Against the odds: resilience in mathematics students in transition

1. Introduction

Much has been written about the concern for the decline in mathematics (and mathematically-demanding subjects) participation at pre-university and university levels in the UK (Roberts, 2002; Royal Society, 2008) and other industrialised nations (e.g. in the USA: National Academies, 2007; in Australia: Slattery & Perpitch, 2010). Recent research in mathematics education in England (Nardi & Steward, 2003) shows that an increasing number of mathematics students at school follow a profile of ‘quiet disaffection’ with the subject that includes tedium, isolation, rote-learning, elitism and depersonalisation. Furthermore, we (Williams et al., 2008) have highlighted that the institutional culture of performativity that the government promotes reinforces practices such as ‘spoon-feeding’ and teaching to the test that can seriously damage learners in their progression in mathematics. Other researchers (Drake et al., 2009) have also noticed that assessment at all levels of schooling remains largely focused on procedural reasoning and routinised calculations, with the effect that classroom mathematics remains the same.

This paper derives from our two Transmaths1 projects, which aimed to understand better how different practices during transition from school to college and later to university2 impact on students’ dispositions and identity, hence influencing their choices and future success in subjects that demand high levels of mathematics. A particular strength of this paper is that the data from both projects allowed us to compare these two important transitions and, indeed, in both we found a very similar discourse of ‘independence of learning’ and the need to approach mathematics learning in a more ‘grown-up’ way. Thus, we argue, the similarities in these two very differently situated transitions provides support for our analytic generalisations.

We know that institutional transitions can pose new challenges and obstacles to students that can threaten their progression and many students and teachers consider mathematics as particularly problematic during these transitions. The majority of the literature on transition in mathematics education comes from a psychological perspective where the ‘transitional gap’ is defined as a cognitive jump: algebra during the transition to college and calculus and ‘proof’ during the transition to university (Tall, 1992; Malisani & Spagnolo, 2009). However, a key feature in our work is that we take a sociocultural perspective on transition, where ‘identity’ is implicated in the challenges (e.g. their sense of what a mathematician is might be challenged and their identity is developed due to these challenges) (Jooganah & Williams, 2010; Hernandez-Martinez et al., 2011). Therefore, mathematics during transition does not only pose a cognitive challenge that learners find particularly hard or challenging (as opposed, perhaps, to other subjects in the curriculum that, unlike mathematics, do not require previous knowledge to build on hierarchically) but it also involves a sudden change of the pedagogical culture (e.g. the meaning of what it is to ‘do mathematics’ changes and ‘understanding’ of mathematical concepts becomes different and is said to be ‘more important’ after the transition).

We build on some of our previous results to point out how some students, in spite of many difficulties and apparently against the odds due to their disadvantaged cultural and socioeconomic backgrounds, persisted and completed the transition successfully; these students would usually be regarded as ‘resilient’. Our aim is, therefore, to try to comprehend what makes these students ‘resilient’ and how mathematics teaching could promote more resilience. In particular, this paper aims to understand and explain the concept of resilience and its role in our students’ transition from a sociocultural point of view, given that traditional resilience theories do not provide us with a satisfactory explanation. In the following section we make a brief review of these traditional theories and contrast the stance that this paper adopts in relation to resilience from a sociocultural perspective.

2. Background literature

Historically, resilience theory has its roots in the 1970s studies of children who proved resilient despite adverse childhood environments (e.g. schizophrenic mothers) and later expanded to include multiple adverse conditions such as socioeconomic disadvantage, parental maltreatment, urban poverty or catastrophic life events. Earlier definitions of resilience focused on individual characteristics and ‘Individual Resilience Theory’ continued to inform many research studies well into the 1990s. For example, Vaillant (1993) defined resilience as the ‘self-righting tendencies’ of the person, ‘both the capacity to be bent without breaking and the capacity, once bent, to spring back’ (p. 248).

As work in this area evolved, researchers acknowledged that resilience can derive from factors external to the child. Studies moved beyond the individual to consider the family and the community as sources of resilience. Children born in poverty or as part of a minority ethnic group, for example, were considered to be ‘at risk’. Risk factors are those hazardous, adverse and threatening life circumstances that result in individual vulnerability (e.g. crime, poverty etc.). At the same time, protective factors are those that enable individuals to resist life stress, such as social support (emotional support, social networks etc.) or material support (Masten & Garmezy, 1985). Most of the research that is currently done in this area and the social inclusion programmes in community and schools in today's England are driven by what France and Utting (2005) call the ‘Risk and Protection Paradigm’ of prevention (see Poole and Lefever 2009 for an example of a programme aimed to support first year university students within this paradigm).

