CHOOSING MATHEMATICS, CHOOSING IDENTITIES?

1. CHOOSING MATHEMATICS, CHOOSING IDENTITIES? Self-positioning, resistance and refiguring in women mathematics students Yvette Solomon Manchester Metropolitan University

2. Fragile identities: existing on the margins • Many successful mathematics learners, but especially girls and women (Bartholomew, Boaler, Mendick, Solomon), say they are anxious and ‘don’t belong’. • Stress points are top set cultures, issues in depth of understanding, being ‘good at maths’, being ‘feminine’. • Research suggests that gender discourses and institutional practices (eg Laura Black’s work) interact to constrain the range of identities available to mathematics learners - girls appear to lack a niche in this world. SO: • What is the nature of women’s responses to university mathematics (a path that they have chosen)? • How do they position self and others? • How do women resist ascribed positions (if at all)? • What resources do they draw on to do so?

3. Self-positioning in mathematics: theoretical tools for this analysis • Figured worlds(Holland et al, 1998:52): ‘particular characters and actors are recognized, significance is assigned to certain acts, and particular outcomes are valued over others’ • Self-positioning through narrative(Sfard & Prusak 2005: 17): ‘it is our vision of our own or other people’s experiences, and not the experiences as such, that constitutes identities. Rather than viewing identities as entities residing in the world itself, our narrative definition presents them as discursive counterparts of one’s lived experiences.’

4. Narrated selves • Sfard & Prusak (2005) – ‘designated identities’: • ‘…Narratives presenting a state of affairs which, for one reason or another, is expected to be the case .... because the person thinks that what these stories are telling is good for her, because these are the kinds of stories that seem appropriate for a person of her sociocultural origins, or just because they present the kind of future that she is designated to have according to others, in particular according to people in the position of authority and power.’ (Sfard & Prusak, p.18)

5. Identities and choice (?) • More often than not, however, designated identities are not a matter of deliberate rational choice.A person may be led to endorse certain narratives about herself without realizing that these are “just stories” and that there are alternatives. .... Identities are products of discursive diffusion—of our proclivity to recycle strips of things said by others even if we are unaware of these texts’ origins …. designated identities are products ofcollective storytelling —of bothdeliberate molding by others anduncontrollable diffusion of narratives that run infamilies and communities. (pp.18-21) • But: what options might there be for resistance to, or refusal of, offered positions? • Is there evidence that women in post-compulsory mathematics have done this?

6. Back to figured worlds - resistance and refiguring Holland, Lachicotte Jr, Skinner, & Cain (1998): exploring the interplay between collective narrative and individual agency Identities are enacted and produced, and individuals take up positions in accordance with the day-to-day and on-the-ground relations ofpower, deference, andentitlement, social affiliation anddistance(pp. 127-128) BUT: The everyday aspects of lived identities … may be relativelyunremarked, unfigured, out of awareness, and so unavailable as a tool for affecting one’s own behavior. … [But]Rupturesof the taken-for-granted can remove these aspects of positional identities from automatic performance and recognition tocommentaryandre-cognition. (pp.140-141)

7. Agency through reflection ‘When individuals learn about figured worlds and come, in some sense, to identify themselves in those worlds, their participation may include reactions to the treatment they have received as occupants of the positions figured by the worlds.’ (Holland et al 1998, p.143) ‘.... Narrative acts may reinforce or challenge these figured worlds.’ (Skinner, Valsiner, & Holland (2001 para 10)

8. Mathematical positioning: some teachers’ narratives about boys and girls Mary: Boys blame the question … blame the teacher. I think girls tend to blame themselves. Whereas often they are a lot better than the boys. Mark: Lads more often than not are quite willing to have a bash whereas girls are just slightly more insecure in terms of ‘am I doing this right?’ – not often that they aren’t – but they have to know that before they move on, whereas lads are a lot more slapdash ... Girls need a lot more coaxing, giving them confidence in a quiet manner, whereas the lads need more of a matey feel - ‘come on you can do it’ - whereas with girls it’s a question of trying to draw them out and stop them being so withdrawn.

