1. Educational Option Choice in Secondary School. A Multinomial Multilevel Approach Maarten Pinxten, Bieke De Fraine & Jan Van Damme Presentation Earli Sig Interest Group 18 (Leuven) 2010

2. They say the definition of madness is doing the same thing and expecting a different result T.H.E.H.I.V.E.S. Presentation Earli Sig Interest Group 18 (Leuven) 2010

3. 1. Introduction Structure of Flemish educational system ► Different tracks - Academic track - Technical track - Vocational track ► Different cycles - Cycle 1: Grade 7 + Grade 8 (orienting scope) - Cycle 2: Grade 9 + Grade 10 (specialization) - Cycle 3: Grade 11 + Grade 12 (further specialization) Presentation Earli Sig Interest Group 18 (Leuven) 2010

4. 1. Introduction Educational option choice: A Flemish perspective - The term ‘option choice’: In contrast with other countries no subject choice but choice of a fixed package of subjects For example: ‘Latin/Mathematics’ in Grade 9: core curriculum + 4hours/week of Latin + 2hours/week supplementary math - Number of option choices fans out progressively due to further specialization - Two important decisional thresholds: transition from Cycle 1 to Cycle 2 (end of Grade 8) and transition from Cycle 2 to Cycle 3 (end of Grade 10) Presentation Earli Sig Interest Group 18 (Leuven) 2010

5. 2. Determinants of Subject Choice 1.Student level determinants ► Gender - Uptake math & science courses in favour boys - Weaking gender gap of gender-stereotypical choice? * ICT & math: typical male * Humanities and expressive arts: typical female ► Socio-Economical Status (SES) - In general: higher social background > more Math & Science - Interesting interaction effects with gender * For example: High SES girls tend to make more gender atypical choices compared to low SES girls (Smyth & Hannan, 2006) Presentation Earli Sig Interest Group 18 (Leuven) 2010

6. 2. Determinants of Subject Choice ►Absolute achievement - Absolute performance in a subject is indicative for choosing that subject (e.g., high grades in math, choosing more math subjects) ►Relative achievement (Jonsson, 1999) - Different comparative profiles for boys and girls * Girls: comparative advantage in social sciences * Boys: comparative advantage in math - This comparative profile reduced the gender effect with 10 to 30% Presentation Earli Sig Interest Group 18 (Leuven) 2010

7. 2. Determinants of Subject Choice ►Individual psychological constructs 1. Interest (e.g., Elsworth et al., 1999) “intrapersonal influences predominate in school subject choice and show a particularly clear and persuasive pattern of direct relations between interests and subject choices” (p.313) 2. Economic utility and future relevance (e.g.,Stokking, 2000) 3. Academic self concept, self-efficacy beliefs (e.g., Dickhauser et al., 2005) 4. Subject enjoyment and subject appreciation (e.g., van Langen, 2006a, 2006b) Presentation Earli Sig Interest Group 18 (Leuven) 2010

8. 2. Determinants of Subject Choice 2. School level determinants ► In general: school level effects are rather small in comparison with individual level effects (e.g. Daly & Ainley, 1999) ► Some examples - Dryler (1999) found that in schools with a high proportion of students with parents working in humanities that the odds for boys choosing engineering reduced significantly - Ayalon and Yogev (1997)observed that the link between ability and choice of math/science subjects is intensified in more able environments - A liberal school policy with regard to curriculum access seems to narrow the gender gap in the uptake of mathematics subjects (Lamb, 1996). Presentation Earli Sig Interest Group 18 (Leuven) 2010

9. 3. Purpose 1. What is the effect of student level (e.g., achievement, gender, SES) and school level (e.g., gender-composition, SES-composition) determinants on option choice and is it possible to identify major (and minor) determinants of option choice? What is the relative impact of academic interest on option choice? 2. Are there differences between schools with respect to the option choices of their students? Are the log odds of choosing option A in contrast with choosing option B different between schools? Presentation Earli Sig Interest Group 18 (Leuven) 2010

