Students’ positionings with
respect to cultural models of
mathematics: a socio-cultural
analysis
Laura Black
Analysis of PREMA data
2 Key Concepts:
• Positioning in relation to Cultural Models
(Gee 1996, 1999) which draw on wider
Discourses
• States of Mind (Kleine, Bion – c.f. Waddell
(1998)
Methodological Stuff…
• Interviews as narrative biographies (Sfard &
Prusak 2005) outlining self identity - the reflexive
'story of the self', that we tell ourselves and
sometimes others
• Students storying themselves within the
interview & in response to the interviewer
• But students are boundary crossers from other
social practices and so these biographies are
inter-textually connected to prior experience
The Discourses of the two students
• Gerry – liberal humanist – wants to do art to
express her creativity & individualism
• Becca – also liberal humanist – enjoys maths
and science but has not decided on future
• N.B. in our sample of 50 students from the TLRP
project this kind of discourse was evident in
interviews with students from higher SES
neighbourhoods – suggesting it maybe classed!
Cultural Models
• “Everyday theories' which are situated in
social and cultural experiences and which
inform action (behaviour).” (Gee 1992)
• Distributed threads
• ‘cultural’, Discourse, Ideal
• Elements that are used to
construct/narrate one’s self – position the
self in a ‘figured world’
What cultural models are drawn on
in the narrative to construct this
imagined leading identity?
• Gerry on maths:
–
–
–
–
Maths lacks opportunity for creativity & individualism
Maths is easy and non-stressful
Being good at maths comes naturally for me
Doing maths successfully involves properly
understanding
– Maths is competitive
• Gerry’s other cultural models:
– I need to be challenged & challenge = being creative
– Education for enjoyment & interest
– Resistence to exchange value of educational
qualifications
Maths lacks scope for creativity
….but I do, I really like to be challenged…
um and I do enjoy writing the creative
aspect… as you can see of the other
subjects. But I still like, yeah, I still found
maths quite… like almost relaxing you
know its not stressful really because… its
just, you don’t have to um you don’t have
to sort of create. So that would sort of
appeal to some people.
Doing maths involves
understanding
• I have always found it much easier in maths and its
probably why I’m good at it, I have to understand why
something works because then I can work it… out
whereas if I’m just memorising a formula it means
nothing to me. So I’ve always like it when teachers can
really explain something so you think then. And that’s the
best way.
• I asked questions a lot when I didn’t understand ???
which may have made me look more stupid a bit
sometimes but actually normally no one else would
understand so it was good to ask questions.
Education for Enjoyment
• like I said I am not one to take something just
because I’m good at it. Even if art history I know
is quite a big challenge because it’s a public
school subject… and we only have maybe three
people in our class but um, [J:yea] you know it’s
a difficult exam but because I’m really interested
in it I’m sure I’ll do much better than I would
otherwise… [J:yea] because I don’t [J:yea] you
know [J:yea]. I think it’s more important to do
what you enjoy, that’s all. [J:yea] [J:yea]
Resistance to exchange value of
maths
• I suppose you get pushed more into academic… if you’re
good at something like maths I think… it’s pretty good
these days but even if its rubbish people like the idea of
you doing something that’s more academically rigorous
[J:yea] IF you’re good at maths [J:yea] you’re you’re
encouraged that way …um… so that is a difference.
[J:yea] You’re taken a bit more seriously. [J:yea]
• J: So talk to me about why doing well in art, art history is
important?
C: Um, because I enjoy it, that’s why it’s important to me.
What cultural models are drawn on
in the narrative to construct this
imagined leading identity?
• Becca on Maths
– Doing maths successfully involves the need to
understand & connect ideas
– Maths as disciplined & ordered
– Maths as enjoyable
– Maths has exchange value
– Maths isn’t hard
Doing maths involves
understanding
• J: What makes YOU good at Maths? So you got
encouragement then?
• Yeah. Erm, just just wanting to know what was
going on, how things are, how things are found
out. …I wanted to know the reasons for things I
guess. ... There’s a formula, someone gives you
a formula and there like here’s pi it like why, why
would you use pi? There must be a reason… its
like Pythagoras, well how does that work why
does that work? And just just working out how it
works which is really interesting.
Maths as disciplined & ordered
• Erm… most interesting… it’s a very hard question…
probably formulas just the way the formulas work and…
now I am on A level we learn about theorems like…
looking at people’s theorems about…and we look into
those it’s just amazing how someone can sit there… for I
don’t know how long… and work out these things and
give a specific number which works out every time… it’s
just its just amazing how they do that… and its good that
we get we get shown it and… then shown how it works
and its just just amazing… seeing how it works and then
see it and then we can use it now, still from years and
years ago when it was made, I mean I love learning that
kind of thing.
Maths as Enjoyable
• J: So… Maths, Physics, Further Maths… was
that… an easy choice to make?
