Social Dynamics of Mathematics Course-Taking for Boys and Girls

1. The Social Dynamics of Mathematics Course-Taking for Boys and GirlsKenneth A. FrankMichigan State UniversityChandra Muller University of TexasKathryn SchillerSUNY AlbanywithRobert CrosnoeSam FieldAmy LangenkampJennifer PearsonKelly Raley Catherine Riegle-Crumb Anna Strassmann MuellerUniversity of Texas

2. Support • *This work was supported by grants from the National Institute of Child Health and Human Development (1R01HD040428-01) from the National Science Foundation (REC-0126167) to the Population Research Center, University of Texas at Austin. Additionally, this research uses data from Add Health, a program project designed by J. Richard Udry, Peter S. Bearman, and Kathleen Mullan Harris, and funded by a grant P01-HD31921 from the National Institute of Child Health and Human Development, with cooperative funding from 17 other agencies. • Opinions reflect those of the authors and do not necessarily reflect those of the granting agencies. The authors are solely responsible for the contents.

3. Motivation “The adolescent is choosing how to invest time, and … the choices depend greatly on the social system surrounding them.” page 346 of Coleman’s “Vision for Sociology”.

4. Friendship Influence B Friendship AB Friendship AC C Friendship AD A D

5. Critique of Friendship Influence • Friends accept adolescents for who they are (Harter and Fischer 1999; Lightfoot 1997; Bearman and Bruckner 2001) • Adolescents more likely to select friends with similar interests than to be influenced by existing friends (Dornbusch 1989; Matsueda and Anderson 1998)

6. But Peers can be Influential • Friends provide • Emotional support • Information • Instrumental resource (e.g., homework) • As rational actors, adolescents may seek friends or draw on them for resources →Adolescents can be influenced by those with whom they would like to be friends (potential friends) (Giordano 2003)

7. Who are Potential Friends? • Potential friends are theoretically important, but how to find them • Similar interests and characteristics (Blau) • Opportunities to observe others’ behaviors and interactions (Leiffer) • Opportunities to initiate interaction (Leiffer)

8. School as Social Organization Defines Structure for Forming Friendships • School is dominant social institution for adolescents (Coleman 1961) • School structures opportunities for interaction (Moody 2001) • School cultivates certain interactions (Quiroz et al 1997)

9. Conceptualizations of Social Organization of Schools • Academic Tracks • Defined by course levels • Honors/college prep, general, vocational • Implications for exposure to academic material and opportunities for advancement • Gamoran; Hallinan; Oakes • Salience of academic tracks? • Age of detracking (Hallinan) • May never have been tracks, especially outside of core areas (Lucas)

10. Return of the Social Category • Jocks, nerds, burnouts, leading crowd • Observed by Coleman in Adolescent Society (1961) • Still relevant • Ethnographies (Eckert 1989; Leslie, McClure, and Oaxaca 1998; Foley 1990; Milner 2004) • Psychologists (Barber, Eccles, and Stone 2001) • Economists (Akerlof and Kranton 2002)

11. Influence of Members of a Social Category • Adolescents conform to those in the social category as part of identity (Akerlof and Kranton [AK] 2002, Coleman 1961) • Identity: perceived relationship with group • Identity: “both a student’s assigned category and the payoffs associated with self-image” (AK: 2002: 1172).

12. How is Identity Influential? Effects of Identity in AK Utility function Pursuit of Human Capital Status of Category Fit in Category Effort to Conform to Category Human capital (p): wage rate per unit of skill (w) the ability of person i (ni ) and the effort of person i (ei). Identity (1-p): social status associated with the nerd category (IN), identity loss from an adolescent’s distance from the ideal ascriptive characteristics in the nerd category (t), effort (ei) adolescent exerts to fit into her social category, where e(N) represents the ideal effort level (on academics) for an adolescent who is a nerd.

13. Interpreting the Utility Function • Niche picking: balance between status of social category against fit and effort needed to conform to norms • psychological link between micro (through individual perception) and macro level (social category) phenomenon within social organizations • schools can maximize academic effort given student composition: • different standards for different categories • Maintains engagement for those with lower ability

14. Limitations of Conceptualization of Social Categories • Categories (and tracks) are a priori and fixed • Common across schools • Decided by researchers or administrators • Unchanged by adolescent behavior and over time • Difficult to measure • “How can we know that being in one social category or another reflects anything more than individual tastes and endowments? For example, there may be no such thing as a group of nerds: those who are called nerds may just be those who are smarter and more academically inclined. The empirical task is to establish that membership in a social category, independent of tastes, affects behavior” (AK: page 1176).