10. 4. Data ► Data of LOSO project ( Dutch acronym for Longitudinal Study of Secondary Education ) ► LOSO-project followed the educational career of 6411 students in 90 schools ► We only considered option choice in academic track 1. Homogeneity in the offer of option choices over schools 2. Inclusion of all tracks: number of categories to large ► Students that repeated a grade were included in our sample Presentation Earli Sig Interest Group 18 (Leuven) 2010

11. 4. Data ► Grade 9: (N = 2518 – 22 schools) - Economical/Languages (N = 559) - Economical/Sciences (N = 722) >>> Reference Category - Classical/Languages (N= 250) - Classical/Sciences (N = 565) - Mixed/Social (N = 423) ► Grade 11 (N = 2871 – 24 schools) - Economical/Languages (N = 579) - Economical/Sciences (N = 405) - Classical/Languages (N = 304) - Classical/Sciences (N = 900) >>> Reference Category - Mixed/Social (N = 684) Presentation Earli Sig Interest Group 18 (Leuven) 2010

12. 4. Data ► Student level variables - Gender (0=Male / 1=Female) - SES (1 factor score: Income/Cultural capital/Occupational Level/Highest Diploma) - Academic self-concept (1 factor score: 9 items) - Dutch & Mathematics achievement (IRT – Grade 8 & Grade 10) - Numerical & Verbal intelligence (GETLOV scores – Grade 7) - Interest in Business – Sciences – Social - Literature (OII – Grade 7&Grade 12) ► School Level variables - SES composition - Gender composition - Math composition Presentation Earli Sig Interest Group 18 (Leuven) 2010

13. 5. Method Multinomial Multilevel Regression Estimation method: Markov Chain Monte Carlo (MCMC) - PQL1 starting values - 50 000 iterations - orthogonal parameterization Missing data: EM algorithm Software: MLwiN Presentation Earli Sig Interest Group 18 (Leuven) 2010

14. 5. Method 1.Logistic regression: A short introduction ► Unordered categorical dependent variable (option choice) ► We will apply one of the most widely used transformations of probabilities, that is, the log odds: ► Interpretation: an increase of 1 of predictor x, increases the odds of choosing A versus not-A with a factor e β Presentation Earli Sig Interest Group 18 (Leuven) 2010

15. 5. Method 2. Estimation Method ► Multinomial models cannot be estimated with ML methods in MLwiN ► Alternative: Marginal Quasi-Likelihood (MQL) and Penalized Quasi-Likelihood (PQL) in combination with a first or second order Taylor-series approximation (e.g., MQL1 vs MQL2): * MQL1: raw estimates, downwardly biased fixed and random estimates * MQL2 and PQL1: only small improvements * PQL2: generally considered as best Pseudo-Likelihood estimator. However, computationally less stable ► Recently: Bayesian MCMC methods offer an improvement on PQL2 methods (Browne & Draper, 2006) Presentation Earli Sig Interest Group 18 (Leuven) 2010

16. 5. Method 3. Multinomial warnings ► Results rely heavenly on the chosen reference category - Objective criterium: largest category ► When the number of categories grows: number of parameters gets doubled, tripled… - Convergence problems! ► Option choices were clustered - Supply-demand: some option choices are offered by some schools and not by others - Too many clusters: scattered results/interpretation meaningless - Some option choices are very alike (e.g., EC-MA & EC-SC) Presentation Earli Sig Interest Group 18 (Leuven) 2010

