[Maths-Education] Socio-Mathematical Identity

[David H Kirshner]

Foo Keong,

I teach a course on mathematical enculturation/acculturation. 
I don't have a generally satisfactory theorization of identity to work
from, but I do have a way to connect mathematical culture to individual
agents, namely through the construct of dispositions: "Enculturation is
the process of acquiring cultural dispositions through enmeshment in a
cultural community. I interpret dispositions broadly as inclinations to
engage with people, problems, artifacts, or oneself in culturally
particular ways" (Kirshner, 2002, pp. 52-53). Collective dispositional
tendencies, thus, characterize a culture, even though they are embodied
at the level of the individual. 

Within a particular reference culture, one identifies valued
dispositions, and inculcation of particular dispositions can become a
pedagogical agenda:

"In mathematics education, the reference culture usually is presumed to
be mathematical culture, wherein a wide range of distinctive
dispositional characteristics has been identified as instructional
objectives. These include mathematical proof, the characteristic mode of
argumentation by which new knowledge is established for the community
through logical (rather than empirical) considerations (Lampert, 1990);
a single-minded tenacity in grappling with non-routine problems
(Schoenfeld, 1994), together with highly specialized heuristic
approaches to solving such problems (Polya, 1957); an aesthetic
appreciation of the "mathematically elegant" solution (Yackel & Cobb,
1996); a recognition of the instrumentality of notations and the
arbitrariness of definitions within axiomatic systems (Arcavi, 1994);
and a propensity for posing problems, rather than just solving them
(Brown & Walters, 1990). (See, also, Cuoco, Goldenberg, & Mark, 1995,
for a list of "habits of mind" specific to the various mathematical
subbranches.)" (Kirshner, 2004, p. 768).

The latter paper goes on to consider enculturation and acculturation as
social/psychological processes that can be tapped into as a basis for
pedagogy. Acculturation, as the volitional adoption of cultural
dispositions, does implicate cultural identity. 

David Kirshner

Kirshner, D. (2002). Untangling teachers' diverse aspirations for
student learning: A crossdisciplinary strategy for relating
psychological theory to pedagogical practice.  Journal for Research in
Mathematics Education, 33(1), 46-58.

Kirshner, D. (2004). Enculturation: The neglected learning metaphor in
mathematics education. In D. McDougall & J. A. Ross (Eds.), Proceedings
of the twenty-sixth annual meeting of the International Group for the
Psychology of Mathematics Education, North American Chapter (vol. 2, pp.
765-772), Toronto: OISE/UT.


-----Original Message-----
From: maths-education-bounces at lists.nottingham.ac.uk
[mailto:maths-education-bounces at lists.nottingham.ac.uk] On Behalf Of Ng
Foo Keong
Sent: Sunday, March 21, 2010 9:57 AM
To: maths-education at lists.nottingham.ac.uk
Subject: [Maths-Education] Socio-Mathematical Identity

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hi all,

i am doing a PhD study on "(Socio-) Mathematical Identity"
and i wonder if anybody has fully operationalised the
concept of Mathematical Identity.  [a person's identity with
respect to mathematical practices or how "mathematical"
one is]

i am generally following Anna Sfard's approach of defining
identity as a narrative, but i got shot down by my reviewers
because i have not shown in full detail what Mathematical
Identity really entails i.e. what are all the aspects/dimensions
of mathematical identity.

any help or pointers would be deeply appreciated.

Ng, FK
PhD student