Torquetum

 

Identity is a term thrown around a lot in educational and other literature. Sfard and Prusak felt that a definition of identity that is operational is needed if it is to be useful. First and foremost, they define identity as stories about people. The notion of identity differs from other terms such as character, nature and personality in that it is not as “tainted” with undertones of biological determinism and as such is better suited to research located in a sociocultural context. 

 

“[I]n particular, identity features prominently whenever one addresses the question of how collective discourses shape personal worlds and how individual voices combine into the voice of a community” (p. 15) [so group to individual and individual to group] and “the question of the mechanisms through which the collective and the common enter individual activities also lies at the center of educational research on learning” (p. 15). It is known that culture shapes learning. There is a “complex dialectic” between learning and its sociocultural context and identity seems tailor-made to bridge the gap. However, identity can only be really useful if it has an operational definition. The authors says “it is the activity of identifying rather than its end product that is of interest to the researcher”, whose focus is not on identity so much as the “complex dialectic between identity-building and other human activities” (p. 17). 

 

But why not beliefs or attitudes as the bridge between learning and sociocultural context? Beliefs are tricksy things as they imply an existence which is discourse-independent yet how is an analyst to perceive and objectively identify them? Attitudes are similarly tricksy. 

 

Sfard and Prusak refer to Blumer’s test of admissibility, which is something I have not read the original of and probably should seek out. For a concept to be applicable in research it has to meet 3 conditions: we have to know what to look at in order to pinpoint the concept, we need to know how to identify things which are not the concept, and it needs to “enable accumulation of knowledge” (p. 15). Beliefs and attitudes don’t meet these criteria and, in fact, identity is at similar risk unless an operational definition can be found. The authors criticise others’ usage of the word identity without an explanation of what it is or how to use it, however they like Gee and other’s use of the term or idea of narrativisation, of people telling stories about who they are. The flaw they find in this is the postulation of there being some sort of internal thing about which you are telling stories. They call this an “essentialist vision” of identity and consider the notion of identity being something that is extra-discursive and independent of action to be both untenable (it gives us no idea of what to look for) and potentially harmful (descriptors can become self-fulfilling). 

 

Instead of beliefs or attitudes, Sfard and Prusak support the use of identity as a descriptive tool. They provide a collection of definitions which operationalise identity. 

Identity: “we suggest that identities may be defined as collections of stories about persons or, more specifically, as those narratives about individuals that are reifying, endorsable and significant” (p. 16) 

Reifying: the use of verbs such as be, have or can (rather than do) and with the adverbs always, never, usually, etc. that stress repetitiveness of the action. 

Endorsable: the “identity-builder” would agree that the story “faithfully reflects the state of affairs in the world” 

Significant: any change in the story is likely to affect the storyteller’s feelings towards the identified person. Often the most significant stories are those about inclusion in or exclusion from a community. 

 

Actual identity: stories about the actual state of affairs; present tense; formulated as fact 

Designated identity: stories about a state of affairs expected to be the case in the future, having the potential to become part of one’s identity; future tense, or expressed in words evoking obligation, commitment, necessity, wish; not necessarily desired, but always binding; sometimes the person is not aware that there are alternatives; the most important source is narratives authored by others; 

Critical stories: “those core elements that, if changed, would make one feel as if one’s whole identity had changed” (p. 18); without these elements the person would find it hard to tell which stories about him/her were endorsable or not. 

Significant narrators: influential people, “carriers of those cultural messages that will have the greatest impact on one’s actions” (p. 18). 

 

They then define learning as closing the gap between actual and designated identities. 

 

Any narrative can be seen as a triple BAC where A is the identified person, B the storyteller and C the recipient. Without going on any further it is clear that there are therefore multiple identities for any one person, which really has to be part of any definition of identity. Whether any of these three are the same person or not allows us to define three “levels” of identity narrative: 

AAC: the storyteller is the identified person: first-person identity 

BAA: the story is told to the identified person: second-person identity 

BAC: all three are different people: third-person identity 

AAA is a particularly special identity, a first-person self-told identity which is possibly what many people mean when they speak of identity – it has potentially the most impact on one’s actions. Second- and third-person identities have the potential to be incorporated into our first-person designated identities (p. 18). 

 

A merit of this narrative definition of identity is that “human agency and the dynamic nature of identity are brought to the fore” (p. 17); the focus of attention is on things being said, not on something existing behind what is said. As stories, identities are human-made, have authors and recipients, and can change according to need, they are accessible and investigable. A criticism of this narrative definition is that “text” cannot replace experience. Wenger in particular stresses that the words used to express or represent identity are not the identity itself. Sfard and Prusak argue that, while they agree with Wenger that identities originate in the “experience of engagement”, it is the stories one tells about experiences, or the visions of these experiences, that constitute identities, not the experiences themselves. 

 

Of all the theoretical texts on identity which I have covered so far, it is this narrative one I like the best. One reason is that I am wanting to use theory to look at some data I have and that data is largely in the form of interviews. Perhaps on a different data set I might prefer a different theoretical tool. Still, this definition of identity as story, with a split into actual and designated identities with learning drawing those two together really works for me. I shall try to apply this to my data and see what comes out! 

 

Blumer, H. (1969) Symbolic Interactionism: Perspectives and Methods. Englewood Cliffs: Prentice Hall.