17. 6. Results (Final Model Grade 9) Parameter βS.E.Exp (β) FIXED EFFECTS (student level) Cons_Classical/Languages- 0.5033.203 Cons_Classical/Sciences 2.2741.792 Cons_Economical/Languages- 3.5351.850 Cons_Mixed/Social- 2.9953.871 Girls_Classical/Languages 0.2330.304 Girls_Classical/Sciences- 0.2510.206 Girls_Economical/Languages 0.474 **0.194 1.60 ** Girls_Mixed/Social 0.668 **0.218 1.95 ** SES_Classical/Languages 0.320 **0.092 1.38 ** SES_Classical/Sciences 0.418 **0.073 1.52 ** SES_Economical/Languages - 0.197 **0.071 0.82 ** SES_Mixed/Social 0.0210.073 Self-concept2_Classical/Languages 0.0180.089 Self-concept2_Classical/Sciences 0.1120.074 Self-concept2_Economical/Languages - 0.283 **0.068 0.75 ** Self-concept2_Mixed/Social- 0.0290.072 Presentation Earli Sig Interest Group 18 (Leuven) 2010

18. 6. Results (Grade 9 - Continued) Parameter βS.E.Exp (β) FIXED EFFECTS (student level) Achievement Dutch2_Classical/Languages 1.263 **0.165 3.54 ** Achievement Dutch2_Classical/Sciences 1.219 **0.126 3.38 ** Achievement Dutch2_Economical/Languages- 0.1310.083 Achievement Dutch2_Mixed/Social- 0.0590.098 Achievement Math2_Classical/Languages 0.0120.127 Achievement Math2_Classical/Sciences 0.660 **0.107 1.93 ** Achievement Math2_Economical/Languages - 0.458 **0.080 0.63 ** Achievement Math2_Mixed/Social- 0.0840.091 Verbal Intelligence_Classical/Languages 0.333 **0.110 1.40 ** Verbal Intelligence_Classical/Sciences 0.215 **0.088 1.24 ** Verbal Intelligence_Economical/Languages 0.0320.077 Verbal Intelligence_Mixed/Social 0.1450.086 Numeric Intelligence_Classical/Languages- 0.1800.107 Numeric Intelligence_Classical/Sciences 0.0950.087 Numeric Intelligence_Economical/Languages - 0.423 **0.079 0.66 ** Numeric Intelligence_Mixed/Social- 0.1390.086 Presentation Earli Sig Interest Group 18 (Leuven) 2010

19. 6. Results (Grade 9 - Continued) Parameter βS.E.Exp (β) FIXED EFFECTS (student level) Interest Business1_Classical/Languages- 0.0290.091 Interest Business1_Classical/Sciences - 0.164 **0.072 0.85 ** Interest Business1_Economical/Languages - 0.139 **0.069 0.87 ** Interest Business1_Mixed/Social - 0.353 **0.073 0.70 ** Interest Sciences1_Classical/Languages 0.1020.111 Interest Sciences1_Classical/Sciences 0.0980.087 Interest Sciences1_Economical/Languages - 0.284 **0.082 0.75 ** Interest Sciences1_Mixed/Social - 0.188 **0.088 0.83 ** Interest Social1_Classical/Languages 0.1590.109 Interest Social1_Classical/Sciences 0.0860.089 Interest Social1_Economical/Languages 0.0010.082 Interest Social1_Mixed/Social 0.0080.088 Interest Literature1_Classical/Languages 0.702 **0.104 2.02 ** Interest Literature1_Classical/Sciences 0.222 **0.079 1.25 ** Interest Literature1_Economical/Languages 0.195 **0.075 1.22 ** Interest Literature1_Mixed/Social 0.280 **0.081 1.32 ** Presentation Earli Sig Interest Group 18 (Leuven) 2010

