The Discourse Strand:The Discourse Strand:Whose Mathematics?Whose Mathematics?Which Mathematics?Which Mathematics?

Suspend your belief in the innocence of words and the transparency of language as a window on an objectively graspable reality.

Maggie Maclure (2003)

Morwenna reminded us of Morwenna reminded us of this quotethis quote

Major themes in this strandMajor themes in this strand

The discourse of mathematics itselfThe discourse of mathematics itself Construction of mathematics as a subject Construction of mathematics as a subject Subject positioningsSubject positionings

These all deal with issues of power and These all deal with issues of power and controlcontrol

Suppose you had a garden this shape and you were in a helicopter right above your garden looking down on it.

Which of the following shapes would be like yours?

Steve Lerman – using Bernstein Steve Lerman – using Bernstein to understand power and to understand power and control in pedagogycontrol in pedagogy

Typical incorrect answersTypical incorrect answers

Robyn: Why did you take that shape [the square]?Girl: Because it looks like the shape of my

garden.R: Is your garden at home like that?Girl: Yes.

Boy: None of those.R: Why aren’t any of them the same?Boy: My garden goes like that [draws a semi-

circle in the air].”

The production and The production and reproduction of disadvantagereproduction of disadvantage

Forms of control Forms of control (invisible/visible pedagogy)(invisible/visible pedagogy)

Schools are middle class by Schools are middle class by definition: disadvantage definition: disadvantage reproducedreproduced

Language: elaborated and Language: elaborated and restricted codes restricted codes

Principle of Principle of recontextualisation – play of recontextualisation – play of ideology ideology

The shopping sum – The shopping sum – ‘You have 10p, ‘You have 10p, a yacht costs 2p, how much change a yacht costs 2p, how much change do you have?’do you have?’ - illustrates the issue - illustrates the issue

But there are limits to But there are limits to Bernstein’s analysisBernstein’s analysis

Identities are multiple and Identities are multiple and overlapping in discourses, overlapping in discourses, and his analysis helps us and his analysis helps us analyse pedagogic analyse pedagogic discourses, not others. For discourses, not others. For students in the classroom, students in the classroom, how they appear to their how they appear to their peers, which behaviours will peers, which behaviours will gain acceptance from gain acceptance from important others, important others, techniques to avoid being techniques to avoid being noticed by the teacher, noticed by the teacher, issues associated with race, issues associated with race, gender, ethnicity, sexuality, gender, ethnicity, sexuality, and so on are much more and so on are much more important than engaging in important than engaging in the pedagogic discourse.the pedagogic discourse.

Tom on the curriculum: an Tom on the curriculum: an analysis of textbooksanalysis of textbooks

Are learners able to see Are learners able to see selfself or their or their interestsinterests represented within the text book? represented within the text book?

Broad political categories: gender, race, social class, sexuality, special needs – Broad political categories: gender, race, social class, sexuality, special needs – for example:for example:

– Do they favour boys rather than girls? Do they favour boys rather than girls? – How stereotypical are they? How stereotypical are they? – Is the textbook gender neutral? Is the textbook gender neutral? – Are there appropriate male and female role models?Are there appropriate male and female role models? – What careers/ occupations are represented?What careers/ occupations are represented?

Other self-identifications related to inclusion or exclusion: cool, nerdy, logical, Other self-identifications related to inclusion or exclusion: cool, nerdy, logical, expressive, creative, cleverexpressive, creative, clever

Text Text – Spacing & styleSpacing & style– Colour/ B&WColour/ B&W– LanguageLanguage

ImagesImages– Cartoon charactersCartoon characters– Clip ArtClip Art– Photographs of real people/ artefactsPhotographs of real people/ artefacts

The art teacher:Logical. Logical thinkers, perhaps absolutist. The technology teacher:Me because I have an engineering backgroundPeople who want to understand more about

the world around them. [There is] mathematics for thinkers and

mathematics for doers.Vocational maths I suppose would be

engineering.

Morwenna’s interviews:Morwenna’s interviews:Constructions of mathematics - Constructions of mathematics - people who can do it are…..people who can do it are…..

Construction of mathematics Construction of mathematics as a subject: Heather on as a subject: Heather on “maths is hard!”“maths is hard!”

