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Developing gendered identities of exclusion and inclusion in mathematics Yvette Solomon Department of Educational Research, Lancaster University, UK

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The issue Mathematics is associated with strong emotions but these are not necessarily related to levels of success in the subject (eg undergraduate women - Solomon, 2007). There are important elements in the classroom community of practice which contribute to this range of relationships and the development of identities of participation for some learners but not for others (Solomon, forthcoming). Identity is part of a complex web of cultural influences and institutional structures in which teachers and pupils interact in the process of constructing particular identities for particular learners. Dominant discourses of gender and ability are visible in the ways in which boys and girls are positioned, and position themselves, in mathematics classrooms.

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“A classroom, and indeed every human community, is an individual at its own scale of organization. It has a unique historical trajectory, a unique development through time. But like every such individual on every scale, it is also in some respects typical of its kind. That typicality reflects its participation in still larger- scale, longer-term, more slowly changing processes that shape not only its development but also that of others of its type.” (Lemke, 2000 p. 278) Lemke asks: ‘how do moments become lives?’ – I will ask: ‘how do mathematical moments become mathematical lives? Emergent social groupings and the interaction between short- and long-term processes

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Interaction patterns and beliefs in classrooms are important Girls and boys appear to participate differently in classroom discussions because they are taking up, negotiating and maintaining those positions which are open to them within the context of pedagogic discursive practice. As Gee (2001) points out, some of the available discourses are more accessible and ‘culturally appropriate’ than others. The discourses and practice of mathematics include and endorse some powerful beliefs about: –the nature of ability –the supposed inherent difficulty of mathematics –the manifestation of ability to do maths is not merely getting right answers, but getting them quickly and with an apparent lack of effort –this is associated with having a natural aptitude for mathematics

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The potential for excluding pedagogies in UK setting practices: top- and lower- set cultures Faced with higher ability sets, teachers are more likely to focus on pupil learning and involvement with the subject, and to engage in between-equals banter, particularly with the middle class male subset who ‘belong there naturally’ (Bartholomew, 1999) Adverse effects on low ability group students: –less discussion and more boardwork –a reduced curriculum –a ‘polarized curriculum’ which limits exposure to mathematics –lower expectations –different kinds of teacher-pupil interactions Girls in top sets are likely to see themselves as having ‘less right’ to be there and to experience a high level of anxiety (Boaler, 1997) “The culture of top set maths groups, and of mathematics more generally, makes it very much easier for some students to believe themselves to be good at the subject than for others.” (Bartholomew, 2000: 6)

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I wanted to explore how individual relationships with mathematics develop in terms of the dynamics of emerging pupil identities and their interaction with classroom cultures. I asked them about: –learning mathematics and the nature of mathematics knowledge –perceptions of themselves and others as mathematics learners –success, ability and effort –SATs –boy/girl differences –setting Mathematics identities of pupils in Years 7, 9 and 10, in an comprehensive

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The Year 7 mixed abilities students: Competing public versus private discourses of effort, luck, ability and gender Sylvia: effort is important but … everybody is just better at something different and understands different things …you’d have to get [weaker students] to listen more and try and take part more in group activities and concentrate a bit better [but] … there’s a lot of people can, do pay loads of attention and still can’t do it. Becky: the perpetual insecurity of being good at maths: [Did you feel anxious about the SATS?] Slightly, because in some of the practice papers we did every now and again I’d get a paper that we’d do and I’d do quite well and then other times I got a low mark … it depended on the questions and what type of questions I got as to what level I would get.... I found the paper really hard … but it was like the luck of the draw with what paper.

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Year 7: Speed, gender and behaviour Jonathan: I think girls are usually a lot better at a lot of mental things than boys are but when you look at all the chess champions and intellectual champions they’re always boys. … And like there’s, it sounds very, very sexist but there’s hardly a girl amongst the intellectual ranks of the world. Nicola: boys mess about; Carol: the boys in the higher ability sub-group don’t make a [visible] effort. Sylvia: I think the boys aren’t usually afraid to put their hands up and the girls will usually sit there quiet but… the girls tend to just sit there and watch. …. I’m like that though, I don’t like putting my hand up that much [because you’re worried about looking stupid or … what?] yeah, that’s it basically … they’re always joking about looking silly anyway so it doesn’t usually matter as much to them.

