Mathematical relationships: identities and participation
A psychoanalytic perspective?
Tamara Bibby, Institute of Education, University of London
I would like to use this seminar as an opportunity to share some tentative early thoughts about
the ways in which psychoanalytic perspectives can help us to think about learning and teaching.
How do psychoanalysis and education relate to each other? Britzman’s (2003) suggestion is
that both are about making a connection to ‘the unknown and the incoherent’. A suggestion that
prompts me to wonder whether we may need to rethink the ways we conceptualise knowledge
itself. Education proposes knowledge as something we can be sure of. What is important may
be contested but what ‘knowledge’ is remains relatively recognisable as the content, the stuff,
of what gets taught.
The psychotherapist most associated with work on the nature of thought, thinking and
knowledge is perhaps Wilfred Bion. Bion talks of ‘cannibal knowledge’ – ‘knowledge about’,
knowledge that can be extracted from someone or somewhere without giving back – the kind of
knowledge that education focuses on. If you find out that I have a birthday in June, that is
‘cannibal knowledge’ – it doesn’t really affect you or your relationship with me. If together we
develop a realisation that I carry around a sense of loss, that is knowledge of a different order –
it becomes part of the knowledge held in our relationship and it emerges from talk of our
experiencing of each other. What is notable, talking to children of all ages about knowing and
learning, is the extent to which they know that what and how they know content is intimately
bound up in relationships. What is equally interesting is the way many teachers work to deny
this link. Perhaps this denial relates to a fear of contact with the unknown or the inchoate,
maybe a fear of the implications of some kind of more personal intervention being needed?
Britzman suggests that, if we could manage to bear contact with the inchoate, if we could bear
not to know, tolerate the emptiness and loneliness of not knowing, then we could start to learn
and to know differently. This is identified as a process which “entails being able to lose not the
object [knowledge] but its idealisation” (p163). It is education’s valorisation of knowledge and
knowing that idealises it (as the great key turner, personal developer, life-fixer, economic driver
etc) – this defends against the terror of the unknown (what happens when we die?, what will the
world be like for the next generation? What will happen if I don’t get L4 in my SATs? What
would it mean if I was a success? Or a failure?).
The particular question we have been asked to focus on in this seminar is: How do pedagogic
practices (e.g. teaching styles, tools and resources, the use of ICT) impact on learner
identities in relation to mathematics? So I also want to use this seminar to rethink what I
understand by ‘pedagogy’ and to explore the implications of my chosen definition and
‘theoretical lens’ in general terms and also in relation to the particularities of the mathematics
classroom. Making use of psychoanalytic notions of knowledge changes the ways we can think
about the act of teaching and learning, and the desires or aims of pedagogy.
Even contemporary, supposedly “child-centred” definitions of pedagogy fail to account for the
ways relationships and subjectivity constitute knowledge. They tend to focus on the teacher’s
and learner’s rational acts and conscious processes. For example:
Modern pedagogy is moving increasingly to the view that the child should be aware of
her own thought processes, and that it is crucial for the pedagogical theorist and teacher
alike to help her to become more metacognitive – to be as aware of how she goes about
her learning and thinking as she is about the subject matter. (Bruner, 1996: 172)
Pedagogy is: “any conscious activity by one person designed to enhance learning in
another.” (Watkins & Mortimore 1999:16)
I find these kinds of definitions problematic and, with Winnacott, would want to acknowledge
more unconscious processes:
In human affairs, thinking is but a snare and a delusion unless the unconscious is taken
into account (quoted by Britzman, 2003: 97)
So I will ally myself rather with Dewey who defined pedagogy as ‘the interrelationships of
persons’. What does it mean to define pedagogy as being about relationships? Relationships are
hard work, they involve knowledge and thinking that goes beyond the rational – what space is
made for such thinking in schools and classrooms? And where does this leave any notion of a
‘pedagogic practice’ be that ‘teaching styles, tools and resources’ or something else?
How do the rational ‘technologies of teaching’ (assessment, planning, inspection etc) –
currently highly valued – fit with the idea of pedagogy being about relationships? A
psychoanalytic perspective might suggest that they are defences against something – the
question is: what unbearable knowledge have the systems been constructed to defended
against?
Given all this – how can I make sense of the data emerging from the research I am currently
involved with? I attach two extracts from the data – these are quite long and I may not use them
(all) but they give a flavour of the kinds of data we are getting.
References
Benjamin, J. (1988). The bonds of love: Psychoanalysis, feminism, and the problem of
domination (Vol. 1990). Reading: Virago.
Bion, W. R. (1961). Experiences in groups and other papers (2004 ed.). Hove, East Sussex:
Brunner-Routledge.
Bion, W. R. (1970). Attention and interpretation (3rd (1993) ed.). London: Karnac.
Bollas, C. (1987). The shadow of the object: psychoanalysis of the unthought known. London:
Free Association Books.
Britzman, D. (2003). After-Education: Anna Freud, Melanie Klein, and psychoanalytic
histories of learning. Albany: State University of New York Press.
Pitt, A., Robertson, J. P., & Todd, S. (1998). Psychoanalytic encounters: Putting
pedagogy on the couch. Journal of Curriculum Theorizing, 14(2), 2-7.
