1. ESRC Seminar Series Mathematical Relationships: Identities & Participation Seminar 6 The Socio-cultural Strand

2. Themes Identity & practice Tools Agency - structure

3. Identity & Practice Reciprocal relationship – identity is mediated by practice and vice versa ‘From a social practice perspective it is through cultural practices as people ‘do life’ that social identities are constructed (Nasir and Saxe, 2003).

4. Practice & Identity Jo Boaler – Railside Students Pedagogic practices – ‘relational equity’ –Commitment to the learning of others –Respect for other people’s ideas –Learned methods of communication and support Production of relational learner identities

5. A different kind of identity Interests/beliefs –Not instrumental or conceptual –Maths viewed as a language or form of communication Agency –Active learners –Wanting to communicate & express ideas motivated their action Authority –Relational notion of mathematical authority

6. Two connected ways of understanding identity Julian Williams & Pauline Davis –Identity in Practice – produced through transactions/participation in a practice – what we do –Self Identity – being a certain kind of person – who we are –Connection – ‘One becomes what one does’ – through reflexivity & social positioning

7. Julian Williams & Pauline Davis Sociable maths pedagogy – outside peer discourses used to facilitate mathematical interaction ‘never dis the calculator’ ‘crazy twenty’ Identity in Practice = maths is fun etc. They suggested this may be initial steps for students in identifying or accepting being a ‘maths person’ The learner’s experience of maths pedagogy is not just through their participation but also the way they interpret and act on their world (Edwards 2006).

8. Teachers do this too… Barbara’s Community of Inquiry Engagement, Imagination and Alignment In LCM, teachers and didacticians engage in practices in workshops and school settings and align themselves with existing or emerging practices related to the particular setting. Imagination contributes to emergence of new modes of practice. Seeing teaching mathematics as participation in the social practice of creating opportunity for mathematics learning We use inquiry as a tool, to promote inquiry as a way of being in practice

9. Agnes … in the beginning I struggled, had a bit of a problem with this because then I thought very much about you should come and tell us how we should run the mathematics teaching. This was how I thought, you are the great teachers …

10. … but now I see that my view has gradually changed because I see that you are participants in this as much as we are even though it is you that organise. Nevertheless I experience that you are participating and are just as interested as we are to solve the tasks on our level and find possibilities, find tasks, that may be appropriate for the pupils, and that I think is very nice. So I have changed my view during this time. (FG_060313. Translated from the Norwegian by Espen Daland)

11. Tools Tools are integral to shaping practices/activities which mediate identities (id in practice) Example – Birgit Pepin identified national differences in tasks/textbooks in England, France & Germany –Variations in context embeddedness (tasks which make connections with what students already know, ‘real life’) –cognitive demand/formal statements/generalisations- tasks which emphasise relational rather than procedural understanding, tasks which make connections with the underlying concepts being learnt; –mathematical representations- tasks which make connections within mathematics and across other subjects, tasks which connect different representations. Mathematical activities in textbooks are fundamental in shaping learner identities across cultures… Tasks shape what learners think about maths & how they feel about it..as well as what they do

12. Agency - Structure Learner is always positioned and is positioning themselves – agency & structure are always involved. How is this achieved/enacted? –Discourses/Cultural Models – Gee/Holland et al Drawing on Bakhtin both concepts emphasise how the ‘voice’ of the institution is there in the semiotic tools people use in their identity work – ‘speech without the speaker’

13. Dylan Wiliam on Assessment as an example Assessment creates categories which children are labelled & label themselves with They are ‘objects of history’ – culturally, historically and institutionally written – multi- voiced Yet using these categories involves sense making/interpretation which leaves space for agency Thus, students can potentially exercise agency within constraints/affordances that the assessment systems offer

14. Assessment – being positioned Sharon:I think I’ll get a two, only Stuart will get a six. I:So if Stuart gets a six what will that say about him? Sharon:He’s heading for a good job and a good life and it shows he’s not gonna be living on the streets and stuff like that. I:And if you get a level two what will that say about you? Sharon:Um, I might not have a good life in front of me and I might grow up and do something naughty or something like that.

15. Ability Grouping - Positioning JB:Do you like math? V:No, I hate it. JB:Why do you hate it? V:It's just too, I'm into the history, English (…) It's like too logical for me, it always has to be one answer, you can't get anything else BUT that answer. (Vicky, Lime school) B: I used to love math, but now I think, it's like I'm going to make sure that I don't major in math or anything because it's starting to be like too much competition, it's so weird. When it came to calculus and precalculus, I just kind of lost interest. It's like I'm going to do this for the points, I don't really care. I care more about science and English, stuff that makes sense to me where I think I'm learning morals and lessons from this, where I can apply it to something. (Betsy, Apple school)

16. To Conclude… Socio-cultural theory is about change & development…. It seems to me that if we’re trying to make changes to the way maths is viewed and related to – then we need to think about the issues at a number of levels: –The institution –The school –The teacher –The task & the environment –The learner