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Year 7: Epistemologies of mathematics The norm – eg Carol: Maths has got straight answers and [in] English there’s lots of different answers that you can get but maths is simple and there’s only one right answer so I think it’s simple in that way. The exception - Nicola: Maths is like a lot more … complicated thinking than … science or English because… well, in English there’s only a few … sentences and things like that, whereas maths is a whole … different thing and a whole variety of things to be introduced to… I think there’s lots of different subjects but in the subjects there are lots of different things that … come back together. So one subject, say algebra, there’s actually different topics in that … range but they … somehow fit in together.

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Emergent identities in Year 7 Who says they are good at maths? Nicola: I think it’s a bit hard sometimes because if you don’t understand a lot of it it’s a bit embarrassing sometimes if you put your hand up and say “I don’t get it”… If we have a test and everyone else gets a higher level than me I do feel a bit … embarrassed. Jake : I’m quite a strong mathematician, probably because I like working out things. Jonathan: I am gifted and talented …. I approach maths in a very different way to a lot of people. I do it, I tend to use more tricky methods which doesn’t always work out right but that’s how I like to do it… I don’t usually like conform to what the teachers say to do because I’ll do what I want.

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Living out the ability group discourse Michael (Year 9 top set) - selected for top set: because … it’s just the rate of work when we were all mixed. Probably a bit of natural talent as well because some people can just see the answer in their head so if they can just look at it and work it out it saves a lot of time … because you’ve got to be born - some people are good at English, some people are good at maths. But Jenny (Year 9 top set) says: Boys just scribble it down and I don’t think they really care what happens with it … “try and get more done”, quantity not quality.… there is more lads than lasses that go faster and … the hand writing is dead scruffy and you can’t read it. But they go dead fast.

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Making connections: participative teaching and learning in the top set Luke (Year 9 top set) - prioritises making connections: … I can understand how it works and I can see how it works and when I take time and think about it and look at it I can see it and I can do it right and correctly. … Whereas [others] … might be thinking “Oh, what’s this?” and I’m … “Oh yeah, I’ve done something a bit like this so I can use that knowledge to help me with this”, and then maybe the two things actually combine together to make a different thing…. What distinguishes him from other pupils who are less able at mathematics is ‘the difference between being able to do maths and being able to do the maths investigations’. Daniel (Year 9 top set) – comparing with the lower sets:.. we do more of little bits of more things whereas the people who are lower down do more things with little bits so they don’t see as much.. we sort of see it, we sort of see all the maths problems and how they connect to each other and we understand it more.

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Top set relationships with teachers: teacher as resource Michael (Year 9, top set): [The teacher’s role is] mainly just trying to explain things…. Once we get rolling we’re usually quite independent and … we’ll run it through her just to make sure she thinks we’ve gone about the right way of doing it. But that’s about it really …. I only ask her as a last resort. I usually ask the people around me first. Georgia (Year 9, top set): It won’t be the same as anybody else’s idea. You get to add a part of you into the project ….you’re using what you already know and then adding some bits that maybe you didn’t know with the teacher’s help or whatever. … If you don’t understand something you can try and connect it to something else that you do understand which might make it easier for you to get better at it.

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Lower ability groups and lower expectations: facts, performance, and getting by Trevor (Year 9, lower set): I want to be a truck driver so I’ve got to see how many hours I’ve done. And then you’ve got to try and get, work out the exact mileage and everything. …When I go with my dad and my mum shopping, like buying stuff and it’s seventeen point five per cent, they might need to work it out before they go up and buy it… Lizzie (Year 9, ex-top set): The teachers say you’ll need maths when you’re older. But you’re not going to need simultaneous equations or graphs when you’re older unless like you’re an accountant or something.... You’re not going to need to know all this. But I think it’s just to prove how clever you are sort of thing.

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A lower set perception of mathematics investigations Ben (Year 10, lower set): You want to get to the lesson and just get into it … and you’re wanting to find more than other people I didn’t hardly speak at all, I did a lot of work in that [And what was the end point?] There were lots of different ways [pause] can’t quite remember [What was your target?] As many as possible and trying different grids and how many different, enlarging the grids [Did you actually generate any kind of formula for how things related to each other?] No I don’t think so. [So what did you learn maths-wise?] Puzzles sort of thing [pause] [Is there anything you’ve learnt from it that you’d be able to apply next time?] [pause] I don’t think so, no.