9. Girls are too neat …. Mark: Girls I often find would spend maybe too long making sure it’s all written down perfectly, making sure it’s all neat and it’s all nice and maybe not get so much done. So in terms of stretching them you have to push them along pace-wise, throw in questions at them …. whereas with the lads maybe it’s a bit easier sometimes because they will finish things quicker therefore we can give them extension resources to get on with whereas with the girls sometimes they don’t want to stop what they’re doing to get on with extension stuff because it will look unfinished … whereas the lads would rather rush through and say ‘yes we want to get on to that other cool stuff’ and it may be harder to stretch the girls…

10. Being good at maths – no place for girls? ‘Girls, at the nexus of contradictory relationships between gender and intellectuality, struggle to achieve the femininity which is the target of teachers' pejorative evaluation. They often try to be nice, kind, helpful and attractive: precisely the characteristics that teachers publicly hold up as good — asking all children to work quietly or neatly, for example, while privately accusing the girls of doing precisely these things. Thus they are put in social and psychic double-binds. Few girls achieve both intellectual prowess and femininity.’ (Valerie Walkerdine, 1998, p.162)

11. Dealing with fragility? The university experience – previous research • Relationships with tutors • women seek positive relationships with tutors – they need to be approachable and interested in them as a person Gendered roles in the learning context • women are more likely to seek out peer group help and to say they need help • their tendency to ask questions and to admit to problems breaks the ‘ground rules’ (Seymour & Hewitt, 1997) • they can be ‘invisible’ (Rodd & Bartholomew, 2006) Legitimacy and understanding • women play down achievements, berate themselves for ‘not understanding’ (Solomon) • being seen to be good at mathematics continues to conflict with femininity (Rodd & Bartholomew)

12. The SIGMA study • interviews/focus groups: 33 mathematics undergraduates, in their 1st/2nd/3rd years, 19 men and 14 women • questionnaires: 130 2nd year students, 77 men and 53 women • 3 different universities in England – “Bradley”, “Farnden” and “Middleton” • covering perceptions of mathematics as a subject, contrasts with their pre-university mathematics experience, individual approaches to learning, perceptions of other mathematics students, relationships with tutors

13. The questionnaire data – principal factors and findings • (1) confidence, interest and positive attitude • (2) positive relationships with tutors • (3) positive attitude towards group work • men scored more positively than women on factor 1 • men scored more positively on factor 2 • women scored more positively on factor 3

14. Factor 1 – feeling positive, being confident • ‘Since coming to university…. • ‘I feel more positive about mathematics’ • ‘My university experience has resulted in me being more confident with mathematics’ • ‘I feel I have the knowledge and confidence to help others in the class’ • ‘Most mathematics students are cleverer than I am’

15. The figured world of the undergraduate – the same old stories Tamsin: Some people are just naturally good at maths … they just know it straight away. … sometimes someone can put so much effort in and another can put not as much and the not as much can do better. Roz: There are some people who find at this level all of maths easy, because they can naturally see it and they can intuitively understand it. Caitlin: For some of them they just pick it up so quickly, so what they can do in the lecture is enough for them to pass the exam. Whereas others of us will have to do all the exercises, and all the past papers and revise really hard to just get the same as they do. Farnden 2nd Year

16. Genius – the select few • I don’t know where they get it from, … but they seem to know exactly what to do and they’re just integrating and differentiating all over the place and I have to wait for the lecturer to do it. That’s why I think I’m not good at maths. …. There’s this one guy and I’m sure he’s a mathematical genius, I’m sure he works it out. But I just wouldn’t. Diane, Bradley 1st year • Nick: I could have told you in primary school what I was going to do. … I just loved doing maths so I never really …[ too much noise to hear as they laugh and joke] even when I was 3 or 4 … • Megan: You’re a genius Nick …. everyone’s good at different bits (Nick is just good). … • Liang: [if] Nick needs some intelligent conversation, he’s got to talk to himself! Middleton 2nd years