20. 6. Results (Grade 9 - Continued) Parameter βS.E.Exp (β) FIXED EFFECTS (school level) SES-composition_Classical/Languages 0.2000.563 SES-composition_Classical/Sciences- 0.0360.317 SES-composition_Economical/Languages 0.3430.332 SES-composition_Mixed/Social 0.4200.700 Girls school_Classical/Languages- 1.2741.230 Girls school_Classical/Sciences- 0.1850.733 Girls school_Economical/Languages- 0.3290.759 Girls school_Mixed/Social- 2.1671.473 Mixed school_Classical/Languages- 1.9931.165 Mixed school_Classical/Sciences- 0.3010.663 Mixed school_Economical/Languages 0.0160.677 Mixed school_Mixed/Social- 1.2931.337 Math composition_Classical/Languages- 0.8341.375 Math composition_Classical/Sciences - 2.412 **0.7240.09 ** Math composition_Economical/Languages 1.0670.733 Math composition_Mixed/Social 0.9581.444 Presentation Earli Sig Interest Group 18 (Leuven) 2010

21. 6. Results (Grade 9 - Continued) S.E. RANDOM EFFECTS Level 3 – School level Cons_Classical/Languages.Cons_Classical/Languages2.3251.064 Cons_Classical/Sciences.Cons_Classical/Sciences0.7040.290 Cons_Economical/Languages.Cons_Economical/Languages0.7490.300 Cons_Mixed/Social.Cons_Mixed/Social2.8561.314 Cons_Classical/Languages.Cons_Economical/Languages0.9450.454 Cons_Classical/Sciences.Cons_Classical/Languages0.8850.445 Cons_Classical/Sciences.Cons_Economical/Languages0.6500.273 Cons_Mixed/Social.Cons_Classical/Languages0.9900.743 Cons_Mixed/Social.Cons_Classical/Sciences0.5510.416 Cons_Mixed/Social.Cons_Economical/Languages0.8520.462 Level 2 – Student Level 1.0000.000 Level 1 – Multinomial Variance 1.0000.000 Presentation Earli Sig Interest Group 18 (Leuven) 2010

22. 6. Results (Final Model Grade 11) Parameter βS.E.Exp (β) FIXED EFFECTS (student level) Cons_Classical/Languages - 0.9092.001 Cons_Economical/Languages 0.6941.774 Cons_Economical/Sciences 0.2251.773 Cons_Mixed/Social 0.7413.138 Girls_Classical/Languages - 0.2620.239 Girls_Economical/Languages - 0.1270.202 Girls_Economical/Sciences 0.1270.203 Girls_Mixed/Social - 0.0620.189 SES_Classical/Languages - 0.1140.086 SES_Economical/Languages - 0.431 **0.078 0.65 ** SES_Economical/Sciences - 0.452 **0.079 0.64 ** SES_Mixed/Social - 0.432 **0.070 0.65 ** Self-concept4_Classical/Languages- 0.1050.084 Self-concept4_Economical/Languages - 0.0660.075 Self-concept4_Economical/Sciences - 0.0260.077 Self-concept4_Mixed/Social - 0.244 **0.069 0.78 ** Presentation Earli Sig Interest Group 18 (Leuven) 2010

23. 6. Results (Grade 11 - Continued) Parameter βS.E.Exp (β) FIXED EFFECTS (student level) Achievement Dutch4_Classical/Languages 0.266 **0.112 1.30 ** Achievement Dutch4_Economical/Languages - 0.448 **0.095 0.64 ** Achievement Dutch4_Economical/Sciences - 0.676 **0.096 0.51 ** Achievement Dutch4_Mixed/Social - 0.541 **0.088 0.58 ** Achievement Math4_Classical/Languages - 1.114 **0.106 0.33 ** Achievement Math4_Economical/Languages - 1.161 **0.097 0.31 ** Achievement Math4_Economical/Sciences- 0.0230.107 Achievement Math4_Mixed/Social - 0.870 **0.094 0.42 ** Verbal Intelligence_Classical/Languages- 0.1040.099 Verbal Intelligence_Economical/Languages - 0.296 **0.090 0.74 ** Verbal Intelligence_Economical/Sciences - 0.280 **0.090 0.76 ** Verbal Intelligence_Mixed/Social - 0.235 **0.082 0.79 ** Numeric Intelligence_Classical/Languages - 0.288 **0.098 0.75 ** Numeric Intelligence_Economical/Languages - 0.443 **0.087 0.64 ** Numeric Intelligence_Economical/Sciences - 0.221 **0.091 0.80 ** Numeric Intelligence_Mixed/Social - 0.323 **0.081 0.72 ** Presentation Earli Sig Interest Group 18 (Leuven) 2010

