In this paper I offer some of my work on power and how mathematics teachers talk about it. I am intrigued by the work of Michael Foucault on the circulation of power and attempt here to use this notion to consider the formation of the interactions and organisation of the mathematics classroom. I move on to explore a number of concerns including the constitutive and constituted nature of teachers’ practice and teacher ideology. and how power, in this sense, might legitimate certain classroom actions.
I will start with a brief account of an incident that I hope will help locate the concerns of this writing. I have joined a Y8 class where a PGCE student is working with the class teacher. The teacher approaches me and says,
I have been dissatisfied with theoretical frameworks that construct the actors in the education arena as oppressor or oppressed and that discuss power as something wielded by a few over the many. This does not reflect for me what it feels like to be a teacher (or be a human being). I have found that the theories of Michel Foucault on the operation of power within groups and institutions provide me with tools with which I can develop a more recognisable account. I have used those ‘tools’ to give me a way of looking at teaching and learning interactions, and particularly, teachers' talk about how they plan their work and how they view their practice and I have found that the careful use of these tools can highlight previously unexamined areas for me.
I want here to introduce some of the ideas from Foucault's work on discursive practices and power relations that I have found helpful and consider in some depth their applicability to the mathematics education context. I have arranged these under 4 headings: Power is the relation, Power is productive, Discursive practices, Power conceals itself.
Later, by drawing on the discussion that followed a presentation of these notions to colleagues at the BSRLM conference in June 1997, I will give a example of how these tools might be used to work on a particular account of a lesson and start to see what (new ?) meanings might be made of the teaching and learning interactions. What is here is very much a beginning. My future work will extend into a fuller analysis of the circulation of power in the mathematics classroom.
‘What characterises the power we are analysing is that it brings into play relations between individuals (or between groups )... In effect, what defines a relationship of power is that it is a mode of action which does not act directly and immediately on others...The exercise of power consists in guiding the possibility of conduct and putting in order the possible outcome’
Maggie McBride (1989) tries to apply this notion of power for her mathematics classroom. She writes: ‘Foucault claims that power does not act directly on people but on their actions.’ and ‘Power is made and exists in every social interaction and classroom....the site of power is within individual students and teachers.’
I want to argue that power brings into play the relation at the same time as it is constituted through the relationship itself. In other words, in accepting the constitutive nature of power and knowledge I need to be careful ( in using power in Foucault’s sense) not to pretend to the possibility of separating out the entities - people, their actions, their relations, their institutions and power itself.
Foucault considers how knowledge is actually produced and induces power through what he calls 'discursive practices' in society. ‘Discourse’ is a central term for him. In its broadest senses it means anything written, said, or communicated using signs. A connection can be made here with Structuralism (see for example Levi-Strauss ) and its dominant focus on language. He describes a discursive practice as
‘There is no knowledge without a particular discursive practice and any discursive forms’
In the context of my researches these theoretical notions allow me to look at my classroom (set within the wider mathematics education culture) as a discursive practice, and I can consider how the actions and reactions of the people in it are constituted by the discourse and, at the same time, the discursive practice is actually constituted by their actions. This enables me to consider how power is formulated within teaching practices and interactions with curriculum texts.
In looking at aspects of classroom practice one task (and that task was set out by Foucault (Foucault and Deleuze 1972 p 208 ) is to try to reveal the power that is operating there. He argues that one of power's characteristics is that it is often invisible, hidden. And one of the tricks of power is that it makes things look natural, obvious, and unquestionable. One task of a researcher then would be to try to reveal that hidden power.
The foregrounding of language and texts marks a shift away from seeing cultural norms as formed and perpetuated through traditions and practices to seeing a process of normalisation coming about through descriptions and a particular way of ordering things. The constitution of the National Curriculum for Mathematics in the UK is a example of mathematics described in categories (ordered into levels and (5, no it should be 4) attainment targets) - a ‘constructed naturalness’. The nature of mathematics is somehow changed as a result, this categorisation becomes a cultural norm, regulation through descriptions that come to be taken as natural and obvious. The way that mathematics is constructed, the determination of mathematicians’ and mathematics teachers’ consequent actions and the power relation itself can all remain hidden.
I find this notion of power as hidden and best exercised when people are unaware of it key in education researches. On an electronic mailing list dedicated to the work of Foucault (A posting on the subject of Foucault and Habermas to the Foucault electronic mailing list @jefferson.village.virginia.edu), Sam Binkley (1995) remarked
What follows is the transcript of a video extract taken from ‘From The Trouble with Numbers’ broadcast on BBC2 Thursday 30th January (further information available on http://www.bbc.co.uk/education/cmi/tblnum.htm) that formed the basis of the discussions with maths education colleagues mentioned earlier. The task I set to focus our viewing of the video was to reveal the power that may not initially be on view and to consider the questions –
Curriculum project leader comment: In order to convince our teachers that they can actually do this we felt it important to provide them with precise lesson plans, so that we have in our document quite clear-cut lessons that, in fact, indicate to the teacher what they should be doing, what they should be covering in each of the lessons with their classes.
