Keeping open the door to mathematically demanding F

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Keeping open the door to mathematically demanding
FHE programmes

• Laura Black
• Pauline Davis
• Paul Hernandez-Martinez
• Graeme Hutcheson
• Maria Pampaka
• Su Nicholson
• Geoff Wake
• Julian Williams

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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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Programme effectiveness
Classroom practices
Learner identities
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Jan 06
Preparation
Classroom practices
Programme effectiveness
Learner identities
March 06
Questionnaire design
Pilot case studies
Conferences
Sept 06
Oct 06
(i) initial interviews
(i) initial questionnaire
Case studies in UoM and traditional AS
Feb 07
(ii) interviews round 2
June 07
(ii) post test
June 07
(ii) follow-up interviews
Sept 07
(ii) delayed post test
Follow up case studies
Dec 07
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Outcomes

• Knowledge about how mathematics teaching and
  learning cultures can support better
  participation in mathematics
• Measurements of the effectiveness of two
  distinctive programmes of mathematics on learning
• Development of theories of learner identities in
  maths contexts

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Disposition to study more maths
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Disposition to enter HE
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Identity Questions

• What kind of maths learner identity are there?
• How are identities narrated? (Bruner, 1996)
• What resources/CMs do students use in their
  identity work?

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Cultural models

• Story-like chains of prototypical events that
  unfold in simplified worlds .. (including)
  metaphor (HQ,87)
• they allowing humans to master, remember and use
  knowledge requireed in everyday life
• Everyday theories' which are situated in social
  and cultural experiences and which inform action
  (behaviour). (Gee?)
• More?

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Examples

• Is the pope a bachelor? (Fillimore)
• US campus dating scene jocks bitches
  nerds etc (Holland Skinner)
• Coffee (Gee)

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CMs are

• Distributed threads
• cultural, Discourse, Ideal
• Elements that are used to construct/narrate ones
  self
• Fragmented
• In our model boundaries between classroom and
  storying of the self.

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Gemmas story

• Draws on some positive maths cultural models,
  but others that one might hope for do not seem to
  be available
• Cultural models can be ambivalent, i.e. used to
  tell opposite stories
• Models of maths learning may be influential but
  not necessarily leading the story

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Lees story

• Lee arrived in AS with stronger grades at GCSE
  but got dropped
• Claims maths is hard and boring
• He appears to have been marginal in his AS maths
  classes

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Some CMs evident in interviews

• Maths is hard but challenging versus maths is
  hard and dull
• Maths is black and white versus your own
• Maths is on your own versus learning with
  others/ sociable
• etc

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Does pedagogy make a difference?

• One notable contrast between Lee and Gemma the
  sociability of maths for them
• Might different pedagogies offer different CMs,
  or different positionings in relation to CMs?
• Over to Pauline

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Identity

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

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Classroom Discourse/Practice
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• We often 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.
• The micro data shows an alternative discourse
  where there is flip flopping between themes,
  maths and non-maths (every-day teenage) talk
• The tenor (or voice) remains broadly the
  same.crazy 20

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• Cultural models associated with this classroom
• Maths as negotiable, not black and white
• Maths as fun
• Maths as hands on/practical
• Maths as sociable

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• K And like not only you think for yourself but
  like we can ask other people why they got that
  and its not just like black and white, like you
  get to a different way to work it out.
• J it sounds daft but youre having fun while
  youre doing it cos you can sit and you can talk
  to people but talk about the work but you can
  its 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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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 its just fun, rather than just textbooks
and notebooks all the time Kso its quite good,
you always know the faces and stuff like that,
where in other lessons you dont even know them,
you dont even know theyre in your lesson, so
its really good.
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Ownership, understanding/conceptual, fun, joint
activity
No, it isnt just about having fun. I mean that
obviously, its part of it, because, just number
crunches on data can be sort of boring, cant it?
So, the fun element is a part of trying to make
stats a bit more fun. Its not my favourite topic
of maths, I have to confessBut I also think that
if you just write some numbers on the board and
put a couple of extreme values for example, then
well, whats the point of them? So theres an
understanding of why there are these sort of
extreme values, so even though its been you
saved yourself of data collectionAnd also I
think there is, its ownership as well, which I
think just makes it Yeah, OK we havent got the
full purpose, we havent got a comparison, I am
not going to do much work afterwards, but its
their data, theyve done something with them,
theyre finishing of byyou know make it look
nice and using it.
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• 1. The teacher wanted 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/alternative 'cultural model' of
  'being a maths person/learner'. youre a
  mathematician
• 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 dont 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 discourse
  is accepted in the classroom, possibly even
  encouraged. These interactional features (tenor
  etc) then facilitate mathematical interactions
  that is talking mathematics becomes an accepted
  part of the banter of peer talk (in the
  classroom).

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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.