A Leading Identity: The Key to Persistence thru Math?

Posted on March 23, 2012 by

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Black, L. 2010. Developing a ‘leading identity’: the relationship between students’ mathematical identities and their career and higher education aspirations. Educational studies in mathematics 73 (1): 55.

Methods:

  • The data reported here focus on two students, Mary and Lee, who each have different experiences in their current college programmes and show contrasting aspirations in their interviews (p.5).
  • Investigated students’ participation in post compulsory mathematics education (aged 16-17 years) in England with the aim of comparing two Advanced Subsidiary (AS) level programmes: Mathematics and Use of Mathematics with a view to understanding how pedagogy impacts on students’ dispositions towards studying mathematics, and electing to study mathematically demanding courses, (e.g. Science, Technology, Engineering etc.) at university. (p.5)
  • As part of this project, we conducted interviews with 40 students focusing on their background history, their experiences with mathematics, career aspirations and disposition towards future study. (p.5)
  • It looks to explore how such experiences interact with students’ background social factors (e.g. class, gender etc.) to shape learning outcomes, identities, dispositions, and the key choices made surrounding transition into university. Mary was a participant in both of the above projects so we have 5 interviews spanning a period of 3 years. (p.5)
  • We now have five interviews with Mary which cover the period from the start of her AS level studies to the end of her one year Foundation Degree in Mechanical Engineering at university.
  • Mary’s interviews have been analysed using narrative analysis. This draws on the work of Bruner (1996) who emphasises the importance of narrative not only in construing how we understand ourselves in the world but also the ‘reality’ in which we operate.
  • We present our students’ interviews as biographical narratives, made up of inter-connecting sub-stories which can then be connected (or disconnected) through a reformulation process. The latter involves the identification of a central ‘plot’ within or across a number of interviews and sub-stories told by the student are considered in terms of their proximity to this (Goodson and Sikes 2001). On this occasion, we have used the constructs of leading activity and leading identity as the central plot. A leading activity is identified where we see a significant shift in the student’s motive to engage with a particular activity or others like it and where this shift in motive is implicated as significant in shaping the student’s trajectory. This can be seen within a particular sub-story the student recounts where s/he reflects on the shift in some way or it may be more apparent when comparing sub-stories regarding the same activity(ies) at different points in time (i.e. between two different interviews).
  • The interviews are designed not to reveal some arbitrary ‘truth’ about our students’ biographies, but rather to offer an opportunity to narrate shifting motives, leading activities and identities and how mathematics may enter the story (p.6)

Constructs to Read the Data:

  1. Leading Activity: Used to identify an activity which involves a significant shift in the student’s motive to engage with that activity or others like it. This may relate to a particular sub-story the student recounts or may refer to shifts in motive which are apparent when comparing the sub-stories told at different points in time (i.e. between the first and second interviews)
  2. Leading Identity:  Identity statements pertaining to the new relations between motives, emerging through
    the student’s engagement in leading activity. Identity statements may refer to either their state of being (in the past, present or future) (e.g. I am, I will be, I was, etc.) or themselves in action (e.g. I do, I got, I will do). The intention is to establish if/when one particular significant identity acts as a driver to both the student’s sub-stories and our subsequent interpretation of the data
  3. Cultural Models: The identification of cultural models is thematic, focusing on beliefs, propositions or value statements, e.g. those made about mathematics and learning mathematics. Central to the identification of such statements as cultural models is establishing them as socially shared (or culturally derived). This was achieved through an empirically grounded cross-sectional analysis of the whole interview data set which highlighted beliefs as common amongst the whole sample or specific clusters of students. Additionally, some of the cultural models we refer to, such as ‘maths is hard’, also draw on wider discourses about maths and have been identified in previous research (Mendick, 2006; Solomon, 2007)
  4. Troubles/Obstacles:  Drawing on Bruner (1996), we sought to identify sub-stories where the student recounted ‘troubles’—problems or challenging events in their experience of being in college which may bring about a shift in motive/identity for the student through reaching some kind of resolution or rationalisation (not always positive). We are particularly interested in those ‘troubles’ which may signify some kind of ‘crisis’ for the student—Leont’ev notes that a ‘crisis’ may occur when a youngster’s ‘potentialities’ are not matched to their social reality (the activities they engage in) (p. 7)

