What Can We Learn From: Identity As It Relates Mathematics Learning

1
What Can We Learn From Identity As It Relates
Mathematics Learning?

• Gaye Williams
• Deakin University
• Education Burwood Campus
• gaye.williams_at_deakin.edu.au

2
Identity

• Participating practice
• (Cobb et al,in press)
• Or
• Stories we tell about ourselves that include
  stories others tell about us
• (Sfard Prussak, 2005)

3
Different Perspectives on Identity
Commonalities

• Human beings in action and mechanisms
  underlying human actions (Sfard Prusak, 2005,
  p. 14).
• Identity Man made and constantly created and
  recreated in interactions with people (Sfard
  Prusak, 2005, p. 14).

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Each Lens On Identity

• Has a present state
• And
• A state yet to be realised

5
Change in Identity

• Seen as closing the gap.

May be useful methodologically
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Participation in Practice Cobb, Gresalfi, Hodge
(in press)

• Identities that children develop in mathematics
  classrooms
• Cobb, P., Gresalfi, M., Hodge, L. (in press). A
  design research prspective on the ientities that
  sudents are dveloping in mthematics cassrooms. In
  B. Schwarz, T. Dreyfus R. Hershkowitz (Eds.),
  Transformations of knowledge in classroom
  interaction. Amsterdam Elsevier.

7
Participating in Practice

• Normative identity practices a competent student
  is considered to undertake in that classroom
• Personal identity How an individual participates
  in that classroom
• (they may resist, comply, or engage)

More than developing the language (Catherine
Beavis) can be developing argumentation
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Change in Identity

• Narrowing the gap between students own way of
  participating in the classroom and the ways a
  student seen as competent participates in that
  classroom

9

• Is this change in identity always productive?
• (The ways in which people perform in different
  context, Catherine Beavis)

10
Identity As Narative (Sfard Prusak)

• Constructs developed to study differences
  between the persistence of students who were
  recent immigrants from Russia and local Israeli
  students
• Sfard, A., Prusak, A. (2005). Telling
  identities In search of an analytical tool for
  investigating learning as a culturally shaped
  activity. Educational Researcher, 34(4), 14 - 22.

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Sfard Prusak (2005)

• Identity A set of reifying, significant,
  endorsable stories about a person.
• Learning closing the gap between actual and
  designated identity.

12
Identity Constructs

• Actual present perceived state of affairs
• Designated what is expected for some reason to
  be the state of affairs in the future
• (like projective identity, Catherine Beavis on
  Gee Seeing the virtual character as ones own
  project in the making)

13

• Present tense actual
• Future tense designated

14
Words That Are Taken Seriously and that Shape
Ones Actions

• Influence of the significance of the story teller
  to the subject

15
Usefulness of Identity as a Construct

• identity talk makes us able to cope with new
  situations in terms of our past experience and
  gives us tools to plan for the future (Sfard
  Prusak, 2005, p. 16)

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Linking These Ideas With My Research?

• Not all students are inclined to explore, some
  resist working with unfamiliar mathematical ideas
  (Williams, 2005). In terms of identity
  constructs
• They resist participating in the normative
  activity of inquiry classrooms (Cobb et al, in
  press).
• The stories they tell of themselves in the
  present tense do not include a capacity to
  explore unfamiliar ideas (Sfard Prusak, 2005).

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Not Inclining to Explore

• Wanting to remain within the confines of what is
  already known and achieve success through
  memorisation and repetition.

18
Linking Inclination to Explore with
Resilience/Optimism

• An optimistic child sees failures as
• temporary
• specific
• possibly influenced by some external factors.
• They see successes
• permanent
• pervasive
• personal
• Seligman, M. (with Reivich, K., Jaycox, L.,
  Gillham, J.). (1995). The Optimistic Child.
  Adelaide Griffin Press.

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Optimism (Seligman, 1995)

• Inclination to explore associated with
  orientation to successes and failures (Williams,
  2003).
• Optimistic students are inclined to step into
  unknown territory and explore new ideas because
  they see
• not knowing as temporary and
• able to be overcome through personal effort by
• looking into the situation to find what can be
  changed to increase chances for success.

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Optimism (cont)

• They see their successes as
• Permanent
• Pervasive
• Personal

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Pervasiveness as Key to Identity-Building /
Optimism-Building

• turning properties of actions into properties of
  actors (Sfard Prusak, 2005, p. 16, naratives)
• Building the pervasive nature of success through
  repeated successes in flow situations
  (Seligman, 1995)
• I am good at this, I can

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Optimism Building

• Flow
• State of high positive affect occurring when
  students set intellectual challenges and overcome
  them by developing new knowledge. (Developing
  themselves in new sports rather than familiar
  ones can produce conditions for flow Katherine
  Meldrum)
• Seligman found
• Optimism builds when students experience flow /
  gain pleasures associated with overcoming
  self-set challenges.
• Question
• Is it just wanting to replicate pleasure or is
  there a building of pervasiveness as well as
  described by Sfard Prusak?

• Csikszentmihalyi, M. (1992a). Introduction. In M.
  Csikszentmihalyi I. Csikszentmihalyi (Eds.),
  Optimal experience Psychological studies of flow
  in consciousness (pp. 3-14). New York Cambridge
  University Press.

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• This is an important area for future study.
• Not only in mathematics education but in all
  areas of education.
• What builds student ability to think for
  themselves rather than remain within the confines
  of what they have been taught?
• How can we build such capacity in school
  students, prospective teachers, and teachers?
• Gaye Williams
• gaye.williams_at_deakin.edu.au

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Dean Failure as Temporary

• 19. Int How do you learn something like that
  lesson?
• 20. Dean Um how do I learn it?
• 21. Int What helps you?
• 22. Dean Well I write it down
• 23. Int I see yeah soft
• 24. Dean in my book and then
• 25. Int yep
• 26. Dean when I got like when hes talking or
  something that I have already known or something
  then I just look over it again.
• 294. Dean Well when I first get a um sheet
  which Ive never done before then I um I get
  a bit stressed small laugh seems to be at self
  rather than anxiety
• 295. Int Oh okay.
• 296. Dean Cause I k- I- cause the first time um
  I do stuff um I always dont get it at
  first- it takes me like a little while- thats
  why I go over it and over it
• Key pause. text Researcher comment

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Dean Success as Permanent, and Personal

• 746. Dean Im going alright but um if like
  here like the teacher or somebody asks me a
  question I just remember what I have done like
  in my books and what Ive known and stuff like
  that and then I just put it all together and
  then work it out I guess yeah.
• Dean perceives his past experiences of looking
  in his books and thinking about what he knows
  will lead to him being able to answer more
  questions in the future (Success as Permanent and
  Personal).

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Dean Failure as Specific

• 451. Dean I always put I didnt know where
  the corners went in it like I did- I thought
  um- see when he told me you put the corners
  facing in
• 452. Int Yes?
• 453. Dean but I was- I was doing it all
  different- I was facing them out and up but
  the corner has to be facing in the middle
• 454. Int So when you had those little pieces of
  paper- you recognise the corners did you?
• 455. Dean Yeah thats why you rip em
  instead of cut em
• When he was not succeeding, Dean was able to
  look into the problem to identify what was
  causing problems.

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Success as Internal

• 506. Dean // No I thought it up- yeah I thought
  it up by myself