Keeping open the door to Keeping open the door to mathematically demanding F&HE mathematically demanding F&HE

programmesprogrammesJulian WilliamsJulian Williams

Pauline DavisPauline Davis

Geoff WakeGeoff Wake

Laura BlackLaura Black

Su NicholsonSu Nicholson

Graeme HutchesonGraeme Hutcheson

Maria PampakaMaria Pampaka

Paul Hernandez-MartinezPaul Hernandez-Martinez

Email: Email: pauline.s.davis@manchester.ac.ukpauline.s.davis@manchester.ac.ukWebsite: www.lta.education.manchester.ac.uk/TLRP.htmlWebsite: www.lta.education.manchester.ac.uk/TLRP.html

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AimAim

We aim to understand how We aim to understand how cultures of learning and cultures of learning and teaching teaching can support learners in ways that help widen can support learners in ways that help widen and extend participation in mathematically demanding and extend participation in mathematically demanding courses in F & HE.courses in F & HE.

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T & L

Classroom culture

Mathematical

learner identity

Programme

institutional culture

Technology

Rules of

assessment

Problem solving

Cultural

Models

Discourses

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IdentityIdentity

We build our identities (i) in practice and (ii) We build our identities (i) in practice and (ii) discursively using cultural models;discursively using cultural models;

What models are there of ‘ways of being a What models are there of ‘ways of being a mathematician/learner of mathematics?’mathematician/learner of mathematics?’

How can mathematics learner identity be mediated How can mathematics learner identity be mediated by mathematics classroom social practice?by mathematics classroom social practice? Can we Can we expand the repertoire?expand the repertoire?

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Classroom discourse/practice clip 1Classroom discourse/practice clip 1

‘‘Luna CollegeLuna College’’

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Classroom Discourse/Practice clip 2Classroom Discourse/Practice clip 2

‘‘Wind College’ (K and E)Wind College’ (K and E)

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Typically, we find student identities are double-discoursed in a genre adopting Typically, we find student identities are double-discoursed in a genre adopting a dual register, one of student and the other (sometimes more quietly spoken a dual register, one of student and the other (sometimes more quietly spoken and ‘hidden’) of everyday teenage talk, indicating tensions between these and ‘hidden’) of everyday teenage talk, indicating tensions between these opposing voices. This could be seen in the first clip.opposing voices. This could be seen in the first clip.

The micro data shows a flip flopping between maths and non-maths (every-The micro data shows a flip flopping between maths and non-maths (every-day teenage) talk; its not that the code flip-flops, but the theme flip-flops day teenage) talk; its not that the code flip-flops, but the theme flip-flops seamlessly;seamlessly;The tenor (or voice) remains broadly the same.The tenor (or voice) remains broadly the same.…crazy 20…crazy 20

This links strongly with literature that says bring the culture of the community into This links strongly with literature that says bring the culture of the community into

the classroom, but we could argue that is not just to make students feel the classroom, but we could argue that is not just to make students feel connected but makes for a different kind of mathematics...crazy 20.connected but makes for a different kind of mathematics...crazy 20.

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K: K: Yeah, actually, usually I get along better with girls… Yeah, actually, usually I get along better with girls… you just sit and talk to them but I was on this table you just sit and talk to them but I was on this table with two boys and I really made good friends with Jeff with two boys and I really made good friends with Jeff and Mike and then there’s other people that you just and Mike and then there’s other people that you just see in college and you talk to them about the lesson or see in college and you talk to them about the lesson or stuff like that and cos we move around we’re always stuff like that and cos we move around we’re always talking to different people, so it’s quite good, you talking to different people, so it’s quite good, you always know the faces and stuff like that, were in other always know the faces and stuff like that, were in other lessons you don’t even know them you don’t even know lessons you don’t even know them you don’t even know they’re in your lesson, so it’s really good. they’re in your lesson, so it’s really good.

A: …A: …more funmore fun than than just doing examples all the time just doing examples all the time and we have the whiteboards and like all the games and we have the whiteboards and like all the games that …the teacher.. makes us play and like… it’s just that …the teacher.. makes us play and like… it’s just fun, rather than just textbooks and notebooks all the fun, rather than just textbooks and notebooks all the time, we have to do that as well…time, we have to do that as well…

C: C: Yeah because you bring life into it. Say if you’re Yeah because you bring life into it. Say if you’re doing and you know what to do… then you can still doing and you know what to do… then you can still have a conversation about your life and still do the have a conversation about your life and still do the work. It keeps the lesson interesting so you don’t fall work. It keeps the lesson interesting so you don’t fall asleep.asleep.

