Reflections, Selections, and Deflections in Conceptions of

Identity in Mathematics Education Research

William R. PenuelSRI International

A Shared History

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

• 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

• 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

• 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

• Origins– 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 Threats

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

Steven Spencer

Claude Steele

Diane Quinn

Identity as Vulnerable to Situational Threats

Reflects Selects DeflectsInner processes of identity becoming salient within particular situations

Cues and prompts that increase anxiety in the performance of tasksSamples focus principally on undergraduates

Origins of stereotypesRole of classroom processes, especially at the K-12 levelInteractions with specific subject matter learning

Identity as Vulnerable to Situational Threats

Lower Math Performance

Situational Prompt

Increased Task Anxiety

Cultural Stereotype about Math

Ability

Disidentification with Math

Identity as Vulnerable to Situational Threats

Study 2 Results: More Selective

University

Study 3 Results: Less Selective

UniversityGraphic 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 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

• Origins– 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 Positioning

Jo Boaler Jim Greeno

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

Identity as Social Positioning

Reflects Selects DeflectsStructuring role of social practices ‘Production and consumption’ of positions (enactment, uptake)

Classroom processes, particularly discourse as focal point for analysisRelationship between identity and knowing for different topic areas of mathematics

Variation and individual differencesInformal positions that emerge from informal interactions

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 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

• Origins– 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 Activity

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

Nai’lah Nuad Nasir

Melissa Sommerfeld Gresalfi

Identity as Stance Toward Activity

Reflects Selects DeflectsVariation in how individuals appropriate resources (including positions) over time to construct identities

Change and variation across individuals over timeInside-out and outside-in perspectives on developmentDiscipline-specific dispositions

Individual differences that help explain variability in stances (biological, psychological)How mechanisms might operate differently over different timescales

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 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 Activity

Identity as Stance Toward Activity

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?

• 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

• 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

• 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?

Relating Inside-Out and Outside-In Perspectives

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 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

• 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

Testing Alternative Forms of Action

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

Contact me at:william.penuel@sri.com

650.859.5001