and meaningful ways. Caitlin: If I ask him a question. They’re of the same ability and can understand what you say. In so doing. [She laughs]. Having a feel for the game is important. I know it’s a good thing really. She is clearly used to conversing in this way at home. In so doing. as an effective technique. She displays a high level of self-motivation and has a series of strategies to employ in a test situation. she has a strategic “feel for the game” (Bourdieu. This style of conversation is most compatible with interactions that take place in her mathematics classroom and clearly illustrates a high level of agreement between home and school habitus. Caitlin is already familiar with that structure from home and even recognises it. The linguistic habitus she has been able to create through her familial interactions are exchangeable within the economy of the school. Caitlin clearly felt her opinion was valued and equally valued her mother’s and her teacher’s opinion. A specific example of the linguistic capital Caitlin has received from home came when Caitlin described how her father helps her with homework when she is staying with him. I know people don’t but I like it because it’s independent”. 1990. albeit a little reluctantly. The use of questioning to help scaffold a student’s thinking is common in most classrooms. The transference of the habitus she has developed through her interactions with her father has enabled her to engage with the game played by the teacher. anticipate actions and engage in activities in a meaningful way. It’s frustrating. Part of the habitus includes aspects of language whereby not only the spoken and written language are valuable. As is the case in both the UK and Australia. it enables the player. in this case the student. The linguistic capital is utilised in school. It would appear from our interactions with Caitlin’s family that such attributes have been fostered. This description could have been about a teacher helping a student. While it is not possible to argue here with any certainty. Her comment indicates fluency and familiarity with the discursive practices adopted by the school and was evident in her interactions with her father. says “I quite like tests actually. but also the ways of interacting become important. he asks me to read it out and he goes ‘you know this one what is it about?’ Then he makes me work it out for myself and just keeps asking questions to help me. students are expected to engage with problems that are novel so they need to have a repertoire of skills that enable them to sustain interest in order to solve the task. it would appear that her father’s questioning techniques may also have created a habitus in which Caitlin has a strong sense of mathematical processes and questioning. this habitus is recognised and validated by the practices within school mathematics. If you work in a group in the tutor group sometimes you have to explain things to them and they have to explain things to you. This is evident when she talks about the experiences within her group and her interactions with the tutor: Caitlin: I just get along with everyone. Bourdieu refers to this as the linguistic habitus. . predict the expectations. to be able to read the game. she has a respectful manner but participates as an equal. p. Many of the practices in school mathematics require individual work and problem solving. Caitlin enjoys working independently and.Structural exclusion through school mathematics 231 Caitlin attended parents’ evening with her mother and contributed fully to the conversation. Like the question about the cake in the test. However. Unlike Caitlin’s family. . We see this language of “hope” as a recognition that the system is already positioning Cory and his family as having little control of their education. I think people like Cory should be taught and concentrated on practical and everyday maths. Then I worked it out in a few different ways and got different answers and then decided what was the most logical one. Cory’s family had a very different position on school and mathematics as evident in his mother’s comment: I don’t think a lot of the maths taught are necessary as most of the kids will never use the difficult stuff again. I’ll work the completely wrong answer out but then it’ll bring me closer to the real answer. Jorgensen et al. Or work out a few different ways if you can’t remember how you did it before. he lives with his mother and two siblings. I: Why do you think you’re able to work question out that way? C: I don’t know… it just comes to me. I: How do you think you did that? C: First I tried to ask myself the question in different ways so I understood it better. I didn’t understand it at first but ended up getting it correct. in addition.232 R. A disposition for perseverance and engaging with a problem is a key characteristic for success in many classrooms. the same age as Caitlin but who is placed in the lowest-ability group. Cory is hoping to be a sports coach and his mother “hoped” he would be able to achieve the grades to enable him to go to college. enabling the construction of a particular mathematical habitus—one that aligns well with the practices within her high-ability group. When I don’t really understand the question. What is clear from Caitlin’s case is that her parents have been inducting her into particular patterns of practice. She has developed a mathematical habitus that aligns with the recognised practices of the mathematics classroom so she is able to exchange these dispositions for rewards. and a healthy concept of herself as a learner of school mathematics. 