Tales of power: Foucault in the mathematics classroom

Tansy Hardy

Sheffield Hallam University

 

Abstract

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,

‘You can see the enormous ability spread in this class. The difficulty is the books. They are supposed to be a set 2 so we use these red books - but some really need the examples and reinforcements that are in the green books. Some need extra support to work on even the basic examples in the red books. How am I supposed to teach them as a class? I’m finding it so difficult.’ Incidents such as this have caught my attention and generated an interest in how teachers talk about what empowers them or limits them; an interest in what they say is controlling or disempowering or enabling in their professional lives. In particular I have become interested in the power relation between mathematics teachers and the descriptions of mathematics teaching and the school mathematics curriculum that seem to abound in current documentation and guidance. My intention here is to develop an account of how that power relation works.

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.

 

 

Theoretical Tools

 

Power IS the relation

I start by investigating Foucault's (1972a ) statement that ‘Power is in the relation. It is not exercised in a repressive sense from outside the individual’ Foucault starts from the premise that, primarily, knowledge and power work through the language; that as we learn to speak we pick up the basic knowledge and rules of our culture at the same time. He extends this to see that all human sciences define human beings at the same time as they describe them, and that these organised forms of knowledge working together with their associated institutions, have significant effects on people ( particularly in terms of positioning them and determining their possible actions ). He talks about this in a variety of places and in various ways; relating specifically to power he writes:

 

‘Individuals are the vehicles of power, not its points of application.’
Foucault in Gordon (1980)
 

‘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’

Foucault in Dreyfus and Rabinow (1983 p217/220)
 Foucault makes a powerful shift here away from individualistic ways of viewing power to a notion of power that is not outside of an individual or invested in one individual to exert over another. Here power is in/of the relation between people and of the institutions that they work in. It is this sense of power that I argue can be appropriately applied to my context as a member of the mathematics education community and can offer a fresh view of our environment. But I am aware that it is powerful but not an easy shift for me (or other educationalists ) to make.

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.

 
 

Power is productive.

For Foucault power is internally contradictory. It oppresses and enables.
  ‘If power were never anything but repressive, if it never did anything but to say no, do you really think one would be brought to obey it? What makes power hold good, what makes it accepted, is simply that fact that it doesn’t only weigh on us as a force that says no, but that it traverses and produces things, it induces pleasures, forms, knowledge; it produces discourse. It needs to be considered as a productive network which runs through the whole social body, much more than as a negative instance whose function is repressive.’
Foucault in Rabinow (1990)
 Referring back to Foucault's words in Dreyfus and Rabinow (1983 ), the exercising 'of power consists of guiding the possible conduct, putting in order the possible outcome'. This introduces the notion that when power is circulating it determines, to some extent, what are possible ways of acting and limits in some way what can be done and enables one to act. The productive and determining effects of power are important for my analysis. To use this appropriately I need to remain aware that I might tend to look for the inhibitory nature and limiting effects of power and that this might lead me to a skewed and incomplete account.

 

Discursive practices

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

 

‘a body of anonymous, historical rules, always determined in the time and space that have defined a given period’.

‘There is no knowledge without a particular discursive practice and any discursive forms’

Foucault (1970, p117, p183)
 A discursive practice is constituted by the actions of the members, their interactions with each other and the texts and communications and artefacts from within that practice and Foucault argues that these discursive practices have profoundly shaped the structure of our society.

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.

 

What might be my research task ?

 

Power conceals itself

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

 

‘In fact as in Nietzsche’s critique of morality, he (Foucault) would say that the mere pretence to operate on a realm free of power relations is perhaps the most cunning and sinister play of power there could be, which masks itself behind a benign facade of liberal (Christian) generosity, a mode of domination specific to the period of modernity.’ In his work looking at medicine for example Foucault was not interested in what characteristics (personal characteristics) doctors had. He was interested in the role that those who practised medicine must follow to maintain their position and be seen as doctors. In the same way, an appropriate classroom research strategy would be to look at what roles, what ways of talking, what ways of behaving the teacher, the pupils, the text, the activity must take in order to be able to stand in that position.

 
 

Revealing the Power

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 –

and (You may want to read this transcript with these questions in mind and see whether you recognise in the discussion that follows the themes that took our attention in that session.

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

Teacher: Excellent

Pupil A: Your hypotenuse is always opposite the right angle

Teacher: Excellent

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

Derek: no...

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.

(Extracts from the (transcribed) discussion are formatted and inset like this)

 

Maths as right or wrong

‘The nature of the mathematics contained in the video clip is one where there’s a right answer and a wrong answer and we might say from what the teacher was writing on the board at the end, there was one correct method as well. That isn't how mathematics has to be seen. It is just one formulation of mathematics. The teacher said that there is just one thing wrong with it

- it deviated just a tiny bit from ‘the right way’.

That adds emphasis to there only being one way to do it.’

 This draws our attention to the constituting nature of discursive practices. As McBride (1989) says,‘(Mathematics) needs to be understood as a constructed discourse that, with its rules and practices, effects our concept of truth, accepted methods of learning, and many attitudes within the classroom’

 

Handling the questions

‘The teacher said it’s difficult to answer (unpredictable) questions. We could ask ‘What questions?’ To me there were none asked in the extract. Nor were the pupils faced with any questions.

