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

1. Reflections, Selections, and Deflections in Conceptions of Identity in Mathematics Education Research William R. Penuel SRI International

2. A Shared History

3. 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)

4. 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

5. 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?

6. 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

7. 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)

8. 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

9. Identity as Vulnerable to Situational Threats

10. Identity as Vulnerable to Situational Threats Cultural Stereotype about Math Ability Situational Prompt Increased Task Anxiety Lower Math Performance Disidentification with Math

11. 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.

12. 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

13. 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)

14. Identity as Social Positioning Jo Boaler Jim Greeno Image Sources (left to right): University of Sussex, Stanford University

15. Identity as Social Positioning

16. 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

17. 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)

18. 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)

19. Identity as Stance Toward Activity Nai’lah Nuad Nasir Melissa Sommerfeld Gresalfi Image Sources (left to right): University of California, Indiana University

20. Identity as Stance Toward Activity

21. 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

22. 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)

23. Identity as Stance Toward Activity

24. Identity as Stance Toward Activity

25. 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

26. 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

27. 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

28. 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?

29. Relating Inside-Out and Outside-In Perspectives

30. 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

31. 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

32. 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

33. Testing Alternative Forms of Action

34. 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)

35. Thank You Contact me at: william.penuel@sri.com 650.859.5001