The language of risk and protection, however, fails to acknowledge the dynamic nature of the relation of individuals with their contexts and, in that sense, seems to place resilience either within the individual or within the context.

For example, Borman and Overman's (2004) study of mathematical academic resilience suggests that a communitarian model of school, with a safe and orderly environment and positive teacher–student relationships, is likely to promote resilience in poor ethnic minority students. They also suggest that students with characteristics such as strong mathematics self-efficacy, a more positive outlook toward school, higher self-esteem and those that are engaged in academic activities are likely to show resilience. This viewpoint leads to the conclusion that resilience resides whithin the context and then is ‘transmitted’ to individuals or that these contextual protective factors might just be shielding or nurturing resilient characteristics that were already present in the child. To put it in the words of one of our project students: ‘I'm not sure whether the people are successful because they pay attention (in the classroom) or they pay attention because they're smart and successful’.

Thus, from this point of view, individuals are shaped by their context but, more importantly, they also act and in turn shape the context that afords them agency.

There are few studies to our knowledge that take a sociocultural perspective on resilience. Some of these studies (e.g. Abelev, 2009) can be placed in the ‘Risk and protection paradigm’, although others (e.g. Bottrell, 2009) recognise the dynamic nature of resilience and the dialectical relationship between the subjects and their context. Nevertheless, there is a need for further research in this area and for theorisations that explain resilience as a dynamic, relational process. We will now explain the theoretical framework that informed our analysis of the data.

3. Theoretical framework

We take the perspective that educational ‘resilience’ is a function of the set of relationships of the learner with other people and with the educational field. In particular we adopt and adapt Bourdieu's relational view of social and cultural capital as that capacity to exercise agency in a field which is (1) incorporated in the habitus, (2) objectified in artifacts or (3) institutionalised (e.g. as credentials).

An important issue in defining resilience in sociocultural terms is that of a learner's agency to act in the world. Adams (2006) has pointed out the debate that exists amongst scholars about the ‘reflexivity thesis’: on one end of the spectrum are the supporters of ‘self-reflexivity’ such as Giddens (1991), who posits that individuals organise their ways of life through a reflective day-to-day biography in which conscious decisions are constantly taken. On the other end are those who have a deterministic view about the self and for which decisions about life are unconscious and largely pre-determined. Many authors have placed Bourdieu at the deterministic end of this spectrum, claiming that his concept of habitus, as an embodied phenomenon, reflects a shared cultural context that becomes ‘a modus operandi of which he or she is not the producer and has no conscious mastery’ (Bourdieu, 1977, p. 79).

McNay's (2001) analysis of Bourdieu is of particular relevance to how learners might be able to exercise agency in an educational field (and therefore, contribute to building their resilience). She argues that it is also ‘moments of disalignment and tension between habitus and field, which may give rise to social change’ (p. 146). This breakdown or lack of fit provides the space where reflexivity can emerge, particularly in times of crises (e.g. death of a loved one, loss of a job or failure in exams). Moreover, Chapman-Hoult's (2010) ‘passionate’ accounts of resilience in adult learners seem to match the critical moments when the death of a loved one or a sudden serious illness provide the space to challenge their core assumptions of how the world works and provide resilience to pursue further education.

Other authors (Archer, 2003; Sayer, 2004) stress the role of our ‘internal conversations’ in how individuals evaluate their relations with reality, therefore theorising that self-reflexivity plays for some an important role in agency.

We believe that reflexivity is the key to understand how some few individuals are able to ‘escape the failures of the system’ and therefore help to explain how they become resilient. We take a position that reflexivity is possible (and we agree with scholars that think Bordieuan concepts allow for it) but it is not something that is frequently experienced (as some supporters of ‘self-reflexivity’ would argue). However, it is the occurrence of these ‘rare’ conscious reflective moments (especially in critical moments) that, we will argue in this paper, allows for the development of valuable capital that individuals can use to negotiate a transition or, in other words, that give them agency in a new field.

Thus, to Bourdieu's notion of social and cultural capital, we add this note of reflexivity: that students can develop capital through reflection. It is that capital that allows for agency in new fields (for example, during transition) and the possibility to exercise that agency, negotiating successfully (aligning) their habituses with the conditions of the new field (resilience).