Some biographical notes
I have a fine art degree and ended up as the maths co-ordinator in a primary school because no
one else would do it. Having been given the post I was forced to return to my own maths story:
I had been ‘good at maths’ (i.e. I could do it and get it right without too much trouble) until A
level when the subject became more difficult and, for that and a variety of other reasons, I
dropped out. When I later returned to do A levels I was entered for the wrong exam. I failed
and that stopped me getting into the university and course I wanted. Throughout this my
feelings about myself and maths swung from positive to negative. Doing things like the 20 days
maths course with Mike Askew, Linda Maple and Rob Briscoe turned that back around and I
did an MA and doctoral studies in maths education but always felt less into the maths and more
into the people and the strange things that seem to go in in some classrooms when maths is the
focus.
Now, I think of myself mostly as a primary teacher (rather than a maths person) and I struggle
to make sense of what classrooms have become since I left the profession in 1992.
This comes from an interview with three girls (Naila, Hafsah and Sabrina) – it took place while
they were in Y5. They have been telling the researcher (Alice) about the drawings they did
showing times when they are learning and a time/situation when they didn’t learn. They were
encouraged to do speech or thought bubbles saying what the different people were
saying/thinking. This extract comes from quite early in the interview and follows a section
where they have talked about various teachers (as people) and their teaching (what it was like
to be in their classes). Miss South is their class teacher.
N:
A:
N:
Miss Souths not in the picture but I want to talk about Miss South [laughter from all 3]
OK we’re going to let Naila here talk for a minute about what she wants to say
OK, Miss South, she sometimes ignores me and stuff and I don’t really like it, yeah she
sometimes ignores it, I don’t really like it
A:
Right, so what sort of times does she ignore you
N:
Yeah, if I want to show my work, then everyone quickly just comes yeah and she goes
with them
A:
So if you don’t get there first you get ignored?
H:
You can’t tell Miss South that
A:
Miss South won’t know this. So what does that do to you, how does that make you feel
when that happens?
N:
It hurts my feelings
A:
It hurts your feelings, yeah, and I wonder does that make it easier to learn or harder?
N:
Harder, and like I open my book and I see that I get all the questions wrong, wrong,
wrong, wrong
A:
Oh no, so you feel ignored and then you’re feeling that you haven’t got it right?
H:
Can I say something for a minute
A:
Are we just letting Naila talk for a minute?
N:
... and it’s not my fault that I got everything wrong, it’s Miss South’s fault that I got
everything wrong
A:
So what happens when you get it wrong
N:
I feel guilty
A:
you feel guilty?
N:
Yeah
A:
Because?
N:
Miss South ignored me [Laugher from all 3]
A:
So, when Miss South ignores you you feel less like learning and then you get the
question wrong and you feel guilty
N:
Yeah
A:
I’m not quite clear about why you feel guilty
[Laughter, esp from H, A whispers to her that what N is saying is very important]
N:
She’s [H] gone hyper
A:
this is very important
H:
OK I’ll be quiet
N:
I don’t know why I feel guilty…..it’s still quite my fault because I got the questions
wrong a bit, but it’s normally Miss South’s fault
H:
Well I feel like that, it’s because Miss South like, I put my hand up and she never
chooses me, especially like in maths, she loves the other yr 5 class and then like um she
A:
H:
N:
A:
N:
S:
A:
N:
S:
N:
A:
N:
H:
A:
H:
A:
H:
N:
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Z:
A:
N:
A:
H:
blames me if I’ve got it wrong, it’s like ‘Hafsah you don’t understand’ but it’s her, she
doesn’t understand and then when I’m ignored I don’t like it, I feel left out and nobody
ignores me! But then she says I only ignore you, it’s because you’re so clever, but then
that’s not true
What do you think is true?
I think it’s just she doesn’t like me, no Alice it’s true, I don’t think she likes me that
much
Me neither
You don’t think she likes you either?
No
No
Oh dear and you too?
Yeah and every maths time, we pay this game and I put my hand up and she doesn’t
choose me
Miss South doesn’t really do that much to me
she really likes her
Sabrina?
She really likes Sabrina
when you keep on being left out, you think of something, you think that oh maybe they
don’t like you and that’s how I feel
And what happens to you when you’re trying to get on with learning things and you feel
that your teacher doesn’t like you? Does that make a difference
Yes, it’s a bit difficult to like concentrate and then she’s like ‘you’re not concentrating
properly’, but then when you tell her that ‘you’re leaving me out’ then she doesn’t know
how you feel because it’s not happening to her!
Because she’s not being left out?
Yeah cos she’s being, like everyone’s surrounding her going Miss South, Miss South!
If I was Miss South yeah and Miss South was me yeah, I’d just squash her like a fly
(Laugher from all 3)
What would you do Sabrina?
I’d ignore her as well
Yeah but you can’t really ignore a teacher so well, it doesn’t work so well that way
round does it?
Send her to the head teacher
Send her to the head teacher?
I would ignore them or this is what sometimes I feel like to do with this boy in my
maths group, getting a ruler and wacking it on his head….yeah that’s what I feel like to
do with Miss South, cos teachers need things like that …