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Reflections, Selections, and Deflections in Conceptions of Identity in Mathematics Education Research. William R. Penuel SRI International. A Shared History. A Genealogy of Identity. Identity is not a natural concept but a cultural one

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reflections selections and deflections in conceptions of identity in mathematics education research

Reflections, Selections, and Deflections in Conceptions of Identity in Mathematics Education Research

William R. Penuel

SRI International

a genealogy of identity
A Genealogy of Identity

Identity is not a natural concept but a cultural one

As a cultural concept, it is important to subject it to cultural analysis, such as genealogical (Foucault, 1977) and dramatistic analysis (Burke, 1969, Kaplan, 1983)

Some narrow conceptions of identity (e.g., the concept of gender identity as studied by developmental psychologists) might be partly natural

Is identity an ideological and uniquely American construct?

Concepts of identity are “promiscuously mingled” (Holland & Lachicotte, 2007)

dramatistic analysis
Dramatistic Analysis
  • Origins in Burke (1968) in literary criticism
  • Terministic screens are akin to Discourses (Gee, 1991) and social languages (Bakhtin, 1981) in that they refer to characteristic ways of thinking, speaking, valuing, and doing in a community of practice
  • Every terministic screen is:
    • A reflection of reality
    • A selection of reality
    • A deflection of reality

Image Source: University of Minnesota

dramatistic analysis for education
Dramatistic Analysis for Education
  • Terministic screens also imply particular forms of action for educators:
    • Interventions
    • Instructional regimes (Raudenbush, 2002)
    • Youth development programs (NRC and Istitute of Medicine, 2002)
    • Organizing of new social futures (O’Connor & Penuel, 2009)
  • What are the implications of the conceptions of identity currently in play within mathematics education research?
  • If they are unclear, why, and what can and should we do about it?
three conceptions
Three Conceptions
  • Identity as vulnerable to implicit and explicit stereotype threats
  • Identity as the production and consumption of social positions
  • Identity as a stance toward participation in socially valued activities
identity as vulnerable to situational threats
Identity as Vulnerable to Situational Threats


Steele’s notion of stereotype threat, observed among female and African American students in remedial mathematics courses in college

Developed principally within psychology since 1997

A number of experimental studies have demonstrated the effect and the fact that it can be moderated by individuals’ identification with their group (e.g., Schmader, 2002) and with mathematics as a domain (e.g., Keller, 2007)

identity as vulnerable to situational threats8
Identity as Vulnerable to Situational Threats

Steven Spencer

Diane Quinn

Claude Steele

Image Sources (left to right): University of Waterloo, Stanford University, University of Connecticut

identity as vulnerable to situational threats10
Identity as Vulnerable to Situational Threats

Cultural Stereotype about Math Ability

Situational Prompt

Increased Task Anxiety

Lower Math Performance

Disidentification with Math

identity as vulnerable to situational threats11
Identity as Vulnerable to Situational Threats

Study 3 Results: Less Selective University

Study 2 Results: More Selective University

Graphic adapted from Spencer, S. J., Steele, C. M., & Quinn, D. M. (1999). Stereotype threat and women's math performance. Journal of Experimental Social Psychology, 35(1), 4-28.

identity as vulnerable to situational threats12
Identity as Vulnerable to Situational Threats

Implications for social action are explicit in the literature

Research has tested some interventions to remove threat

Making explicit the concept of stereotype threat (John, Schmader, & Martinis, 2005; Pronin, Steele, & Ross, 2004)

Make salient positive group attributions (McIntyre, Paulson, & Lord, 2003)

Scope and limitations of recommended courses of action

Interventions are focused primarily on undergraduates

Interventions tend to be of a short time-frame

They do not address classroom processes

They do not seek to change social stereotypes perpetuated in social practices

identity as social positioning
Identity as Social Positioning


Social practice theory (Bourdieu, 1986; Lave & Wenger, 1991; Lave, 1996)

Figured worlds (Holland et al., 1998)

Poststructuralism (Davies & Harré, 2008; Foucault, 1990)

Poststructuralist-feminism (Weedon, 1989, 1999)

Qualitative and mixed-methods studies have found that classrooms can and do differ with respect to positions available to students, with implications for mathematics learning (Blanton & Stylianou, 2008; Evans, Morgan, & Tsatsaroni, 2006; Hegedus & Penuel, 2008)

identity as social positioning14
Identity as Social Positioning

Jo Boaler

Jim Greeno

Image Sources (left to right): University of Sussex, Stanford University

identity as social positioning16
Identity as Social Positioning

Boaler & Greeno (2000):

Compared different “figured worlds” of mathematics classrooms: ritualized, traditional figured worlds and discussion-oriented figured worlds

Discussion-oriented figured worlds provided more opportunities for engaging in different forms of mathematical communication

Focused on roles and relationships with respect to knowing in classroom processes

For the sample of high school students interviewed, participating in ritualized figured worlds led them to reject mathematics, since their worlds positioned them as more active knowers, a situation they preferred

identity as social positioning17
Identity as Social Positioning

Implications for social action are explicit and focus both on changes to classroom practices and concern for long-term equity in outcomes