17. (not) identifying as “good at mathematics” Jess (Middleton 2nd year) – always second best: I think I’ll be over the moon if I get a 2.1 …. I’ll probably get a 2.2 but I always aim for one mark above - I always remember something a GCSE teacher said to me: he said, “if you only need a B to get into the 6th form then aim for an A so if you get a B you won’t be disappointed” so you always aim for the highest mark that’s going….. I didn’t get A at A-level I only got B, and I didn’t get the A* at GCSE I only got A, so I’m not going to get a first I’ll only get a second. Richard (Bradley 1st year) – better than the others: … when I see a stats problem I can see it quicker than most … I understand quicker than other people … I have realised I am good at it without sounding big headed. … I always knew I was good at maths …

18. What is meant by understanding I didn’t understand… I learnt how to do it, I didn’t understand why, why are matrices there in the first place, why do we have these groups of numbers, what does it mean, what’s the point? You know, I didn’t actually understand what they were for. I like to understand exactly what it is I’m doing …. I like to know what it is [laughs] and I used to, like, knock on the lecturer’s door, “please”, you know, “why with the matrices, what’s the point of it?”. Debbie, Bradley 1st year I think I'm the kind of person who should care about understanding but I don’t … I am competitive … getting the right answer is more important … I understand well enough to carry on. Richard, Bradley 1st year

19. Factor 2 – relationships with tutors • ‘I think most mathematics lecturers are approachable’ • ‘Most mathematics lecturers do try to help me learn’ • ‘When I ask lecturers for help, I often do not understand their explanations • ‘The feedback I receive is sufficient to enable me to make progress with my academic work’ • ‘I think lecturers encourage participation in learning mathematics at university’

20. Tutors as significant others JessIn one of his tutorials - he doesn’t particularly help you. I said “I don’t understand it, can you just look at what I’ve written for this question” and he just looked at it and said “Your answers are strange” and walked away. [Laughter in the group as a whole] EmmaMy tutor seems to have high expectations of me after my results last year but I just hope I get through it and get a decent grade by the end. … I used to think [I can’t get a first] but last year I got a first so it’s kind of a big shock, and that’s why I think my tutor has more faith in me than I do. … I don’t want to say it and then fall flat on my face. Matt I don’t want to sound big headed but I’m hoping for a first. I think I’m on the way to getting that. …. my tutor has been trying to get me to do a PhD…… Middleton, Year 2

21. The importance of tutors’ reactions We had to do the chain rule … and my mind just went … So I went to Dr Fox and … he was like, you know, “oh, you know, you’re gonna have to get sorted out with these type of things, you know”, and I flushed up and everything. But I sit it out, you know, because he’s upset me before but I just think no, I’m determined to learn so I’ll just, even if it’s uncomfortable I’m not bothered. … so I was saying well I learnt it through this DIDO and whatever and he said “well, she’s obviously not a very good teacher your teacher if she’s stressed on that and not on the other”. And I felt disloyal for not sticking up for her afterwards. I thought “no, she is a good teacher, it’s not her fault, I should know it”. Debbie, Bradley Year 1

22. Factor 3 – working with others • ‘I learn a lot from working with student friends’ • ‘I prefer to do my “private study” work with a group of other students’ • ‘If I need help I talk first of all with my friends’ • ‘I wish we had more group work’ • ‘I prefer to learn mathematics on my own’ • ‘I am better at mathematics than most other students on my course’

23. Gendered roles in the learning context: the benefits of group work.... • aid to learning • enables recognition of others’ strengths in comparison to one’s own • a buffer against loss of confidence Roz (Farnden, Year 2) We all enjoy collaborative working because although you might be doing your own project, … you know, “did you get this problem on your set?” Andit’s a kind of reassurance thing that you are actually doing the right thing, you have understood it properly or …..some people are really good at understanding that bit but woolly on that ….. I thinkwe’ve all done better, well I’ve certainly done a lot better than I would have done if we hadn’t had each other.