MATHS IS HARD!Independent research shows that Mathematics is the most

challenging subject at A-level. Nationally, last year's AS results in maths were far worse than any other subject.

If you don't really enjoy Maths and if you're not genuinely good at it, don't do it! Two years of struggling and constantly being 'stuck'

is not an experience we would wish on anyone.Success at A-level Mathematics usually depends on:

Positive attitudes. Do you enjoy solving problems? Do you like Maths?

Persistence. Do you give up easily and ask for help? Or do you prefer to get the answer for yourself?

Independence. Do you need spoon-feeding every step of the way? Can you learn it by yourself?

Heather: ‘maths is hard’ relies Heather: ‘maths is hard’ relies on various discourseson various discourses

hard vs. easy subjects… knowledge is separable knowledge is separable

into different subjects that into different subjects that have stable identities and have stable identities and that can be arranged in a that can be arranged in a hierarchyhierarchy

values and ideas of what values and ideas of what knowledge is hardest, best, knowledge is hardest, best, purest, most rational…purest, most rational…

slippage into discourses slippage into discourses around masculinity and around masculinity and sexuality, hard has sexuality, hard has unspoken opposites – unspoken opposites – easy, soft and yielding…easy, soft and yielding…

Candia on subject positioning in Candia on subject positioning in official discourse: the QCA official discourse: the QCA exampleexample

Once the teacher has established what the pupil is to achieve and how the pupil can achieve it, the pupil is in a position to guide their own learning. The pupil can seek help from suitable sources such as books, other learners and the teacher. When they know what they are trying to accomplish they can forge ahead without reference to the teacher if that is appropriate. This frees the teacher to provide help where it is really needed. When pupils take responsibility in this way their performance standards can rise across the board. It is true that some pupils will resist this, wanting to blame the teacher rather than themselves for their lack of learning, but such methods are surprisingly successful if persisted with.

QCA (2003) Using assessment to raise achievement in mathematics at key stages 1, 2 and 3

Construction of ‘truths’ about Construction of ‘truths’ about the learner and the teacherthe learner and the teacher

Resisting pupils…Resisting pupils…– Are deviantAre deviant– Do not learnDo not learn– Are to blame for their lack of learningAre to blame for their lack of learning– Falsely blame teachersFalsely blame teachers– Will not succeed in their devianceWill not succeed in their deviance

Teachers…Teachers…– Are not to blame for pupils’ lack of learning - if they use Are not to blame for pupils’ lack of learning - if they use

the approved methodsthe approved methods

Tansy: construction of the Tansy: construction of the primary teacher - confidence primary teacher - confidence and competenceand competence

What was done What was done well in Number:- well in Number:- pupils are pupils are becoming more becoming more confident at confident at solving problems solving problems involving missing involving missing numbers. (QCA numbers. (QCA 2004)2004)

Discourse (including language, texts and practices) is seen as the resource through which we come to know ‘what we think we know about’ (Lather, 1991, 2004)

Neoliberalism, choice and Neoliberalism, choice and mathematics education – mathematics education – Valerie WalkerdineValerie Walkerdine

Nikolas Rose: in advanced liberalism we are Nikolas Rose: in advanced liberalism we are compelledcompelled to be free - consumption brings the to be free - consumption brings the idea of freedom of choice – how is this played out idea of freedom of choice – how is this played out in education?in education?

Choice (for instance when shopping) is a product Choice (for instance when shopping) is a product of a complex set of relationships that are not of a complex set of relationships that are not necessarily mathematical necessarily mathematical

These practices produce us as self- regulating These practices produce us as self- regulating and self-managing choosing subjects but the and self-managing choosing subjects but the practices which produce that possibility and the practices which produce that possibility and the discursive positions we can take up become discursive positions we can take up become obscuredobscured

How ‘choice’ might obscure How ‘choice’ might obscure lacklack of choice of choice

The last wordThe last word

So then the choosing subject is equally So then the choosing subject is equally both a fiction in Foucault’s sense, both a fiction in Foucault’s sense, produced through self management in produced through self management in Rose’s but also routinely assembled in Rose’s but also routinely assembled in relational dynamics, which involve relational dynamics, which involve fantasy positions (the winner, the rich fantasy positions (the winner, the rich shopper, the perfect mum) which are shopper, the perfect mum) which are created in the social relations of everyday created in the social relations of everyday practicespractices