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KK And like not only you think for yourself but like And like not only you think for yourself but like we can ask other people why they got that and it’s we can ask other people why they got that and it’s not just like black and whitenot just like black and white, like you , like you get to a get to a different way to work it out…elementdifferent way to work it out…element is a part of is a part of trying to make stats a bit more fun. (…) trying to make stats a bit more fun. (…)

J J … it sounds daft but … it sounds daft but you’re having fun you’re having fun while you’re doing itwhile you’re doing it cos you can sit and you can cos you can sit and you can talk to people but… talk about the work but you talk to people but… talk about the work but you can… it’s not a thing where you come down and sit can… it’s not a thing where you come down and sit in silence and you do it, in silence and you do it, you can talk to people you can talk to people and can, you know, do practical thingsand can, you know, do practical things

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‘‘I like maths because its not a boring I like maths because its not a boring lesson, not like a chore going in to it.’lesson, not like a chore going in to it.’ No, it isn’t just about having fun. I mean that

obviously, it’s part of it, because, just number crunches on data can be sort of boring, can’t it? So, the fun element is a part of trying to make stats a bit more fun. It’s not my favourite topic of maths, I have to confess…But I also think that if you just write some numbers on the board and put a couple of extreme values for example, then well, what’s the point of them? [ ] So there’s an understanding of why there are these sort of extreme values, so even though it’s been …you saved yourself of data collection…And also I think there is, it’s ownership as well, which I think just makes it… ‘Yeah, OK we haven’t got the full purpose, we haven’t got a comparison, I am not going to do much work afterwards, but it’s their data, they’ve done something with them, they’re finishing of by…you know make it look nice… and using it.

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1. It seems there are some signs that ‘the teacher’ wants to construct a 'sociable' 1. It seems there are some signs that ‘the teacher’ wants to construct a 'sociable' pedagogy, and part of this involves accepting 'where the kids are coming from' (her pedagogy, and part of this involves accepting 'where the kids are coming from' (her identity ...).identity ...).

2. This is arguably an attempt to construct a new 'cultural model' of 'being a maths 2. This is arguably an attempt to construct a new 'cultural model' of 'being a maths person/learner'.person/learner'.

3. There is data from the students interviews that suggests they at least in part buy 3. There is data from the students interviews that suggests they at least in part buy into this; they like maths and when thinking of going to university maths "I don’t see into this; they like maths and when thinking of going to university maths "I don’t see why not" (and also it seems 'being accepted socially' might be an important factor in why not" (and also it seems 'being accepted socially' might be an important factor in this).this).

4. There is evidence that the 'outside school' peer interaction is accepted in the 4. There is evidence that the 'outside school' peer interaction is accepted in the classroom, possibly even encouraged. These interactional features (tenor etc) then classroom, possibly even encouraged. These interactional features (tenor etc) then facilitate mathematical interactions: that is, the theme/field of mathematics becomes facilitate mathematical interactions: that is, the theme/field of mathematics becomes an accepted part of the banter of peer talk.an accepted part of the banter of peer talk.

Hypothesis:Hypothesis: This acceptance of mathematics into the peer discourse/sociality of This acceptance of mathematics into the peer discourse/sociality of the students may be the first sign in a chain of acceptance of a 'mathematical the students may be the first sign in a chain of acceptance of a 'mathematical identity'. In other words, the discourse is a sign that, perhaps, they are accepting identity'. In other words, the discourse is a sign that, perhaps, they are accepting "being a maths-person" as part of their self/identity ... themselves."being a maths-person" as part of their self/identity ... themselves.

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Theoretical contribution(s):Theoretical contribution(s):

1. Cultural models of being a maths-person might 1. Cultural models of being a maths-person might be complex involving many links - as we said more be complex involving many links - as we said more like a narrative, and narratives may need to be like a narrative, and narratives may need to be constructible form the model ... (compared with the constructible form the model ... (compared with the simple models discussed by Holland & Quinn or simple models discussed by Holland & Quinn or Gee)Gee)

2. We are seeing the attempt to construct new 2. We are seeing the attempt to construct new models that challenge dominant cultural - models that challenge dominant cultural - paradigmsparadigms