Developing gendered identities of exclusion and inclusion in mathematics

1
Developing gendered identities of exclusion and
inclusion in mathematics

• Yvette Solomon
• Department of Educational Research, Lancaster
  University, UK
• y.solomon_at_lancaster.ac.uk

2
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.

3
Emergent social groupings and the interaction
between short- and long-term processes

• 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?

4
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

5
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)

6
Mathematics identities of pupils in Years 7, 9
and 10, in an 11-16 comprehensive

• 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

7
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 youd
  have to get weaker students to listen more and
  try and take part more in group activities and
  concentrate a bit better but theres a lot of
  people can, do pay loads of attention and still
  cant 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 Id get a paper that wed do
  and Id 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.

8
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 theyre always boys. And like
  theres, it sounds very, very sexist but theres
  hardly a girl amongst the intellectual ranks of
  the world.
• Nicola boys mess about Carol the boys in the
  higher ability sub-group dont make a visible
  effort.
• Sylvia
• I think the boys arent 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. . Im like that though, I dont
  like putting my hand up that much because youre
  worried about looking stupid or what? yeah,
  thats it basically theyre always joking about
  looking silly anyway so it doesnt usually matter
  as much to them.

9
Year 7 Epistemologies of mathematics

• The norm eg Carol
• Maths has got straight answers and in English
  theres lots of different answers that you can
  get but maths is simple and theres only one
  right answer so I think its simple in that way.
• The exception - Nicola
• Maths is like a lot more complicated thinking
  than science or English because well, in
  English theres 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 theres lots of different
  subjects but in the subjects there are lots of
  different things that come back together. So
  one subject, say algebra, theres actually
  different topics in that range but they
  somehow fit in together.

10
Emergent identities in Year 7

• Who says they are good at maths?
• Nicola
• I think its a bit hard sometimes because if you
  dont understand a lot of it its a bit
  embarrassing sometimes if you put your hand up
  and say I dont get it If we have a test and
  everyone else gets a higher level than me I do
  feel a bit embarrassed.
• Jake
• Im 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
  doesnt always work out right but thats how I
  like to do it I dont usually like conform to
  what the teachers say to do because Ill do what
  I want.

11
Living out the ability group discourse

• Michael (Year 9 top set) - selected for top set
  because
• its 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
  youve 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 dont 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 cant read
  it. But they go dead fast.

12
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, whats this? and Im Oh
  yeah, Ive 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 dont 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.

13
Top set relationships with teachers teacher as
resource

• Michael (Year 9, top set)
• The teachers role is mainly just trying to
  explain things. Once we get rolling were
  usually quite independent and well run it
  through her just to make sure she thinks weve
  gone about the right way of doing it. But thats
  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 wont be the same as anybody elses idea.
  You get to add a part of you into the project
  .youre using what you already know and then
  adding some bits that maybe you didnt know with
  the teachers help or whatever. If you dont
  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.

14
Lower ability groups and lower expectations
facts, performance, and getting by

• Trevor (Year 9, lower set)
• I want to be a truck driver so Ive got to see
  how many hours Ive done. And then youve 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 its 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 youll need maths when youre
  older. But youre not going to need simultaneous
  equations or graphs when youre older unless like
  youre an accountant or something. ... Youre
  not going to need to know all this. But I think
  its just to prove how clever you are sort of
  thing.

15
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 youre wanting to find more than other
  people
• I didnt 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 cant 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 dont think so. So
  what did you learn maths-wise? Puzzles sort of
  thing pause Is there anything youve learnt
  from it that youd be able to apply next time?
  pause I dont think so, no.

16
Excluded identities Learning mathematics as
pointless activity

• Trevor (Year 9, lower set)
• If weve got the right idea but dont get the
  right answer, they dont tell us off, still like,
  at least weve 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 its
  what you want to do. But if you dont chose it
  and you get forced to do it then its different.
  I dont like my teacher this year we do
  pointless things all the time, I know Ive said
  its pointless but we really do. We sit there
  and we have to draw triangles, whereas last year
  we were really working hard.

17
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.

18
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 its quite embarrassing
  to put your hand up and say Oh I dont
  understand it, when everyone else does
• Rachel (Year 10, promoted to top set)
• Maths, I dont really like it because I dont
  see the point of it. I like I dont know
  Like when were doing work, all the algebra
  things, I think what is x and what is n? Why
  are we trying to make that y, whats that all
  about?. I cant understand why Im doing it so
  I cant really understand how to do it.

19
Harry and Sue

• Sue (Year 10, taking GCSE one year early)
• Im quite good
• Harry (Year 10, taking GCSE one year early)
• Im above average
• Sue
• You know, Harrys 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 dont know what to do with
  them.
• Some people really arent as good. Some
  people cant learn as much.

20
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.

21
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.

22
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),
  65-182.
• Gee, J. (2001). Identity as an analytic lens for
  research in education. Review of Research in
  Education, 25, 99-125.
• Lemke, J. (2000). Across the scales of time
  artifacts, activities, and meanings in ecosocial
  systems. Mind, Culture and Activity 7(4),
  273-290.
• Solomon, Y. (2007). Not belonging? What makes a
  functional learner identity in the undergraduate
  mathematics community of practice?' Studies in
  Higher Education 32(1), 79-96.
• Solomon, Y. (forthcoming). Mathematical Literacy
  Developing Identities of Inclusion. Mahwah
  Lawrence Erlbaum Associates.