15. Limitations of Conceptualization of Influence in AK Function • Friends valuable because • Emotional support • Information • Instrumental resource (e.g., homework) • But AK focus on psychological costs of misfit • Recall: Friends likely have: • Similar interests • Observable interactions • Opportunities for interaction • But social categories not rooted in social experience (based on perceptions)

16. Alternative Conceptualization: Local Positions • Clusters of students who take courses together • Preserves duality of data (students and courses) • See Field, Frank et al. (Social Networks, 2006)

17. Conceptualization of Clustering in 2-Mode data From Skvoretz and Faust’s adaptation of p* models Actor 2-stars Event 2-stars

18. Identifying Local Positions • Apply cluster analysis to the set of transcripts in each school • Transcripts represent people and experiences • Define model relating local position membership to course-taking • Maximize criterion from model

19. Model of Effect of Position Membership on Coursetaking Define θ1 from the following model for xij , an indicator of whether student i took course j : where same lpositionij takes a value of 1 if student i and course j are in the same local position, 0 otherwise. When θ1 is large, participation is concentrated within positions. θ1 =log of odds ratio in following table

20. Identify Emergent Positions:Criterion to Maximize Social Structure of Position: Concentration of participation in events Maximize (AD/BC) = Participation within position x Non participation in other positions Participation in other position x Non-participation in position Position Membership

21. Table 1 Courses in Local Positions in Cyprus High

22. Table 2 Estimated Student Composition of Local Positions at Cyprus High for the 94-95 School Yeara

23. Two-Mode Sociogram of Students and Courses at Cyprus High (Hypothetical Data)

24. A B G C H D F E

25. Advantages of Local Positions • Unique in each school • Algorithm applied uniformly to transcript data in each Add Health school, clusters differ by school • Focused around experiences – courses • Emergent from student choices and school constraints • Original data come from transcripts measuring social experience independent of behavior or attitude in survey

26. Research Question • How do members of local positions influence engagement in academics? • AK: adolescents conform to mean behavior • Frank et al.: adolescents adopt popular behaviors to gain friendships

27. Influence within Local Positions:Norms Via Rewards and Sanctions ?

28. Norms Via Rewards and Sanctions ?

29. Norms Via Rewards and Sanctions ?

30. Reminder: Original Utility function Effort to conform Pursuit of Human Capital Status of Category Fit in Category Human capital (p): wage rate per unit of skill (w) the ability of person i (ni ) and the effort of person i (ei). Identity (1-p): social status associated with the nerd category (IN), identity loss from an adolescent’s distance from the ideal ascriptive characteristics in the nerd category (t), effort (ei) adolescent exerts to fit into her social category, where e(N) represents the ideal effort level (on academics) for an adolescent who is a nerd.

31. Alternative Utility Function Pursuit of Human Capital Value of Help Conformity to Mean Conformity to mean (weighted by popularity) Help towards academic endeavors Mean level of effort in local position Mean level of effort in local position (weighted by popularity in local position) Note π+ρ+κ=1.

32. Maximizing Utility with Respect to Effort (first order equations)a Mean (weighted by popularity)of others Value of human capital Access to help Mean of others Effort = Mean math level of others in social contexts Mean math level (weighted by popularity)of others in social contexts Advance in math? Educational Expectations Number of Friends = aAssuming π+ρ+κ=1.

33. Data • Add Health data, nationally representative • Longitudinal: control for prior behavior • Dependent Variable: advanced in math (or not) from 94-95 to 95-96 • Network: • Exposure through course overlap (also have exposure through friends, but sample size reduced) • Three Levels: • students (n=4,000) • within local positions (n=770) • within schools (n=78) • All analysis weighted at level 1 for individual weight • Unit-specific effects reported with robust standard errors used to compensate for possible misspecification of distribution of error terms (conservative).

36. Controls in Models • Ever been retained • Level of math in 1994-95 • Math grades for 1994-95 • Grade level in Fall 1994 • Educational expectations • Latino/a, Black • Parental education • Indicator of whether data were available to construct the measure of friends’ mean math level

37. Interpretation • Boys and girls more likely to advance if they • Have high expectations • Parents disappointed if they don’t go • Never retained • Had high grades • Were at relatively low math levels • Effects associated with local positions • Girls more likely to advance if they occupy local positions in which other girls taking high levels of math • Interpretation: girls advance to make friends – pursuit of social capital. • Effect size: whole extra class of 21 girls advancing out of 9th grade containing 350 girls. • Applies especially to girls at relatively low levels of math

38. Predicted increased stratification between members of low and high local positionson account of conformity to local position means (for girls).

39. Gender Interpretation • Boys may identify more and perceive more competence with math than girls because of societal expectations (Eccles)  boys use social resources to do well in math, girls use math to gain social resources. • Girls may be more savvy about social contexts

40. Realized Social Consequences: Pursuit of Friendships • Do adolescents make friends if they advance and are in local positions in which math is associated with popularity? • Model of change in popularity as a function of advancing and mean level math, weighted for popularity • Answer: Girls: yes; Boys: no

41. Realized Social Consequences: Value of Friendships • Do adolescents who have friends perform better in next course? • Model of Math GPA in 95-96 (controlling for Math GPA in 94-95) • Answer: Girls: no; Boys: yes

42. Conceptual Summary of Influence • Social consequences • Boy may not be able to gain popularity by advancing in math • Girl may not be able to draw on friends to do well in math • Not just differences in adolescents’ perceptions of math (Eccles) • Agents of influence are • Potential nominators (girls) • Existing friends (boys) • Schools can elicit effort indirectly • Determining type and composition of local positions • Symbolic action to elevate popularity of desired behaviors

43. Conceptual Summary regarding Local Positions • Emergent level between individual and school • Individual Agency versus Organizational Constraint • More than just dyads • Group mechanisms operate through local positions – adolescents pursue social capital

44. Limitations • Know courses, not classes • Don’t know extracurricular well • Only a sample in most schools