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Excluded identities: Learning mathematics as pointless activity Trevor (Year 9, lower set): If we’ve got the right idea but don’t get the right answer, they don’t tell us off, still like, at least we’ve tried. Anna (Year 10, lower set): It depends if you want to do it or not … if you choose to do it you enjoy it more because it’s what you want to do. But if you don’t chose it and you get forced to do it then it’s different. I don’t like my teacher this year … … we do pointless things all the time, I know I’ve said it’s pointless but we really do. We sit there and we have to draw triangles, whereas last year we were really working hard.

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Gendered trajectories of inclusion and exclusion: interactions between pedagogy and discourse The Year 9 and 10 students’ accounts suggest contrasting epistemologies of mathematics and experiences of teaching and learning between the top and lower ability groups which are associated with corresponding identities of participation and marginalization. BUT The data do not fall uniformly into such neat categories….. Discourses of mathematics and mathematics learning, and of ability and gender differentiation are intermingled with pedagogic practice. These discourses, and the positions that they make available to students complicate the picture of the impact of pedagogy.

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Top set girls Characterised by a tendency to interpret desire to understand and connect as weakness, and a strong fear of failure. They are more vulnerable to being positioned by the opinions and actions of others: Jenny (Year 9, top set): The teachers tend to show the hard way a lot of the time. They do show you an easier way but only briefly because they just want you to do the complicated way so you probably can pick up more marks or something. Lizzie (Year 9, ex-top set): she is glad not to be in top set any more as she was unable to work at the required speed: ‘it’s quite embarrassing to put your hand up and say “Oh I don’t understand it”, when everyone else does’ Rachel (Year 10, promoted to top set): Maths, I don’t really like it because I don’t see the point of it. I like … I don’t know… Like when we’re doing work, all the algebra things, I think “what is x and what is n? Why are we trying to make that y, what’s that all about?”. I can’t understand why I’m doing it so I can’t really understand how to do it.

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Harry and Sue Sue (Year 10, taking GCSE one year early): ‘I’m quite good’ Harry (Year 10, taking GCSE one year early): ‘I’m above average’ Sue: You know, Harry’s a very good mathematician so his [coursework] is really good. … he is more advanced, he knows more things that we have to do … in tests he can take the formulas out of the front of the paper and put them to the questions and some of them I don’t know what to do with them. ‘Some people really aren’t … as good. Some people can’t learn as much.’

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Trajectories through “Discourse space” (Gee, 2001) Solving the anomaly of the top set girls’ marginalized identities: Girls are positioned, and position themselves, within the different ways of being that are made available in the mathematics classroom Identities – or Discourses - are formed over time and have their roots in earlier experiences and repeated positionings. They include: –Nature-identity (natural ability); –Discourse-identities which draw on mathematics discourses and also a discourse of gender differentiation; –Institution-identity is clearly ascribed in terms of ability group membership; –Affinity-identity appears in the students’ accounts of their within-class groups, such as the gender groupings which girls rather than boys allude to frequently, and ability sub- groups in year 7.

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Developing gendered identities of exclusion and inclusion in mathematics Students experience exclusion from mathematics for a number of reasons: –patterns in pedagogic practices which support engaged learning for some students but not others; –students themselves bring particular histories, experiences and beliefs with them to the classroom which inscribe the identities and positionings which are available; –beliefs about mathematics are also enacted within classroom discourse and practice, itself driven in many respects by institutional constraints and government-level demands. ability grouping, audit and testing have a major part to play Classroom cultures and discourses of ability and gender intersect so that even successful girls can develop relationships with mathematics which are essentially negative.

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References Bartholomew, H. (1999). Setting in stone? How ability grouping practices structure and constrain achievement in mathematics. Paper presented at the Annual Conference of the British Educational Research Association, University of Sussex, Brighton. Bartholomew, H. (2000). Negotiating identity in the community of the mathematics classroom. Paper presented at the British Education Research Association, Cardiff, Wales. Boaler, J. (1997). When even the winners are losers: evaluating the experiences of `top set’ students. Journal of Curriculum Studies, 29(2), Gee, J. (2001). Identity as an analytic lens for research in education. Review of Research in Education, 25, Lemke, J. (2000). Across the scales of time: artifacts, activities, and meanings in ecosocial systems. Mind, Culture and Activity 7(4), Solomon, Y. (2007). Not belonging? What makes a functional learner identity in the undergraduate mathematics community of practice?' Studies in Higher Education 32(1), Solomon, Y. (forthcoming). Mathematical Literacy: Developing Identities of Inclusion. Mahwah: Lawrence Erlbaum Associates.

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