9 Case study 2: Cory Our second illustrative case is of a boy. These can be seen in her dialogue when she talks about how she solves mathematical tasks: I: What do you think you need to do to be successful in maths tests? C: You need to go through everything in your mind when you’re stuck on a question. The language of “hope” here is indicative of the perceived lack of control and agency in this process. and sees his estranged father on a regular basis. Caitlin appears to have developed such dispositions. to the school she becomes positioned as “able” and receives the privileges that become associated with such a label. Like Caitlin. it was clear that he did understand how and why he had given the answers he had. he was usually given few. The group is small but challenging so that not only is there an impoverished offering of mathematics. have created a learner who is not confident of himself as a learner of mathematics. it became apparent that in lessons. he needs longer to do some pieces because I’m not always there to help him. since Cory sometimes can’t explain what he needs to be able to do. if any. Within a Bourdieuian framework. in this case Corey’s sense of himself as a learner of mathematics. the subjective structuring practices. thus positioning him outside the practices of schooling. In the maths class there are some people who I get distracted by. It is far more social. when referring to some questions he had left unanswered. where her family habitus had positioned her well for the practices within her mathematics classroom. Maybe a help leaflet for parents to jog their memory could be sent—it’s twenty years since I left school and I can’t remember how to do much of the stuff. This lack of confidence seems fuelled by his belief that to be good at mathematics you need to “remember a lot and work stuff out quickly”. Cory is less likely to be rewarded by the school and hence has less chance of being seen as successful. Also. They make me laugh. . This creates a very different scenario for Cory than for Caitlin in terms of possibilities for construction of a mathematics habitus. the explanations he gave were not always immediately clear. However. and he needed to be prompted to give further clarification. In fact. which have come about as a result of the structuring practices of assessment. In contrast to Caitlin’s experience. Cory often appeared to understand part of the question but to lack the confidence or ability to infer the full meaning from this. The ethos within Cory’s mathematics classroom is quite different. Whilst Caitlin saw and utilised the interrelated structure of mathematics. Another problem for Cory was in responding to the numerous questions that require students to “Explain your answer”. Within this. he lacks what is seen as valued. I think it should only be sent home when absolutely necessary and then with clear guidelines of how to do it.Structural exclusion through school mathematics 233 Unlike Caitlin. this would translate to problems when trying to write down a written explanation. Cory’s habitus was not aligning with the dominant and powerful practices of school mathematics. it was more that he needed answers to be given some linguistic structure. Unlike Caitlin. Cory’s mother has a strong opinion against homework: I don’t like the idea of homework. and so without them. This is seen when he describes the important values within the field as being linked to being able to remember and work quickly. Again. thus positioning him as a not-so-strong learner of mathematics. Cory has a compartmentalised view of the subject as a series of facts and methods to be memorised—a viewpoint which makes it much more difficult to succeed. and the recognition of dispositions that are validated within the structuring practices of school mathematics. he said that he “thought that’s what it meant” but that he “wasn’t sure”. The familial habitus that is potentially created by Cory is one that is incongruous with the demands and expectations of schooling. in this case ability grouping. we see one of the structuring practices of the field. mathematical prompts. These dispositions convey power in Corey’s mind. has created an environment for the constitution of a particular mathematical habitus. When interviewing Cory. Clearly. he is uncertain about his father’s opinion and indicates that he rarely discusses school with his father. in subsequent discussions with Cory. but the engagement by the group is not with mathematics. She and Caitlin’s father have endowed their daughter with much social. they are taught in. some are disadvantaged. (Boaler. but. might allow Cory to make more connections between concepts and to develop understanding which would move him away from seeing doing mathematics as memorising facts and methods. by teachers who assume such pupils are not (cap)able of higher-order thinking (Zohar. who do not fit the ideal pupil mould. 594) It is unlikely that either pupil will change ability group even at this early stage of their secondary education. cultural and linguistic capital. p. namely the ability group. explanations were accepted without pushing for greater clarity when there was a feeling of having seen evidence of understanding. as this grouping seems in many ways to be a product of much more than mathematical knowledge. 1998. single step. Degani & Vaaknin. in the UK at least. 1997b. it seems to be the grouping that has an effect on the type of mathematical knowledge the two are presented with and consequently how far they are able to attain. The ability grouping of both students in many ways is already showing how it is starting to determine their future attainment. restricted and controlled. 21) Here we can see how Caitlin is systematically and structurally privileged and how her progression through the schooling system has been thoroughly efficient. uses similar language and has similar values. Capital attracts capital. Consequently. therefore. Indeed. of capital. which makes them better players than others in certain field games. On further observation. The consequences of setting and streaming decisions are great. Perhaps a greater emphasis on explanations. 2001. the lessons taught to the lowest-ability group contained less complex language. or identical configurations. cultural distinctions from up-bringing and family connections. we do not enter fields with equal amounts. there is evidence that teachers extend this to their beliefs about pupils’ capabilities. In fact. Some have inherited wealth. will almost certainly dictate the opportunities they receive for the rest of their lives. 1999. 10 Discussion This examination of these two pupils’ differing learning trajectories in mathematics focuses on the influences of familial habitus and linguistic capital alongside the environment. 