 

 

I am interested in finding various theoretical perspectives on identity and identity development of (preferably university) students studying mathematics. After having read widely, I could potentially compare and contrast, but right now I’m just trying to get a sense of what is out there.

 

In this paper, Cobb and Hodge introduce three key constructs of identity, namely normative identity, personal identity and core identity. Here are some definitions, taken from the text:

Normative identity: “The normative classroom identity is concerned with the obligations that a student has to fulfil in order to be an effective and successful mathematics student in that classroom. These obligations involve general norms for classroom participation as well as specifically mathematical norms.” (p. 11); “the type of person the students would have to become to be mathematical people” (p. 16)

Personal identity: “The facets of personal identity that emerged from our analysis concern students’ understandings and valuations of their general and specifically mathematical classroom obligations together with their assessments of their own and others’ developing mathematical competences.” (p. 25); “who they actually become in the classroom” (p. 16)

Core identity: “envisioned life trajectories … , of who the students viewed themselves to be and who they wanted to become” (p. 2); the person’s “life story” is of central importance to core identity, but core identity is not reducible to the life story (p. 27); They link to Gee’s notion of core identity, also Gee’s use of “life stories” which has echoes of Sfard and Prusak’s work. Gee’s identity constructs will be discussed in a later blog post, as will Sfard and Prusak’s.

 

An important feature of the normative identity is that it is classroom-dependent and is co-constructed by teacher and students. They refer to how the teachers and students “contribute to regenerations of patterns” (p. 12 and elsewhere). “ ... students are seen to contribute to the initial constitution and ongoing regeneration of the normative identity, and to develop their personal classroom identities as they do so” (p. 16, emphasis added). The norms that they looked at in their classrooms of interest were social norms and specifically mathematical norms, for instance taking notes and asking questions were social norms, and what constituted a mathematical explanation and how information is presented are mathematical norms. Interestingly, they point out that norms are most obvious when they are transgressed. The authors argue against the notion that students are invited to adopt a normative identity in a specific classroom, independent of their participation. Aspects of the core identity need to be reconciled with the regeneration of the classroom normative identity in order to develop an affiliation with mathematical activities. Or is it the other way around?

 

With reference to Martin’s (2000) study, they consider successful students to have reconciled their core identities with the classroom normative identity through their development of personal identity as doers of mathematics (p. 2). So, let’s see, students enter any classroom with an existing core identity related to mathematics which involves their internal trajectory of where they are going with relation to mathematics. They presumably also have some vestige of a personal identity as a doer of mathematics as constructed in previous mathematics classes, but potentially quite changeable depending on the specific classroom context they find themselves in now. During the practise of classroom activities, the students and teachers co-construct the normative identity (surely the teacher plays the larger role, though?) and it is through this co-construction that personal identities are developed or changed. The greater the sense of affiliation with the mathematical activities, the greater the reconciliation between aspects of core identity and normative identity. Hmm. I’m pretty sure I’m mangling this.

 

Cobb and Hodge report three difficulties they have with prior research on identity. First, they find a contradiction in identity theories from a situated perspective. They use as example Boaler & Greeno (2000) who describe identity as contextual yet also refer to a stable transcontextual identity. Secondly they feel that limited guidance is provided to teachers by other identity formulations. Thirdly they feel the word identity is used in too many different ways. They hope their three constructs counter these three difficulties.

 

They discuss (citing Nasir, 2002) how the development of a sense of identity and affiliation with a community of practice can motivate new learning and the gaining of new skills. They recognise the instructional value of cultivating such affiliation, but also argue that a sense of affiliation with mathematical literacy in general is an important goal in its own right. Again drawing on Nasir (2002), they illustrate the following (linear?) sequence: 

Development of more engaged personal identity leads to

reasoning about data in increasingly sophisticated ways, which leads to

participating in class in new ways, which leads to

affiliation with mathematical activity in class, as well as

increased mathematical competence.

They wield the hefty word equity in reference to the cultivation of interest in mathematics in and out of school and hence development of a personal identity as a doer of mathematics.

 

In closing, some lines from the Discussion (p. 31):

The authors argued “that an analysis of the personal identities that students develop in a particular classroom provides a way of accounting for students’ persistence, interest in, and motivation to engage in mathematical activity as it is constituted in that classroom. In addition, we argued that students’ development of personal identities that involve a sense of affiliation with mathematical activity should be an important instructional goal in its own right in that it related directly to issues of equity in mathematics education”

 

Boaler, J., Greeno, J. (2000) Identity, agency and knowingin mathematical worlds, in J. Boaler (Ed.) Multiple Perspectives on Mathematics Teaching and Learning (pp. 45 – 82). Stamford, CT: Ablex.

Gee, J.P. (2001) Identity as an analytic lens for research in education, Review of Research in Education, 25, 99 – 125. Note: check to see if there are other Gee (2001) refs, this C&H paper is unclear.

Gee, J.P. (2003) What Video Games Have to Teach Us about Learning Literacy. New York: Palgrave/MacMillan.

Martin, D.B.  (2000) Mathematics Success and Failure among African-American Youth. Mahwah, NJ: Erlbaum.

Nasir, N.S. (2002) Identity, goals and learning: Mathematics in cultural practice, Mathematical Thinking and Learning, 4, 213 – 248.