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?

 

Pathologising the pupil

The phrase ‘(questions that) people had difficulty with’ came up in the video. This can be seen to refer to a common-sense and obvious notion that some pupils do ‘have difficulties with’ their homework. This positions the pupil as the one who has difficulties.

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?

 

Ideology and discursive practices

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.

 

The intended audience (for the programme from which this video extract was drawn) may not have been teachers or researchers but a wider audience of television. The message of the piece could be summaries as ‘traditional teaching is best’. Traditional teaching here is signified by the teacher’s and the pupils’ roles, signified by the fact the pupil is using chalk on blackboard, signifying by the use of Pythagoras as an example of mathematics being done. The teacher’s commentary and the pupil’s commentary act to support that particular message. The teacher’s teaching and pupils’ learning are part of an exemplification of a traditional mode of teaching. Earlier in the video the project leader described the class scene as an example of whole class interactive teaching. That expression and others like ‘going back to traditional methods’ are currently heard in the discursive practice within our society. The curriculum project leader’s use of thes,e allow him to occupy the position of technical expert. He is constructed (by the media, by the discourse) as someone who knows something about these issues. Not because of what he knows but because of what he says and how he says it.

 

Surveillance

Much of Foucault’s work is focused on the construct of ‘normalisation’. He claims examination

 

‘is a normalising gaze, a surveillance that makes it possible to quantify, to classify and to punish. It establishes over individuals a visibility through which one differentiates them and judges them’
Foucault (1977)
 

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?

 

32 teachers

One of the pupils said that there are 32 teachers.

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.

..Or/and...

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.

 The process of ‘normalisation’ is the mechanism that categorises people into normal and abnormal (Foucault 1977). Linking the notions of normalisation and power as a productive network allows us to see the process that determines what is considered to be knowledge in the classroom and how that knowledge can be expressed and by whom. It is the process of normalisation that determines who is included and who is excluded in this discourse. Those who conform to these roles are likely to have their voices heard.

 

‘Discursive practices are characterised by the interplay of these rules that typically are not written out; nor can people usually articulate them. Rules determine the possibilities and limitations for the content of a discourse. They determine the conditions under which discourse is used, who can speak, how individuals must speak or write, and who speaks the ‘truth’. Rules also determine what can and cannot be talked about. Another group of rules has to do with the form that theories must take in order to be seen by people as truth within any discourse. These rules determine the vocabulary that must be used in stating the truth. Even the arrangement of statements follow these rules.’
McBride (1989)
 

More on teachers’ role: what teachers do

We should be careful not to generalise and say that telling someone something or leading someone through something is in itself wrong or bad teaching. And, it is interesting to here see how the pupils view it.

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.

 I dwelt a little longer for myself on the theme of ‘32 teachers’ because it points to enabling and silencing characteristics of power that are of particular interest to me. At this stage this produces mostly (more) questions. My future work will need to recast what I do as a teacher when I try to enable my pupils to speak, try to allow questions and comments and to bring out in the open children’s’ own ideas, and in this forum enable them to be mathematical. This will involve a search for new terms and descriptions. I am caught by pre-existing ones: they are never neutral.

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?

 
 

Where does all this get me?

Each society has its regime of truth, its ‘general politics’ of truth: that is, the types of discourse which it accepts and makes function as true.....The problem is not changing people’s consciousness - or what’s in their heads - but the political, economic, institutional regime of the production of truth. It’s not a matter of emancipating truth from every system of power (which would be a chimera, for truth is already power), but of detaching the power of truth from the forms of hegemony, social, economic, and cultural, within which it operates at the present time
Foucault in Rabinow (1991)
 

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.’

Foucault and Deleuze (1972 p208)
 I said that I intended ‘a struggle aimed at revealing and undermining power where it is most invisible and insidious’ (Foucault, Deleuze (1972). Have I revealed that power? I think through discussion of a range of power themes related to the video extract that I have at least started. More importantly, I have identified some tasks to engage in as part of that struggle. I have identified some areas that will reveal the discursive practice(s) of mathematics education and the ways this positions people within the classroom, limiting their actions and determining what each has to say to be heard.

 

‘The work of an intellectual is not to mold the political will of others; it is, to re-examine evidence and assumptions, to shake up habitual ways of working and thinking, to dissipate conventional familiarities, to re-evaluate rules and institutions and starting from this re-problematization ...to participate in the formation of a political will
Foucault (1989)
 The formation of a political will involves enabling people to act in society. There is a need, as Foucault shows, to identify tasks and questions that work ‘to sap power’ and so enable me to act. He does indicate to me that such re-problematisation is hard but imperative. Our discussions around the video extract point to important, and I would argue, not easy steps I can take to reproblematise aspects such as teachers’ role. I admit that it is challenging to articulate these tasks in practical terms

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

 
 

Bibliography and References

Althusser, Louis: 1994, ‘Ideology and Ideological State Apparatuses’ in The Spectre of Ideology Zizek, Slavoj (ed), Verso, London

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