2003). Her mother may not currently possess a huge amount of economic capital. questions were usually closed and easily understandable. but this does not hold her back. her capital earns her an enhanced reputation. p. at a very young age.234 R. Zohar. she has distinct advantages. which will continue to adversely affect his test results. the set or stream that students are placed into. Yet this form of organisation becomes natural and normal to the school and the teachers. Furthermore. already possess quantities of relevant capital bestowed on them in the process of habitus formation. so much so that. As she enters the educational field. The pupils such as Cory. with greater exploration of the “why”. as in the case of education. Jorgensen et al. a comfortable position in the highest-ability set and high attainment. Caitlin shares many similarities with her classmates. Cory is not exposed to the richer language common in Caitlin’s classroom. She lives in a similar area. Conversely. experience a mathematics education that is considerably structured. it is inconceivable to many/most mathematics teachers to consider how it might be otherwise. Some individuals. (Grenfell. It also affects his understanding of what it means to “do mathematics”. As Grenfell summarises. This means he is not given so many opportunities to develop his linguistic competence. Zohar & Dori. . The linguistic structure at home and school shares many commonalities.Structural exclusion through school mathematics 235 Her familial habitus is in close agreement with that of the school and has required little adjustment. so he has been positioned as a poor learner of mathematics—and he himself accepts this. 2012. The conventional is thus taken as natural by all parties—it is the way it is and has to be. A Bourdieuian analysis allows us to conjecture patterns in the practices adopted by those occupying similar positions in the field. Whilst Caitlin receives additional knowledge and develops linguistic . We can expect therefore the experiences of Cory to be not too dissimilar from others who share his engagement in the field. and his culture has little value within the field. Her experiences have effectively created a habitus that aligns with the structuring practices of school mathematics. he sees the purpose of schooling as purely functional and looks at individual skills and knowledge as opposed to the value of an all-round education. his familial habitus is not resonating strongly with the practices of the field. symbolic violence has been enacted against Cory. it is the case that they more fully embrace the middle-class notion of the importance of being well educated. Bourdieu sees this as how the dominated come to accept their own domination as legitimate (Bourdieu & Wacquant. 164). that is. In this way. p. p. but they do not fit together as naturally as Caitlin and the school seem to. 205). This is the case with Cory and his family. 1972. 167) in exactly the way Cory does. His position in the low setting or ability group and the reification of his lack of success act as a form of symbolic violence against the culture that he brings to school. Here. 164). This process. the whole issue of homework in some ways discriminates against Cory. Cory becomes the willing victim of his own limitations. but such violence works only when the participants willingly accept the practices and outcomes—it is “particularly insidious due to the fact that it is exercised with the agents’ full complicity” (Nolan. is termed by Bourdieu as the “doxa” and is described as “The set of core values and discourses of a social practice field that have come to be viewed as normal natural and inherently necessary” (Nolan. the field. In Cory’s case. we see Bourdieu’s idea of “symbolic violence”—which he sees operating though “The complicity of those who do not want to know they are subject to it or even that they themselves exercise it” (Bourdieu. 1992. As with Caitlin. Although schools often emphasise the functionality of what they teach. 2012. Cory’s attitude towards education echoes his mother’s opinions and his impression of his father’s disinterest. Cory’s progression unfortunately has not been so smooth. 1991. The attitudes towards education. In fact. are compatible and help to create a productive approach towards learning mathematics. Cory’s mother is less well equipped than Caitlin’s father to help with mathematics homework. 205) and representing where “There is a correspondence between the objective order and the subjective principles of organization the natural and social world appears as selfevident” (Bourdieu. On a more practical note. largely derived from parental opinion and actions and experiences Caitlin has had. whereby both sides of a social power divide (the orthodox and heterodox in Bourdieu’s terminology) adopt a tacit acceptance of the dominance within the field. In the field of mathematics education. His view of education is narrower than Caitlin’s. p. This enables Caitlin to exchange aspects of her habitus for the rewards of the field so that her culture becomes a form of capital valued within that field. Specifically. p. There is no extreme friction between Cory and the school system. and he has not achieved the same degree of academic success as Caitlin. & Swing. As de Carvalho comments Indeed. By offering this misrecognition of the arbitrary as the natural way of things. from the family point of view. 2001. or as a burden and an imposition. we see that Caitlin learns in an environment better equipped to facilitate learning. capital through completing homework with her father’s input. (Zevenbergen. Then the school field. which is advantageous for Caitlin. 2000. and the teacher. comes the creation of futures. Cory. As a result. and in that process. 1989). It is an example of how the dominant power relations in the field of mathematics are operating to convey an expected orthodoxy (that set of behaviours and relationships demonstrated by Caitlin) and marginalising any heterodoxy (that set of behaviours and relationships demonstrated by Cory). (De Carvalho. possess similar linguistic competence. Within the mathematics classrooms. it forces actors to accept as legitimate that which is possibly against their best interests. fails Cory. Drawing on Vygotsky’s idea of social learning. under-achieves in a test situation as he fails to understand questions. 