24. 6. Results (Grade 11 - Continued) Parameter βS.E.Exp (β) FIXED EFFECTS (student level) Interest Business6_Classical/Languages 0.205 **0.083 1.23 ** Interest Business6_Economical/Languages 0.638 **0.076 1.89 ** Interest Business6_Economical/Sciences 0.663 **0.079 1.94 ** Interest Business6_Mixed/Social - 0.1010.068 Interest Sciences6_Classical/Languages - 0.855 **0.108 0.43 ** Interest Sciences6_Economical/Languages - 1.053 **0.097 0.35 ** Interest Sciences6_Economical/Sciences - 0.888 **0.097 0.41 ** Interest Sciences6_Mixed/Social - 0.776 **0.087 0.46 ** Interest Social6_Classical/Languages - 0.0790.098 Interest Social6_Economical/Languages - 0.327 **0.087 0.72 ** Interest Social6_Economical/Sciences - 0.218 **0.088 0.80 ** Interest Social6_Mixed/Social 0.1330.081 Interest Literature6_Classical/Languages 0.757 **0.101 2.13 ** Interest Literature6_Economical/Languages 0.316 **0.082 1.37 ** Interest Literature6_Economical/Sciences - 0.1070.082 Interest Literature6_Mixed/Social 0.300 **0.075 1.35 ** Presentation Earli Sig Interest Group 18 (Leuven) 2010

25. 6. Results (Grade 11 - Continued) Parameter βS.E.Exp (β) FIXED EFFECTS (school level) SES-composition_Classical/Languages 0.1380.362 SES-composition_Economical/Languages- 0.0770.332 SES-composition_Economical/Sciences- 0.1110.323 SES-composition_Mixed/Social 0.0340.586 Girls school_Classical/Languages - 0.5380.824 Girls school_Economical/Languages - 0.3000.715 Girls school_Economical/Sciences- 0.5790.662 Girls school_Mixed/Social- 1.2301.295 Mixed school_Classical/Languages - 1.3950.720 Mixed school_Economical/Languages- 1.2500.622 Mixed school_Economical/Sciences- 0.8520.619 Mixed school_Mixed/Social- 1.7291.141 Math composition_Classical/Languages 0.8740.624 Math composition_Economical/Languages 0.8420.564 Math composition_Economical/Sciences 0.7020.532 Math composition_Mixed/Social 1.1061.007 Presentation Earli Sig Interest Group 18 (Leuven) 2010

26. 6. Results (Grade 11 - Continued) S.E. RANDOM EFFECTS Level 3 – School level Cons_Classical/Languages.Cons_Classical/Languages0.7440.326 Cons_Economical/Languages.Cons_Economical/Languages0.5520.236 Cons_Economical/Sciences.Cons_Economical/Sciences0.4600.208 Cons_Mixed/Social.Cons_Mixed/Social2.0320.847 Cons_Classical/Languages.Cons_Economical/Languages 0.4330.226 Cons_Classical/Languages.Cons_Economical/Sciences- 0.1170.176 Cons_Economical/Sciences.Cons_Economical/Languages0.2200.169 Cons_Mixed/Social.Cons_Classical/Languages0.7740.409 Cons_Mixed/Social.Cons_Economical/Languages0.8540.400 Cons_Mixed/Social.Cons_Economical/Sciences0.4120.313 Level 2 – Student Level 1.0000.000 Level 1 – Multinomial Variance 1.0000.000 Presentation Earli Sig Interest Group 18 (Leuven) 2010

