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Keeping open the door to mathematically demanding F&HE programmes Julian Williams Pauline Davis Geoff Wake Laura Black Su Nicholson Graeme Hutcheson Maria Pampaka Paul Hernandez-Martinez Email: pauline.s.davis@manchester.ac.uk pauline.s.davis@manchester.ac.uk Website: www.lta.education.manchester.ac.uk/TLRP.html

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

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3 T & L Classroom culture Mathematical learner identity Programme institutional culture Technology Rules of assessment Problem solving Cultural Models Discourses

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4 Identity We build our identities (i) in practice and (ii) discursively using cultural models; We build our identities (i) in practice and (ii) discursively using cultural models; What models are there of ‘ways of being a mathematician/learner of mathematics?’ What models are there of ‘ways of being a mathematician/learner of mathematics?’ How can mathematics learner identity be mediated by mathematics classroom social practice? Can we expand the repertoire? How can mathematics learner identity be mediated by mathematics classroom social practice? Can we expand the repertoire?

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5 Classroom discourse/practice clip 1 ‘ Luna College ’

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6 Classroom Discourse/Practice clip 2 ‘Wind College’ (K and E)

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7 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 and ‘hidden’) of everyday teenage talk, indicating tensions between these opposing voices. This could be seen in the first clip. 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 and ‘hidden’) of everyday teenage talk, indicating tensions between these opposing voices. This could be seen in the first clip. 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 seamlessly; 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 seamlessly; The tenor (or voice) remains broadly the same. …crazy 20 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 connected but makes for a different kind of mathematics...crazy 20.

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8 K: Yeah, actually, usually I get along better with girls… you just sit and talk to them but I was on this table with two boys and I really made good friends with Jeff and Mike and then there’s other people that you just see in college and you talk to them about the lesson or stuff like that and cos we move around we’re always talking to different people, so it’s quite good, you always know the faces and stuff like that, were in other lessons you don’t even know them you don’t even know they’re in your lesson, so it’s really good. A: …more fun than just doing examples all the time and we have the whiteboards and like all the games that …the teacher.. makes us play and like… it’s just fun, rather than just textbooks and notebooks all the time, we have to do that as well… C: Yeah because you bring life into it. Say if you’re doing and you know what to do… then you can still have a conversation about your life and still do the work. It keeps the lesson interesting so you don’t fall asleep.

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9 KAnd like not only you think for yourself but like we can ask other people why they got that and it’s not just like black and white, like you get to a different way to work it out…element is a part of trying to make stats a bit more fun. (…) KAnd like not only you think for yourself but like we can ask other people why they got that and it’s not just like black and white, like you get to a different way to work it out…element is a part of trying to make stats a bit more fun. (…) J … it sounds daft but you’re having fun while you’re doing it cos you can sit and you can talk to people but… talk about the work but you can… it’s not a thing where you come down and sit in silence and you do it, you can talk to people and can, you know, do practical things J … it sounds daft but you’re having fun while you’re doing it cos you can sit and you can talk to people but… talk about the work but you can… it’s not a thing where you come down and sit in silence and you do it, you can talk to people and can, you know, do practical things

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10 ‘I like maths because its not a boring 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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11 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 identity...). 2. This is arguably an attempt to construct a new 'cultural model' of 'being a maths person/learner'. 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 why not" (and also it seems 'being accepted socially' might be an important factor in this). 4. There is evidence that the 'outside school' peer interaction is accepted in the classroom, possibly even encouraged. These interactional features (tenor etc) then facilitate mathematical interactions: that is, the theme/field of mathematics becomes an accepted part of the banter of peer talk. 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 identity...). 2. This is arguably an attempt to construct a new 'cultural model' of 'being a maths person/learner'. 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 why not" (and also it seems 'being accepted socially' might be an important factor in this). 4. There is evidence that the 'outside school' peer interaction is accepted in the classroom, possibly even encouraged. These interactional features (tenor etc) then facilitate mathematical interactions: that is, the theme/field of mathematics becomes an accepted part of the banter of peer talk. Hypothesis: 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 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. Hypothesis: 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 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.

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12 Theoretical contribution(s): 1. Cultural models of being a maths-person might be complex involving many links - as we said more like a narrative, and narratives may need to be constructible form the model... (compared with the simple models discussed by Holland & Quinn or Gee) 2. We are seeing the attempt to construct new models that challenge dominant cultural - paradigms Theoretical contribution(s): 1. Cultural models of being a maths-person might be complex involving many links - as we said more like a narrative, and narratives may need to be constructible form the model... (compared with the simple models discussed by Holland & Quinn or Gee) 2. We are seeing the attempt to construct new models that challenge dominant cultural - paradigms

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