4. Methodology

For the purpose of this paper we present the narratives of two of our apparently resilient students, Jenni3 (transiting from compulsory school to 6th form ‘college’) and John (transiting from school to university), who are representative of those students in our projects that could be considered ‘at risk’ because of their socioeconomic backgrounds but that demonstrated persistence in the face of various problems through their schooling and for which the transition could have been considered a serious risk to their progression. These narratives have been constructed from ‘biographical’ interviews that were conducted before and after they went into college or university, respectively. We asked students to tell us their ‘story’ of previous and present schooling and of transition and of how their choices related to their backgrounds and aspirations, in particular about mathematics.

We use narrative analysis to explore these students’ interview accounts, drawing on the work of Bruner (1996), who poses that narratives, the story of one's own life, is a reflexive construction of the human mind that reflects not only how we come to understand who we are but also the ‘reality’ in which we live. We view these interviews as biographical narratives, made up of interconnecting sub-stories (Gee, 1999), which can then be synthesised and (re)connected in a holistic story, involving a ‘plot’. In the particular cases of Jenni and John, their interviews were read and relevant sub-stories were identified, meanings were negotiated among us as researchers and a plot was created following Bruner's ‘universals of narrative realities’, most significantly: temporality (a plot has a beginning, a middle and an end), hermeneutic composition (no story has a unique construal but it must provide a convincing and non-contradictory account of it), reasons (actions are motivated by ‘intentional states’) and troubles (which signals important changes in the narrative). These stories, or ‘narratives of resilience’ as we call them here, facilitate the researcher's work for inductive analysis and theory building. In these narratives, we argue, it is possible to understand how resilience might have been constituted.

5. Narratives of resilience

6. Discussion

Transitional moments involve a sudden change of field, in which relationships change and power is restructured: when the game changes new kinds of cultural capital become valued. Transition into college and university mathematics poses new challenges and obstacles to students: there are new mathematical competences, new teachers and peers and new rules and there are expectations of a more adult (independent) approach to learning. We argue that resilient students are able to bring to bear particular reserves of capital that resonate with the new field.

In the case of Jenni and John—while good candidates for mismatch to the educational field according to their cultural and socioeconomic backgrounds—they have acquired some capital during their schooling that became very valuable during their transition. The narratives of resilience show how reflexivity was key to the development of this capital and eventually to resilience. In the subsequent paragraphs we discuss in detail, making use of these narratives (and as far as possible selected quotes where Jenni and John can ‘speak for themselves’), our analysis and interpretation of what resilience means.

Jenni's disposition to study by herself, to look for help when needed, to ‘block everyone’ and ‘work her socks off’, supported a smooth transition because her habitus aligned with what is expected from a college student, particularly in terms of mathematics, where practices are structured for individual (some might say lonely) work. Help is available (e.g. Maths zone) but only for those who actively seek it, like Jenni.

John's disposition to be independent, to ‘just keep trying and trying’ until eventually it ‘clicks’, sustained his efforts through rough times, when nothing in mathematics made sense, especially in relation to ‘proofs’. His relationship with his tutor—a pure mathematician who advised him to persist with proofs because these are essential—proved also crucial. Mathematics lecturers might be aware that most students would have never before done a ‘real’ proof (apart from, perhaps, by induction), but nevertheless expect students to persist and to work in an autonomous way, even though they might not grasp the concepts at first.

Jenni's disposition towards mathematics, her ‘mathematics habitus’, was such that for her ‘maths is fab’ and the practices of the new field, in turn, supported that habitus (‘Things you just can't do at GCSE’ and ‘How cool is that (now at college) you can differentiate a blooming graph’). In relation to her mathematics habitus, it is important to track how, from being a ‘hater’ she became a ‘lover’ of maths. That critical moment (‘I've had enough now’) when her aspirations to become an accountant and her identity as someone who is good at finances/mathematics were put in danger by a disruptive class, allowed for a reflective process in search of an adjustment of the reality of the present, a transformation of what is taken for granted, opening possibilities for change. The reflective development of such educational capital provided her with the necessary agency during the transition to make her habitus resonate with the new field and take full advantage of what the new institution offers (in the way of support, like the ‘maths zone’) to such students.

At this point we think is necessary to draw attention to other sources of capital that acted also as resources of Jenni's identity and that have been recognised by others as valuable sources of agency (Clegg, 2011). Jenni acknowledges that her aspirations stem from a caring and supportive family and even the fact that she wants to be ‘different’ points to the importance of community and familial capital.