24. ... versus the individualism of the lecture There was this one girl who, the poor girl, she sort of well “shouldn’t that be negative x or something” and he said “no”. “Oh”, and then she was…. she tried but she was wrong. Which is why I’d never point it out. Diane, Bradley 1st year I think they [men] are more likely to be the ones that are going to point out there is a problem, you know, “there is a mistake on the [board]” or something like that, I have never seen a girl do that, well I have done a couple of times but I never really, I wouldn’t do it in a lecture… they’d probably just leave it, or, you know, say to the person next to them, “that’s wrong” or something like that but I wouldn’t think they were going to shout it out unless they are quite a woman. Sarah, Bradley 1st year

25. Survival and resistance 1: learning spaces as sites for refiguring relationships with tutors • no gender difference in factor 2 scores (positive relationships with tutors) at Middleton, where there is dedicated ‘legitimate’ group working space • Middleton women score significantly higher than men on factor 3 (group work) • If you go to their office …. you know there’s a queue of people behind you, they were doing something before you arrived if there wasn’t anyone in the queue ahead of you so you feel like you’re bothering them, it’s their space as well and you’re going into their office, whereas maths support is neutral ground for everybody … it doesn’t belong to anybody.Roz (Farnden, Year 2)

26. Survival and resistance 2: reflecting critically on gender and ability discourses My brother was quite good at maths as well, but different to the way I am, …I would usually say that guys can usually be the ones who have this amazing ability, just to be able to see it but [there] was a girl and she was just the same as, you would think a guy might be and my brother, I think he just didn’t try actually, to be honest, but he, I think I was maybe better than him … I don’t think I was as natural at it as himbut in a way I did better and I could do it better. But, I think that there are a lot of guys that can’t do maths as well,I used to think that it was more a guys’ subjectbut, I don’t know, recently I think that girls,there are a lot of girls that are good at it as well. Sarah, Bradley 1st year [Theconfidentstudents are] usuallymen .....they’re getting too big headed and they know ‘I can do this’ …. They’re all smug and they sit there and they’re filling in the answers and then they sit back and sort of look over at what the other guy who’s sitting next to them… like, ‘Huh, you’ve done it wrong there’.Diane, Bradley 1st year

27. Survival and resistance 3: reflecting critically on the institution I came here sort of feeling a bit like a second class citizen, “should I really be here?”,… I’m older and I feel like there’s gaps in my knowledge and blah-di-blah. And I think it sort of took me the first term really to get over that and “no, I am all right to be here, I can do it”. … But I’m still here. There was another mature student that left after seven weeks … And I sort of thought “well, no, I’m still here”, you know, “I’m still doing it. SoI’ve got every right to be here ... I’m determined to learn”. Debbie, Bradley 1st year

28. Conclusions • Previous research: the available identities and cultural norms in maths are masculine • Relationships with tutors are central to women’s experience, impacting on confidence and access to mathematics itself • However, some women challenge the status quo, resourcing this by critical analysis of their situation, and by capitalising on the provision of ‘legitimate’ working space which appears to make a significant difference in opening up different ways of being undergraduate mathematics students.

29. Finally: undergraduate mathematics as a contested space The potential for refiguring is, as Holland et al suggest, subject to social and cultural forces which endure despite resistance: the image of the geek and the need not to look stupid persist. “One can significantly reorient one’s own behavior, and one can even participate in the creation of new figured worlds and their possibilities for new selves, butone can engage in such play only as a part of a collective. … The space of authoring, or self-fashioning, remains a social and cultural space, no matter how intimately held it may become. And it remains, more often than not,a contested space, a space of struggle.” (Holland et al, 1998, p.282)