Transcript Slide 1

CHOOSING MATHEMATICS,
CHOOSING IDENTITIES?
Self-positioning, resistance and
refiguring in women mathematics
students
Yvette Solomon
Manchester Metropolitan University
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?
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.’
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)
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 of
collective storytelling —of both deliberate molding by others and
uncontrollable diffusion of narratives that run in families 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?
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-theground relations of power, deference, and entitlement, social
affiliation and distance (pp. 127-128)
BUT:
The everyday aspects of lived identities … may be relatively
unremarked, unfigured, out of awareness, and so unavailable
as a tool for affecting one’s own behavior. … [But] Ruptures
of the taken-for-granted can remove these aspects of
positional identities from automatic performance and
recognition to commentary and re-cognition. (pp.140-141)
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)
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.
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…
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)
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)
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
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
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’
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
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
(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 …
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
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’
Tutors as significant others
Jess In 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]
Emma My 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
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
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’
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?”
And it’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 think we’ve all
done better, well I’ve certainly done a lot better than I would have done if
we hadn’t had each other.
... 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
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)
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 him but 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’
subject but, 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
[The confident students are] usually men .....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
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. So I’ve got
every right to be here ... I’m determined to learn”.
Debbie, Bradley 1st year
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.
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, but one 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)