Commentator: Following the example of Hungary every lesson starts with the previous day’s homework. Any problems children had are sorted out in front of all the class and only then do they move on to that day's lesson.
Teacher comment: The first day we introduced this particular scheme into year 10, one of the children said 'This is the hardest day's maths I've ever done in my life'. and that was because she knew that for the whole lesson she had to keep on task and couldn't have 2 minutes rest while I wasn't watching her while I was attending to somebody else.
Scenes from the start of a lesson
Teacher: Right I want now to go through any of the questions people had difficulty with. Who would like to come up and put any angle in there on B?
Teacher comment: It's very demanding for the teacher because you are in control for the whole lesson and you are having to answer questions that are unexpected questions where as if you set an exercise for children to do for 10 minutes say you have 10 minutes thinking time to get yourself organised for the next bit and you don't have that kind of break in these kind of lessons.
Pupil A comment: If you are up at the board then you don't have to know exactly what you are on about but you've got to have a good idea ’cos you've got the whole of the class that are there to help you. So you've got like 32 teachers instead of one.
A right-angled triangle is drawn on board with sides marked 6 and 8.
Pupil A goes up to board and writes c2 = a2 + b2
Pupil A: Your hypotenuse is always opposite the right angle
Pupil A: so... (and writes on board marking one side as 'hyp')
Teacher: Do you want to put your values in now, into your equation?
Pupil A writes on board c2 = 82 + 62
Derek: no shouldn't it..
Teacher: (to Derek) go on ...yeah... tell her
Pupil A: so 8 squared is 64 (and writes on board c2 = 64 + 36)
Derek: It's not c squared - shouldn't that be c equals 64 + 36
Pupil A: that's c squared
(affirmative mutters of c2, c2 from other pupils )
Pupil A now writes c2 = 100 on board
Teacher: I think that you are out voted on that one, Derek
Teacher: Just a minute. We'll talk about it in a minute.
Commentator: Teaching thirty or so students is always a challenge for the person in charge.
Pupil A continues by writing something we don't see on the video then c = 10
Teacher: do you all agree with that...?
Class chorus: yeah
Teacher: right, there's just one little thing wrong with it and that's that we shouldn't have had that square root of 100 there. We write....
She rubs a line off the board and writes the square root symbol] c = 10
The video extract can be treated as a piece of text. There are different ways in which we may read it. Multiple discourses can be drawn out and we each choose the one/s with which we work. The strategy we used was to look at the event in the detail, at the acts and the setting, and see what is highlighted for each of us. We have to bear in mind ‘the trick of power/knowledge to conceal itself’ and so have to work carefully with the ‘microphysics of power’ (Foucault 1977) wherein forms of licence come about. It is this care that gives value to working with a video clip in this way (without denying the many things that we do not and cannot know, such as whether the teacher moved on to some quite different style of working, and that new accounts may have altered our readings). The task is not to try to establish the truth, to tell the one story that fits.
I give here a brief collage of power themes - it is uneven, incomplete, fragmentary and overlapping - taken from colleagues’ contributions to the discussion after viewing the video clip. These select detailed acts and utterances that may initially seem unimportant or slight but could reveal the workings of power and the conditions of existence of the relations here. The extracts point to what meaning ‘power ... brings into play relations’ might bring to this context and give some formulations of the exercising of power and the creation of knowledge.
I have included further reference to Foucault’s work as seemed appropriate.
- it deviated just a tiny bit from ‘the right way’.
That adds emphasis to there only being one way to do it.’
The teacher’s and pupils’ form of speech was ‘this is a right angled triangle’, ‘this is opposite to this’, ‘this one is the hypotenuse’. Consideration of questions like ‘what if it wasn’t a right angled triangle?’ were not legitimate. What sort of questions would have been legitimate?
It might be important to ask what generated this anxiety about questions for the teacher. What might the pupils have asked ( of her ) in that situation that she wouldn’t have understood or been prepared to deal with?
The difficulty is not with the teacher or the homework. Perhaps I should consider my teaching as poor if not all the pupils couldn’t understand. But, this way of thinking does not appear to be entertained.
Moreover, the curriculum devisors appear as legitimating her position. She seemed to feel she was absolutely right in what she was doing because she appeared to have been told that this was the right way. Is that odd? She wasn’t responding to the students; she was responding to the curriculum.
This removed from her the possibility that there could be difficulties with her teaching. ‘They’re not understanding, and so I need to consider how I can do my job differently to improve this’ wasn’t a legitimate part of her thoughts.
There is an issue for us as teachers to work on here: what is it about what we say and which of our actions position the pupil as the ones with difficulties and our teaching as unquestionable. How can we talk and act differently and still maintain working well in our classrooms?
