As bell hooks (1994: 143), writing mainly within the post-modern, suggests:
Even though students enter the "democratic" classroom believing they have the right to "free speech," most students are not comfortable exercising this right to
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"free speech”.... Especially if it means they must give voice to thoughts, ideas, feelings that go against the grain.
Hooks (1994) provides theoretical possibilities to start thinking about the ways in which the embodiment of mathematics, as white, male and middle classed, brings about bourgeois constructions of collaborative learning into the classroom, and in so doing inhibits and silences many of the learners. As previously discussed, in the analysis of Jalal, returning to mathematics through the spaces of SfL can disrupt expectations, both in terms of the form of the mathematics, and the pedagogy on offer. Traditionally, encounters of mathematics have been experienced under the regulatory gaze of the teacher, with the expectation that the individual should seek to maintain self-control and order in the classroom, hiding their emotions at all costs. It can therefore come as a surprise when mathematical knowledge is framed as a human construct, where the very purpose of knowledge is to bring about discussion through properties that, at will, can be manipulated by the individual and/or the collective.
When Moser (1999) set about reworking the curriculum, he assumed that teachers and learners shared the epistemic and ontological assumptions of the socio-cultural
account. He assumed a shared vision of what ‘new’ spaces of mathematics could and should offer, particularly in relation to empowering learners to find and articulate their own (mathematical) voice. In naturalising the pedagogic technique of collaborative learning, the official discourses ignored the ways in which a spoken positioning of mathematics engendered new feminine qualities (like estimation and caution) into a body of knowledge which had, traditionally, been considered logical and linear (Walshaw, 2007).
I have considered the ways in which Susan used silence to enable her to act in collaborative ways, and Karigalina also used silence in interesting ways. Karigalina (introduced at the top of section 7.4) took on the role of the facilitating teacher, quietly working on her own, but listening to her colleagues to ensure they were on the ‘right track’. The ways in which she discursively constructed her subject position played out in complex ways. Her performance of supporting others did not only come from a gendered location of a caring and supportive mother. In returning to the quote at the
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start of section 7.4, there was an interesting intersection between the isolation of the ‘othering’ as a migrant subject, and her performances of collaborative learning:
Last year I took GCSE English and I noticed that, erm, that I was the only one non-British, so I didn’t get help from any of the students. … yeah so my opinion treat everyone like you want to be treated so since then, erm, I’m trying to keep up to help these ladies because they are behind and sometimes they don’t understand … so I always keep in mind that they might need my help …. so this is why I am keeping an eye on them and doing my own work … I can sacrifice just a little bit of my time right and then I can catch up at home with these questions.
As outlined, Susan internalised her past encounters of schoolroom mathematics as the product of her own faulty character. During the lesson observation, at times she appeared silenced by the expectations of social behaviour in the classroom. She negotiated the spaces that she perceived to be full of conflict through using silences, and was the only learner I observed to demonstrate (and not to repeat) learning points to her peers. As I have explored through using the works of Walshaw (2007), Susan’s practices of not speaking could easily be dismissed as pathologically lacking within the constructivist classroom. However, it would be too neat to simply categorise Susan’s and Karigalina’s behaviour as passive or disinterested. Both (in interestingly different ways) refrained from engaging in vocalised practices with the intent to speak and reveal mathematical ‘truths’. Both positioned themselves as privileged, and each sought to undertake the act of balancing the new construction of their own
mathematical self through identity positionings that polarised the genuine and brilliant mathematicians, but significantly, also distanced themselves from the other 'others' in their class; peers who continued to struggle with the content of the mathematical knowledge on offer.
In very different ways Susan and Karigalina’s mathematical work can be understood as being formed within and through the gaps of the mathematical practices hidden within the classroom. The ways in which they both shaped their mathematical identities fell in and between the expectations of what is assumed to be the most effective way to produce knowledge. Both sought to sustain an illusion of their unitary self as they struggled to reconcile their new and emerging relationship with
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ideal way to learn. Whereas Karigalina looked on to support others, to defend against her own fear of feeling isolated, Susan (like Kath and Sandra) expressed enjoyment in working collaboratively, citing that working with others enhanced her understanding of mathematical practices. In this way, Susan whilst producing herself as a learner of mathematics, pointed towards engagement and participation, but remained censored by her understanding of democratic ‘free speech’ within public spaces, and underwent considerable gendered identity work to not be considered impolite. Susan, on being confronted by ‘success’, immediately compared herself (and her right to speak) to the one individual in the room whom she positioned to be the only ‘natural’
mathematician in the classroom, “Mahmood [her peer] he’s just so fast. So quick, quick, quick and I want to be like that, fast”, and in doing so, she compared her success to what she imagined it would feel like to learn ‘real’ mathematics in the classroom.
Philly’s stories of learning have been deconstructed at some length in Chapter six, but the insights into her injuries can reveal things about how she negotiated the socio- cultural discursive practices of collaborative learning. Philly’s account was the most aligned with Solomon’s et al. (2010) findings of pupils working in lower sets. Philly’s interpretation of the question “tell me about your experiences of collaborative
learning”, led her to demonstrate her ability to care and support others lacking in confidence. Bibby (2011: 75) suggests that “safe spaces (of learning) are often small and hard to find, even for those who would utilise them, let alone outsiders who might judge”, and as we have seen in the previous chapter, her desire for a safe learning environment was vital for her to even be able to enter the classroom, let alone the mathematical space:
most of us sit there with a load of crap in our heads, how on earth does other stuff we really need to get on, stay in our head with all this other stuff going on? … I want to be able to be open as much I can. As much as I’m able to at that
particular time, on that particular issue ... but I close down. Close down, yeah. Philly was not the only participant to internalise the 'problem' of not being able to learn mathematics. Susan and Kath also cited what Steve termed a "stinky attitude" in a bid to reconcile their new found ability to 'do' mathematics in the classroom:
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Steve: When I did my GCSEs again, the people I used to live with, one of them was an electrical engineer and he knew everything and he sat down with me for 2 hours a day showing me fractions. I mean simple fractions and my mind was just not there, and I couldn’t see what he was doing and I think literally …I didn’t want to know. At the time, I thought God why can’t I get it and now looking back I don’t think I could have been that stubborn ... I have always been if my mind is closed then I am just not going to get it … it may have been that.