John's mathematical habitus is one of an ‘able’ and independent mathematics student, who came from a ‘shit school’ where he had to learn by himself, even to the extent of having to take some courses at a distance or blended online. This experience allowed John to develop a habitus that breaks with the predominant school culture of ‘spoon-feeding’, making him very different to most of his peers at university—who struggle to be ‘on their own’ and expect to still be spoon-fed. And although he recognises that now at university he is far from being the best, he still sees himself as being different from others in how he approaches life problems, because he has consciously reflected on his special experience of independence. We do not recognise in John's narrative a moment of crisis per se as with Jenni, but rather a process of self-reflection in which, by facing countless risks to his progression, he made conscious decisions to develop educational capital that made him different to others and that could eventually allowed him to go to a ‘good’ university. The online courses and the further mathematics network provided John with the possibility to develop crucial educational capital that allowed him to persist during his difficult transition and, in a similar way to Jenni, take full advantage of the support that the new institution offered to him (i.e., a personal and encouraging relationship with his tutor).

It is important to note that across the transition, both Jenni and John experienced serious risks to their progression. For instance, Jenni regarded not being able to make new friends (all her previous school friends went to a different, more vocationally oriented college) as a serious potential risk to a successful transition; this lack of particular social capital could have threatened her transition. And for John, the financial situation of his family, which meant he had to take a part-time job to support his studies, could have stopped his university aspirations. This emphasises our view that resilience does not lie only in the context or the individual but rather in the relationship that individuals are able to make with their context.

We feel necessary to add the following caveat: we recognise that perhaps may be other factors that played a role in the development of Jenni and John's resilience and that were not mentioned by these during interview. However, as Elliot (2005) says, ‘individuals make sense of their experiences in the context of a research interview’ (p. 34) and it is therefore likely that the ‘stories’ they told us are an honest account of their subjective experience as they try to organise and explain the ‘story of their lifes’. In saying this, we also acknowledge that some sort of reflexivity goes on during interview and that this could potentially be attributed to the overall reflexivity that we claim was important in the development of these students’ resilience. Nevertheless, we believe that the narratives suggest that real instances of reflexivity took place in Jenni and John's pasts and therefore our data support the conclusions of this paper. For instance, the narratives suggest that both students were very aware that the capital acquired through conscious reflexion had given them an advantage during the transition (they did not need to be spoon-fed, they had a more mature approach to learning, they had self-directing skills etc.), making them ‘different’ to some of their peers.

We have described here resilient students as those who, in spite of their backgrounds that might put them at disadvantage in the educational field, are able to make their social and cultural capital resonate with new fields. The support of a peer group, a support programme, a special teacher, a caring family etc. are all sources of crucial social capital and previous literature on resilience identifies these as ‘protective’ factors that schools and communities should aim to provide. However, this literature fails to recognise that it is exactly the ‘risk’ factors that can play a vital role in resilience. Here we have explained how reflexivity and agency are at the core of what resilience means. Resilient students are those who actively engage with a reflective process (which can be a critical moment) in which they become aware of their need to break with what is taken for granted and therefore are able to develop certain social, cultural (and specifically educational) capital that they can bring to bear in a new field, giving them certain agency to negotiate the transition successfully. Despite the poverty and other factors that put these students ‘at risk’ statistically, they show how significant social capital from their family, school or peer group can make the difference in their conscious acquisition of this educational capital.

The implication for practice, therefore, might be that educational capital is at bottom relational and reflexive and so that processes that encourage reflexivity in students should be incorporated in pedagogical practices at all levels. What we are suggesting is that mathematical learning should incorporate conscious reflective work and that this work can be best achieved by activities that are designed to be challenging and that stimulate the discussion of different and perhaps opposite ideas in and outside the classroom, by the teaching of content that is authentic, useful and that appeals to different students’ aspirations but, more important, by supporting students in overcoming and reflecting back on these experiences that are, in some sense, ‘risky’.

This support requires spaces where learners can relate appropriately to a supportive peer group, teachers, family and community, which are the sources of valuable forms of capital. This approach might usefully be developed in mentoring schemes whereby learners get the opportunity to hear and discuss their own and the experiences of other students who have reflexively created such capital in similar circumstances. Having said this, we have to recognise that Jenni and John may be representative of the few rather than the many that ‘fail’ or drop out of mathematics and that implications for practice implied by this may be beyond the scope of this discussion and, indeed, probably need to be more radical.

We may question ourselves if such reforms could make the difference for the majority of students in an educational system that is driven by exam results, where students are trained to do procedures but where mathematics is almost never authentic, challenging, creative or has any immediate real consequence to students’ lives. Our research does pose this important question, then: given the predominant educational culture of performativity to which schools and, increasingly, universities, are subjected, how can mathematics teaching allow for reflexivity and for the construction of relevant capital for the majority and, ultimately, for the creation of such resilience among all students?