Findings:

  • In previous work (Williams, Davis, & Black, 2007), we have made the distinction between ‘identity in practice’—i.e. identities which are constructed/drawn on in the doing of an activity—and the ‘narrative self’—i.e. the stories we construct about ourselves upon reflection, such as in the context of the research interview (Bruner, 1996; Gee, 1999; Roth et al. 2005). We have argued that these two engagements of identity are held together by cultural models which emerge or are provided by one’s participation in practice(s) and are drawn on in one’s reflections when constructing the narrative self (Gee, 1999; Holland & Quinn, 1987). These are culturally derived rules and schema (Holland & Quinn, 1987) or everyday cultural concepts and conceptual frameworks (Gee, 1996, 1999) which govern what we can perceive, but also what we can tell. (p.3)
  • Leont’ev argues that activities become leading when new motives are generated so that the original motive of actions is surpassed by a new motive, and hence, a new activity. He gives the example of a school-goer who completes her homework so that her parents will allow her to go out to play but who comes to realise that doing homework brings about a new relation with schooling (i.e. it pleases her teachers) and, so, a new motive for doing homework is generated: indeed, homework comes to be part of the activity of ‘schooling’. Thus, the action’s result (getting good marks) becomes more significant for the individual than the original intended motive (to get the job done and go out and play) and a new ‘objectivisation’ of needs emerges (p.4)
  • In a previous paper (Black et al. 2010) we drew on interview data with AS level mathematics (post-16) students to present the concept of ‘leading identity’ which, we argued, defines the student’s motive for study and shapes their relationship with mathematics.
  • We argued that whilst some students might focus on a leading identity of ‘being a student’ and thus, engage with the activity of ‘studying’ merely to gain qualifications, others focus upon ‘studying’ with a vocational future in mind and thus attend to the ‘use value’ of mathematical knowledge beyond the institution of schooling.
  • We argued that this leading identity gave her enough motivation to persist in studying mathematics where others might have dropped the subject. In this paper, we wish to explore the sustainability of this leading identity for Mary as she experiences transition from college to university.
  • Cultural Historical Activity Theory (CHAT) which focuses on transition and development in terms of movement between object orientated and socio-culturally mediated activities (Leont’ev 1981; Beach 1995, 2003).
  • This line of theory implicates the construct of ‘identity’ since individual development is seen as a process of ‘becoming’ someone new – in line with their participation and transition between activities.
  • (Beach 2003) argues that the notion of ‘leading activity’ is an important methodological tool in terms of understanding transition both in terms of individual progression and in terms of macro level change (these two are entwined in such a way that you cannot have one without the other). He draws on (Leont’ev 1981) to define leading activity and its role in development suggesting that human life
  • “is not built up mechanically … from separate types of activity. Some types of activity are leading ones at a given stage and are of greater significance for the individual’s subsequent development, and other types are less important.
  • We have shown that, by adhering to a particular leading identity (becoming an engineer), Mary has found a deeper motive to the activity of studying.
  • Mary draws on its use value not just for qualifications but for her vocational future, whereas Lee’s motive for ‘going to uni’ and ‘becoming a psychology student’ is mediated through the status of the qualifications he hopes to gain and the exchange value of his grades (p.14)
  • Studying is not simply about gaining a qualification but rather it is seen as preparation for the next stage of her life – working as an engineer. We have argued that the motive provided by her leading identity may be resourcing a positive transition providing her with enough confidence to make a new start.
  • We have highlighted Mary’s ongoing relationship with mathematics which is framed in terms of its use value to the activity of ‘doing engineering’ both inside the classroom (education system) and in the workplace.
  • We suggest a move away from strategies which focus on maximising the exchange value of grades. Such a focus encourages students to ‘drop’ subjects which are unlikely to bring about a high return for their efforts. Instead, we encourage interventions which might facilitate students’ reflective and reflexive understanding of their long-term developmental trajectory, and their developing motives for study. (pp.17-18)