A technical note: It can be seen that where Foucault uses the term ‘discursive practice’, Lacan and Marx use the term ideology. Their construal of the notion of ideology is portrayed by Zizek (1989) in his work ‘The Sublime Object of Ideology’. In line with this I use a definition of an ideology as a framework made up by set of nodal points, tenets, principles which when held together generate further consequences beyond their statement or articulation. Agreeing with these tenets puts you in a position of finding that you have subscribed to much more, and are unable to deny some argued consequence. This also runs parallel with Althusser’s (1994) definition of the joy of ideology as the pleasure, the non-critical tautology, in saying ‘yes, the way I see the world IS the world.’ From my reading of Foucault I would claim that he invests ‘discursive practices’ with the same meaning, particularly his sense that discursive formations operate so that the power is exerted, people are positioned and their actions defined. There is a compulsion, a necessity, it could not be other. In this sense we have no choice.
Much of Foucault’s work is focused on the construct of ‘normalisation’. He claims examination
There was a phrase ‘if I wasn’t watching her’. In the language of surveillance - As a teacher I have to watch people to make sure they’re doing things. Learning happens when you are watched.
Also is there an implication that if the teacher is occupied, if demands are made on her for the whole lesson, then the pupils learn more?
How do I have to act to be a teacher? What element of her peers’ actions made them occupy the position of teacher for her? The pupil could have seen herself as teacher as she was at the board. Her peers were sitting behind their desks in straight rows which was facing her and yet she still looked at the whole room as teachers.
They are teachers because they are seeing if something is right or wrong- an arbiter’s role. The teacher said, at one point, to a boy, Derek "Go on, tell her." There are 32 teachers because they can all tell you what you should be doing, what you should be writing.
The pupils’ perception could also be that ‘the teacher is there to help us’. In that particular clip the teacher did say ‘we’ll talk about it afterwards’. Otherwise her comments were of the form 'excellent, excellent', 'just one mistake’ etc. In a sense what the teacher was doing was directing. Is this guiding seen as helping them? Is this guiding seen as a legitimate role for a teacher?
Children can be very emotional about ‘teachers are there to help us’ and they get very angry when teachers do not help them.
But knowing what to teach is important. The pupils couldn’t teach it - they don’t know the key points to draw out, they don’t know how to guide.
In the video extract the class survey a pupil whilst the teacher surveys - what? the rest of the class ? the symbolic representation of knowledge appearing on the blackboard ? the integrity of the classroom scene ? If I take a theatrical metaphor then who is/are the audience, the actors, the chorus ? A pupil is ‘out at the front’ involved in some form of enactment that depends on some form of surveillance for its meaning. This enactment is observed and interpreted. There is arbitration and correction:- ‘32 teachers’, ‘outvoted’, ‘affirmative mutters’, ‘you have to have a good idea’, ‘just one little thing wrong’. This is a public performance of learning, something held up as an exemplar. Am I pushing this too far if I consider this theatre stage to be everywhere about teaching and nowhere about learning ? Can I ask where is and what is the learning that takes place ? In the wings ? Absent from the scene ? Waiting for a costume change?
It is not to awaken consciousness that we struggle but to sap power, to take power; it is an activity conducted alongside those who struggle for power, and not their illumination.’
There is also a tension - Foucault talks strongly about how actions are limited and controlled, whilst in the quotation above he moves to talk about how I can act with some autonomy and not be entirely caught in that controlled situation. Whilst I am a little uncertain about the exact nature of the move that I can make to work on this tension, I believe the strategy of working with newly devised terms and new conceptualisations will be empowering. My future researches and analysis of teachers’ descriptions of their practices aim to tell a previously untold and silenced story and to make me more aware of the workings of discourse practices in the generation of power and truth. This moves me towards being able to take more considered action in my classroom practice.
I would greatly welcome others’ responses to this article and to hear of others’ experiences of using such notions to research their own practice. I am at Tansy@kalliste.demon.co.uk
DFE:1995, Mathematics in the National Curriculum, HMSO, London
Dreyfus, Herbert &Rabinow, Paul: 1983, Michel Foucault: beyond structuralism and hermeneutics, University of Chicago, Chicago
Foucault, Michel: 1972a, The Archaeology of Knowledge , Alan Sheridan, trans. Pantheon, New York
Foucault, Michel & Deleuze, Gilles: 1972b, ‘Intellectuals and Power: A Conversation between Michel Foucault and Gilles Deleuze,’ in Language, Counter-Memory, Practice: Selected Essays and Interviews, 1977 trans. Bouchard & Simon, Cornell University Press, New York
Foucault, Michel: 1977, Discipline and Punish: The Birth of the Prison , Alan Sheridan, trans., Pantheon, New York
Foucault, Michel: 1989, Foucault live :(interviews, 1966-84) ed Sylvere Lotringer, Semiotext(e), New York
Gordon, Colin (ed) et al: 1980, Power/Knowledge: Selected interviews and other writing of Michel Foucault, 1972-1977, trans. 1980, Harvester Press, Brighton
McBride, Maggie: 1989, ‘A Foucaldian Analysis of Mathematical Discourse’, for the learning of mathematics 9,1 February
Rabinow, Paul (ed): 1991, The Foucault Reader, Peregrine, London
Zizek, Slavoj: 1989, The Sublime Object of Ideology, Verso, London