2001) and is unable to structure coherent explanations. Cory’s classmates. which contrasts with the more positive model Caitlin has constructed. So what is actually only one set of responses (Caitlin’s) is seen as taken for granted and natural. depending on variable material and symbolic conditions of diverse families. has few options but to attempt to “pitch the work correctly” and so fails to enrich the language they are exposed to. in a double bind. applies an incorrect level of “appropriateness” (Cooper. most commonly realised through language (Peterson. One important effect of the disparity in linguistic capital is performance in tests. 11 Conclusion What we have tried to illustrate in this paper is the application of Bourdieu’s theory to two illustrative cases. as Bourdieu explains that habitus is an evolving concept. in the other. which from this perspective is the internalisation of social interactional processes. and through this. Cory does not possess the linguistic capital that Caitlin does as a result both of social background and classroom environment. Cory was placed and remains in the lowest-ability group. Caitlin has developed a successful approach to tests. legitimate participation is acquired and achieved through a competence with written or spoken texts. In addition. p. 202) Caitlin has a significant amount of linguistic capital supplied from home. Cory enters the school field with less linguistic capital and is placed in the lowest-ability group. in all likelihood. Cory’s mother struggles to help him. homework may be seen either as a legitimate need and a desirable practice. the classroom environment she learns in is rich in language. To be constructed as an effective learner of mathematics. in particular the classroom setting. 116) Language also plays a huge role in the disparity between Caitlin and Cory. on the other hand. she has the ability to independently decipher test questions and respond to them clearly. he is just a struggler . it is more of a burden. Jorgensen et al. Janick. 1981). p. or both. This. habitus and field act on each other (Wacquant. in turn. In one family.236 R. students must be able to display a competence with these forms of texts. Cory and his family accept his lot. it is an opportunity to share and develop the child’s education. has fostered a limited and unproductive view of mathematics. the parents as the primary socialisers have endowed their child with success or struggle (habitus) in an education system (field) that is providing advantages for some and restrictions for others (capital). The differences originate in social status and familial habitus. A problem here for mathematics education research is that it often (re)presents a field which has incongruencies within the field of mathematics education. She argues there is a set of professional discourses that orient the field to operate in such a way to create Caitlins and Corys. and certainly. . p. 1990. Nolan. Caitlin cannot be a success without the failure of Cory. This process creates the Corys and the Caitlins who become self-fulfilling prophecies of the success and failure. (Bourdieu. 2012. 67) Cory and Caitlin’s position within the mathematics setting system seems to have been determined by far more than “mathematical ability”. Furthermore. 206–211) (and we paraphrase only slightly) that mathematics teachers are pressed for time to deliver a curriculum devoid of creativity and innovation which draws largely from traditional pedagogical paradigms where testing and competition are paramount. By exposing conflicts within current practices. is not assisted by the failure of much mathematics education research to recognise the importance of social backgrounds in mathematics educational achievement. which results in slower progression and continued underachievement in assessments. however. Here.Structural exclusion through school mathematics 237 forced to play a game and yet accepting of playing a game that is not in his best interests. What these detailed case studies of Caitlin and Cory suggest is that there is some substance to the joke about how to be more successful at school—change your parents. largely middle-class. As Bourdieu says: The earlier a player enters the game and the less he is aware of the associated learning. Nolan (2012) used a Bourdieuian analysis to look at the practices of mathematics teacher education where she reminds us that the school is a “site of reproduction and regulation” (p. 212). which results in placement in lower ability sets. We might ask how we can do something about this process of exclusion in the field of mathematics education because it is exercised not only with the complicity of those who ultimately suffer (the Corys of this world) but with the implicit and explicit complicity of teachers of mathematics. the groupings in this one school demonstrate that working-class students are overrepresented in the lower ability sets. For as our analysis has indicated. pp. p. pupils in the higher sets. A possible way forward would be to broaden teacher education courses to encourage new teachers to examine the nature of social conditions in schools and theorise the lack of fit between some but not all pupils and the demands of mathematics education. thereby reproducing the conditions of its own existence. A vicious circle has developed: working class students are disadvantaged on entering the school field as they have a less compatible habitus. thus widening the gap between these students and the. though. we offer a heterodoxy to schools and classrooms which serve as the orthodoxy. This process of self-reflection. 2004. and his unawareness of the unthought presuppositions the game produces and endlessly reproduces. they are surrounded by pupils with similar habitus and linguistic incompatibility with the school mathematics discourse. 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