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

2. 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 this quote

3. Major themes in this strand n The discourse of mathematics itself n Construction of mathematics as a subject n Subject positionings n These all deal with issues of power and control

4. 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 to understand power and control in pedagogy

5. Typical 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 arent any of them the same? Boy: My garden goes like that [draws a semi- circle in the air].

6. The production and reproduction of disadvantage n Forms of control (invisible/visible pedagogy) n Schools are middle class by definition: disadvantage reproduced n Language: elaborated and restricted codes n Principle of recontextualisation – play of ideology

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

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

9. Tom on the curriculum: an analysis of textbooks n Are learners able to see self or their interests represented within the text book? n Broad political categories: gender, race, social class, sexuality, special needs – for example: –Do they favour boys rather than girls? –How stereotypical are they? –Is the textbook gender neutral? –Are there appropriate male and female role models? –What careers/ occupations are represented? n Other self-identifications related to inclusion or exclusion: cool, nerdy, logical, expressive, creative, clever n Text –Spacing & style –Colour/ B&W –Language n Images –Cartoon characters –Clip Art –Photographs of real people/ artefacts

10. The art teacher: Logical. Logical thinkers, perhaps absolutist. The technology teacher: Me because I have an engineering background People 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. Morwennas interviews: Constructions of mathematics - people who can do it are…..

11. Construction of mathematics as a subject: Heather on 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?

12. Heather: maths is hard relies on various discourses n n hard vs. easy subjects… n knowledge is separable into different subjects that have stable identities and that can be arranged in a hierarchy n values and ideas of what knowledge is hardest, best, purest, most rational… n slippage into discourses around masculinity and sexuality, hard has unspoken opposites – easy, soft and yielding…

13. Candia on subject positioning in official discourse: the QCA example 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

14. Construction of truths about the learner and the teacher n Resisting pupils… –Are deviant –Do not learn –Are to blame for their lack of learning –Falsely blame teachers –Will not succeed in their deviance n Teachers… –Are not to blame for pupils lack of learning - if they use the approved methods

15. Tansy: construction of the primary teacher - confidence and competence What was done well in Number:- pupils are becoming more confident at solving problems involving missing numbers. (QCA 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)

16. Neoliberalism, choice and mathematics education – Valerie Walkerdine n Nikolas Rose: in advanced liberalism we are compelled to be free - consumption brings the idea of freedom of choice – how is this played out in education? n Choice (for instance when shopping) is a product of a complex set of relationships that are not necessarily mathematical n These practices produce us as self- regulating and self-managing choosing subjects but the practices which produce that possibility and the discursive positions we can take up become obscured

17. How choice might obscure lack of choice

18. The last word So then the choosing subject is equally both a fiction in Foucaults sense, produced through self management in Roses but also routinely assembled in relational dynamics, which involve fantasy positions (the winner, the rich shopper, the perfect mum) which are created in the social relations of everyday practices