Kath: I know why I didn’t do well (at school) …I messed about and erm was you know, taken out of the maths lesson and made to do like work by myself. So, if you don’t understand … and you haven’t got the teacher to explain it and I was in that frame of mind, ‘oh well I’ll just do it myself.’ And I didn’t do any course work, so stupidly I didn’t do it.
Susan: Well I never did any homework, so I guess it’s my fault that I’m at the stage that I am now, but I also know that the way that some people teach is a bit weird … Well, I didn’t understand it anyway … they would just come in and start talking and they would expect you to be able to catch up.
In placing their 'difficult' selves at the centre of a discourse of blame, all four
participants carefully negotiated the inclusion of what Skovsmose (1994) refers to as the structuring processes of mathematics. However, what was left out of the accounts was also striking. All spoke convincingly of the need to be numerate but none
associated this form of mathematical knowledge with something they felt needed to be mobilised within them. It was only Fatima who spoke of a terrible sense of shame and vulnerability at not having the confidence to check her change:
I feel very confused and nervous to check because I do know that it is a bit difficult for me. So I do look at this to the nearest change for me. So if it was sort of £1 something and erm I gave you £2 and it cost me … 25p. … then I think, you know has he given me £1.50 something. If there is something there, then it’s fine.
Philly spoke of a relief of not making terrific mistakes when buying curtain material, Susan of being chastised by her mother for not being able to perform a percentage calculation in a shop with immediacy, but none placed this sense of loss in a relational account of what they wanted to achieve from returning to the classroom to learn mathematics through the spaces of SfL. The final chapter will reflect on what happens to mathematics when what was once considered impenetrable becomes penetrable. This chapter has sought to interrogate the implications for positioning, given the subjectivities available to participants within the SfL intervention.
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7.4 Summary
By drawing on the works of Walshaw (2004, 2007, 2010) alongside Bibby (2008, 2010, 2011) Brown et al. (2004, 2006)and Brown (2011), this chapter has offered an interrogation of the ways in which the learner participant have variously taken up, negotiated and/or resisted the subject positions offered to them as adult learners of mathematics through discourses of SfL. I have drawn from a Lacanian
psychoanalytical perspective and examined the fantasies and desires as the
participants imagined the ‘ideal’ learning environment and/or value of mathematical knowledge. In taking this approach I exposed how this sample of participant learners have come to reconcile the gaps between fantasies (within the imaginary domain) by creating fabrications of the self to meet the perceived expectations of the ideal learner within the symbolic realm.
Kath, Sandra, Susan, Karigalina and Tony all gave complicated accounts of learning; each were suggestive of the ways in which they have shifted their sense of selfhood towards the notion of being able to do mathematics. Whilst Kath, Sandra and Tony tended to look through a mirror of perfection, each negotiated their own spaces in ways in stark contrast to the collaborative account. Sandra and Tony positioned their emerging identity in relation to the teacher, and Kath, Susan and Karigalina as an external but interesting body of knowledge. I have argued that learners cannot be positioned as agentic, enterprising individuals, ready and able to leave the concerns of the material world outside of the classroom. But neither can they be read as docile bodies simply yielding to the discourses of how they should learn.
Practices of learning and forms of mathematics may be inscribed on bodies, but the ways in which the individuals converse with the big Other in the symbolic domain, and/or the fantasy and desires within the imaginary, shape (and are shaped around) the structuring processes of learning and are productive of a range of positionings. Where most of the learners took up many of the aspects that are vital to the collaborative classroom, Susan and Karigalina used silence to negotiate their mathematical selves in ways that highlighted the importance of the affective domain. Each cited the use of silence as a way to protect themselves and their othered peers, from the prospect of fear, humiliation and failure as productive of, as Susan recalled, “having numbers put
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in their face” and in this way their particular use of silence was at once powerful and powerless. Powerless because the act of silence was inscribed through the gendered production of ‘doing’ mathematics and of speaking within public spaces, but powerful because the product of the silence disrupted the hierarchy of power that traditionally has served the interests of the white, male and middle classed ‘autonomous’
individual, and the discourses that have framed learners as consumers of ‘choice’.
It was through listening to Jalal and Steve’s stories that the impossible fiction of freedom in the classroom was exposed. Through looking at collaborative learning through a mirror of perfection associated with the esoteric domain, both participants became marginalised by the neo-liberal account of the self in the mathematics classroom. For Jalal, the resulting frustration turned to anger and further reduced the resolution of his mathematical gaze, expelling him from collective discourses of the aims and purpose of his course. However, Susan, Karigalina and Sandra negotiated the expectations of social behaviour in the collaborative account, and it is through Žižek’s (2006) understanding of agency as a ‘meta choice’ (for example Susan’s and
Karigalina’s use of silence) that the product of identity work/self-identification can be read as extending the range of subject positions that they assume to be available to them. Discourses of best practice engages the learners and teachers in particular performances of mathematics. The extent to which the administration of the
curriculum allows space for the teacher will be explored in the next chapter as I look to the empirical data to reveal the effects of the "terrors of the performativity" (Ball, 2003) that were outlined in Chapter five.
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