Experimental research is now underway (here at UMass and elsewhere) to explore impacts and relate changes to classroom positions to learning outcomes

Scope and limitations of action

Instructional regimes focused on creating new participant frameworks

Regimes do not address individual differences or the role of peers in structuring informal networks (Field et al., 2006)

identity as stance toward activity
Identity as Stance Toward Activity


Engagement, imagination, and alignment within social practice theory (Wenger, 1998)

Russian literary criticism (Bakhtin, 1986)

Sociocultural psychology (Wertsch, 1991)

Structural-functional linguistics (Halliday, 1978; Lemke, 1995)

Sociology (Wiley & Alexander, 1987)

Qualitative analyses point to how individuals develop dispositions over time, by appropriating resources over different timescales (Gresalfi, in press; Gresalfi & Cobb, 2006)

identity as stance toward activity19
Identity as Stance Toward Activity

Nai’lah Nuad Nasir

Melissa Sommerfeld Gresalfi

Image Sources (left to right): University of California, Indiana University

identity as stance toward activity21
Identity as Stance Toward Activity

Nasir (2002)

Goals and identities formed in practice are central to mathematics learning; motives, goals, and imagined futures drive activity

Learning involves new ways of engaging in activity; new ways of engagement imply new identities

Focus is on two informal activities in which mathematics are part: playing dominoes and basketball

Mathematics: Addition, Multiplication, Probabilistic reasoning, Statistics

Elementary school domino play: Identities in other school settings shaped engagement and social positions

High school: Practice-linked identities shaped engagement and social positions, facilitated by a shared history of playing together

identity as stance toward activity22
Identity as Stance Toward Activity

Gresalfi (in press)

Learning is a process of developing dispositions, ways of being in the world that involve ways of engaging in mathematics across different timescales

Classroom practices constitute a set of possibilities for developing dispositions

Focus on four students in two 8th grade algebra classes that differed with respect to how they organized instruction

Data source: Videotapes of 65 observations focused on how students worked on mathematics activity (Subset of 3 days for each student, spread throughout the school year, when students were working in groups)

identity as stance toward activity25
Identity as Stance Toward Activity

Implications for social action are less well developed for this conception of identity

Drawing on everyday cultural knowledge to build mathematical learning environments

Funds of Knowledge (Moll et al., 1992)

Algebra Project

Culturally-responsive Pedagogies (Lee, 2001)

Carr and Claxton (2002) suggest its potential value for diagnostic assessment and program evaluation

A challenge is the need for accounts for development over longer timescales

They recommend multiple methods that combine inside-out and outside-in perspectives on dispositions

what is to be done
What Is To Be Done?

Nothing: Intervention is dangerous. Who are we to attempt to change youth’s identities?

Focus on building individual resilience: Stereotype threats are ubiquitous, students need protection from them.

Change the learning environment: Provide new participation frameworks and roles for youth that enable them to identify more with mathematics as a way of thinking and making sense of the world

Change the broader institutional ecology of learning: Create new possibilities for identity and recognition within institutions that produce successful outcomes for everyone

an integrative research agenda
An Integrative Research Agenda

Studies should relate inside-out and outside-in perspectives on identity

Studies should employ multiple methods to generate complementary perspectives

Studies should compare or test alternative forms of mathematically-rich social action to advance youth’s futures

relating inside out and outside in perspectives
Relating Inside-Out and Outside-In Perspectives
  • Assumption: Each conception of identity reflects some dynamic process not adequately captured within the other frameworks
  • Aim: Explore interplay of self-construction and recognition
    • Am I ‘good at math’? Who says so?
multi method studies
Multi-Method Studies

Methods for studying identity are diverse, but implicated within particular terministic screens

Experimental designs with survey and interview methods

Longitudinal studies

Institutional and historical analyses

Analyses of discourse

Collection and analysis of life stories

We should not expect different methods to yield convergent findings but rather to help us see what one terministic screen deflects through another

multi method studies31
Multi-Method Studies

Meltzoff and Nasir study within the Learning in Informal and Formal Environments (LIFE) Center

Focus on three types of stereotype linkages: boy-math, girl-math, self-math

Focus on students in grades 1-5

Inside-out measures: Implicit Association Test (strengths of stereotypes)

Outside-in measures: Classroom observations, with a focus on the role of culture and race in mathematics classrooms

testing alternative forms of action
Testing Alternative Forms of Action

These tests could be experimental, but they could also be longitudinal, cross-case comparisons

Social action as a term is intended to capture the broad range of possibilities for improving youths’ futures

The forms of action should be mathematically-rich

Bringing youth into futures where they can use mathematics as a powerful form of discourse to improve their own and other lives

Necessarily involves developing mathematical knowledge, skills, and dispositions

where i hope we go
Where I Hope We Go
  • Organizing:
    • Learning environments that engage young people as active knowers of mathematics (Boaler & Greeno)
    • That draw on rich representational infrastructures (Hegedus, Roschelle)
    • Institutions that allow for diverse ways of measuring success where success can be recognized no matter the “who” or “where” (McDermott)
thank you
Thank You

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