• Yes I think it was… em… maths is something I
have always really enjoyed so I knew I always
wanted to take maths and also an extension of
maths, is something I would love to do… and
physics… was… because… of the subject I
enjoyed as well. I wanted to take two things I
enjoyed … [J:yea] just to make sure that then
I’d…mm… hopefully um want to do one of them
.???eventually [J:yea]
Maths has Exchange Value
• I enjoyed maths and wanted to get good GCSEs I did it
at A level and I wanted to work hard just…just to be good
at it just to say I’ve got an A level in maths. Just to show
people… and then further maths is like well that’s even
further into the maths world [laughs] hopefully that will be
[J: yea] like something people [J: yea] will be really [J:
yea] impressed with.
• J: Would being good at art and humanities, is that
important to you?
• Not as a, ..not as an A level or degree, - as a hobby… if I
enjoyed art I’d love to have something to do, on a CV
thing I could say that ‘Oh I got an A in my er A levels in
maths and physics and further maths… and I enjoy art
and things like that, but then… I don’t know how much of
a difference it would be if I had an A in art and things like
that and then…say I enjoyed mathematics… it wouldn’t
be the same thing would it? [J: yea] It would be kind of
[laughs] yeah ok. [J: yea]
Why do these students position
themselves in alignment/disalignment
with these cultural models?
• Socio-cultural explanation might focus on mediating
influences (e.g. parents)
• Discursive approach might focus on power relations
• Psycho-analytic offers an account of positioning which
recognises internal ‘states of mind’ characterised by
defenses, anxieties and types of relationship (Margot
Waddell)
• This offers an account which blurs the boundary
between our historical and socio-cultural experience with
the external world and the notion of the mind
• States of mind are rooted in the past and encompass a
possible future
Psychoanalytic themes
Similarities across both accounts:
• A need to understand & its association with maths
• Reparation – fulfilling parents incomplete dream
(altruism)
Differences between the accounts:
• Becca – self preservation (egoism) – ‘you can’t say you
enjoy maths as a hobby’ – hence the need to draw on
exchange value of maths
• Gerry – self preservation – avoiding competition &
resisting exchange value
The need to understand
• Giving shape/form to sense data of experience
through use of symbolic terms (alpha function)
• We do this throughout life & it is the means by
which we come to make sense of ourselves in
the world
• As such, we develop a desire to understand
rather than a need to know
• Understanding is about extension of the
capacities of the self rather than merely adding
to a stock of knowledge (or qualifications)
Reparation & Redemption
Becca
• … and also when I was little my Dad… um he was brilliant at
maths, well he still is.. and he always WISHED he’d taken it
further, because he didn’t go to university. So he’s like ‘you
know you’re good… you can keep doing it’, so he encouraged
me a LOT with my maths, a lot…
• He looks back now and he did an open university course in
maths and got a brilliant grade on that and he’s like I wish I
did it so he’s like just ‘Oh do it otherwise you’re just going to
look back and be like oh I wish I did it now’. And em for a long
time he wasn’t really in the job he wanted to be in and now he
is… and I guess for me he wants me to go into something
that…that I’m going to enjoy for my whole life so I guess…
yeah, I guess I think that if I get good grades, then I’ll… even
if I don’t know what I want to do I will have opportunities to do
things… with a good grade.
Reparation & Redemption
Gerry
mmm…Probably because both of my parents are
very artistic um they were… sort of you know
when they were younger they were…obviously
art was not the thing to do and they were pushed
away from it and they never even did it until they
took it up about fifteen years ago [and made
their own business, which is nice. And now my
Dad paints a lot… and I’ve always grown up...
with a lot of classical music from my dad and a
lot…the art cupboard was our playground not a
computer [C:laughs]
Self Preservation
• Becca - I can have art as a hobby but not
maths
• Enjoyment of maths as threatening to the
self (egoism)
• Gerry – the need for individualism &
avoiding competition
• Self preservation afforded by a liberal
humanist discourse
Avoiding competition
• Erm… it’s a bit different for… art based subjects I think
because…there’s there’s more variation in art subjects, [J:yea]
which areas you can be good at and things. Stuff like maths and I
suppose English and sciences its more clear cut the route to
achieving well. I think its more competitive… because you’re doing
exactly the same things at GCSE.
• I suppose it’s more clear you know if there’s always one person
who’s always really fast at doing all of their …sums but then there
are other people like me who go more sort of slowly and get good
marks. …English is a bit more vague I suppose and art is just down,
its just…art is quite free in our school when everyone develops their
own…[J:yea] sort of personality in that subject. Which is not to say
maths is bad its just more clear to see.
Final Thoughts…
• “….States flicker and change with nuancies of
external forces and relationships – forever
shifting between egoistic and altruistic
tendencies” (Waddell 1998, p9)
• Altruistic state of reparation invoked by
relationship with parents
• Becca’s self preservation motivated by positions
available in a wider discourse??
• Gerry’s self preservation afforded by her liberal
humanist discourse
• This begs the question - which comes first?
positioning or state of mind? A constant dialectic.