27. 7. Conclusions and discussion Almost no effect of academic self-concept on option choice Option choice in secondary school is mainly determined by student level factors In 9 th grade: girls tend to choose the options economical/Languages & Mixed/social more often (in comparison with economical/Sciences) In 11 th grade: the effect of gender on option choice disappeared completely after the inclusion of interest in sciences In both 9 th and 11 th grade: opting for Mixed/Social seems to be a negative choice (no effect of interest in social service) Relative importance of achievement (Grade 9) Example 1. Economical/Languages VS Economical/Sciences: Those students do not perform better in Dutch but they perform significantly worse in math. But: greater interest in literature and less interest in sciences Example 2. Classical/Languages VS Classical/Sciences: Those students do not perform better in Dutch but they perform significantly worse in math. But greater interest in literature Presentation Earli Sig Interest Group 18 (Leuven) 2010

28. 7. Conclusion and discussion From an achievement point of view: strong hierarchy between option choices with classical studies at the top From a SES point of view: student with higher socio-economical background tend to choose classical studies over economical or social oriented option choices BUT 1.Chicken or the egg? Interest or option choice? 2.Positive or negative choice? ! Educational option choice is a complex jigsaw puzzle ! Presentation Earli Sig Interest Group 18 (Leuven) 2010

29. References Ayalon, H., & Yogev, A. (1997). Students, schools, and enrollment in science and humanities courses in Israeli secondary education. Educational Evaluation and Policy Analysis, 19, 339-353. Browne, W. J., & Draper, D. (2006). A comparison of Bayesian and likelihood-based methods for fitting multilevel models. Bayesian Analysis, 1 (3), 473-514. Colley, A., & Comber, C. (2003). School subject preferences: age and gender differences revisited. Educational Studies, 29, 59-67. Daly, P., & Ainley, J. (1999). Student participation in mathematics courses in Australian secondary schools. The Irish Journal of Education, 30, 77-95. Dickhauser, O., Reuter, M., & Hilling, C. (2005). Coursework selection: A frame of reference approach using structural equation modeling. British Journal of Educational Psychology, 75, 673-688. Dryler, H. (1999).The impact of school and classroom characteristics on educational choices by boys and girls: A multilevel analysis. Acta Sociologica, 42, 299-318. Elsworth, G. R., Harvey-Beavis, A., Ainley, J., & Fabris, S. (1999). Generic interests and school subject choice. Educational Research and Evaluation, 5, 290-318. Presentation Earli Sig Interest Group 18 (Leuven) 2010

30. References Lamb, S. (1996). Gender differences in mathematics participation in Australian schools: Some relationships with social class and school policy. British Educational Research Journal, 22, 223-240. Miller, L., & Budd, J. (1999). The development of occupational sex-role stereotypes, occupational preferences and academic subject preferences in children at ages 8, 12 and 16. Educational Psychology, 19, 17-35. Smyth, E., & Hannan, C. (2006). School Effects and Subject Choice: The uptake of scientific subjects in Ireland. School Effectiveness and School Improvement,17, 303-327. Stokking, K. M. (2000). Predicting the choice of physics in secondary education. International Journal of Science Education, 22, 1261-1283. van Langen, A., Rekers-Mombarg, L., & Dekkers, H. (2006a). Sex-related differences in the determinants and process of science and mathematics choice in pre-university education. International Journal of Science Education, 28, 71-94. van Langen, A., Rekers-Mombarg, L., & Dekkers, H. (2006b). Group-related differences in the choice of mathematics and science subjects. Educational Research and Evaluation, 12, 27-51. Presentation Earli Sig Interest Group 18 (Leuven) 2010

31. Thank you! If you want more information about this presentation, please do not hesitate to contact me at Maarten.Pinxten@ped.kuleuven.beMaarten.Pinxten@ped.kuleuven.be Presentation Earli Sig Interest Group 18 (Leuven) 2010