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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

6. Results (Final Model Grade 9) Parameter βS.E.Exp (β) FIXED EFFECTS (student level) Cons_Classical/Languages Cons_Classical/Sciences Cons_Economical/Languages Cons_Mixed/Social Girls_Classical/Languages Girls_Classical/Sciences Girls_Economical/Languages ** ** Girls_Mixed/Social ** ** SES_Classical/Languages ** ** SES_Classical/Sciences ** ** SES_Economical/Languages ** ** SES_Mixed/Social Self-concept2_Classical/Languages Self-concept2_Classical/Sciences Self-concept2_Economical/Languages ** ** Self-concept2_Mixed/Social Presentation Earli Sig Interest Group 18 (Leuven) 2010

6. Results (Grade 9 - Continued) Parameter βS.E.Exp (β) FIXED EFFECTS (student level) Achievement Dutch2_Classical/Languages ** ** Achievement Dutch2_Classical/Sciences ** ** Achievement Dutch2_Economical/Languages Achievement Dutch2_Mixed/Social Achievement Math2_Classical/Languages Achievement Math2_Classical/Sciences ** ** Achievement Math2_Economical/Languages ** ** Achievement Math2_Mixed/Social Verbal Intelligence_Classical/Languages ** ** Verbal Intelligence_Classical/Sciences ** ** Verbal Intelligence_Economical/Languages Verbal Intelligence_Mixed/Social Numeric Intelligence_Classical/Languages Numeric Intelligence_Classical/Sciences Numeric Intelligence_Economical/Languages ** ** Numeric Intelligence_Mixed/Social Presentation Earli Sig Interest Group 18 (Leuven) 2010

6. Results (Grade 9 - Continued) Parameter βS.E.Exp (β) FIXED EFFECTS (student level) Interest Business1_Classical/Languages Interest Business1_Classical/Sciences ** ** Interest Business1_Economical/Languages ** ** Interest Business1_Mixed/Social ** ** Interest Sciences1_Classical/Languages Interest Sciences1_Classical/Sciences Interest Sciences1_Economical/Languages ** ** Interest Sciences1_Mixed/Social ** ** Interest Social1_Classical/Languages Interest Social1_Classical/Sciences Interest Social1_Economical/Languages Interest Social1_Mixed/Social Interest Literature1_Classical/Languages ** ** Interest Literature1_Classical/Sciences ** ** Interest Literature1_Economical/Languages ** ** Interest Literature1_Mixed/Social ** ** Presentation Earli Sig Interest Group 18 (Leuven) 2010

6. Results (Grade 9 - Continued) Parameter βS.E.Exp (β) FIXED EFFECTS (school level) SES-composition_Classical/Languages SES-composition_Classical/Sciences SES-composition_Economical/Languages SES-composition_Mixed/Social Girls school_Classical/Languages Girls school_Classical/Sciences Girls school_Economical/Languages Girls school_Mixed/Social Mixed school_Classical/Languages Mixed school_Classical/Sciences Mixed school_Economical/Languages Mixed school_Mixed/Social Math composition_Classical/Languages Math composition_Classical/Sciences ** ** Math composition_Economical/Languages Math composition_Mixed/Social Presentation Earli Sig Interest Group 18 (Leuven) 2010

6. Results (Grade 9 - Continued) S.E. RANDOM EFFECTS Level 3 – School level Cons_Classical/Languages.Cons_Classical/Languages Cons_Classical/Sciences.Cons_Classical/Sciences Cons_Economical/Languages.Cons_Economical/Languages Cons_Mixed/Social.Cons_Mixed/Social Cons_Classical/Languages.Cons_Economical/Languages Cons_Classical/Sciences.Cons_Classical/Languages Cons_Classical/Sciences.Cons_Economical/Languages Cons_Mixed/Social.Cons_Classical/Languages Cons_Mixed/Social.Cons_Classical/Sciences Cons_Mixed/Social.Cons_Economical/Languages Level 2 – Student Level Level 1 – Multinomial Variance Presentation Earli Sig Interest Group 18 (Leuven) 2010

6. Results (Final Model Grade 11) Parameter βS.E.Exp (β) FIXED EFFECTS (student level) Cons_Classical/Languages Cons_Economical/Languages Cons_Economical/Sciences Cons_Mixed/Social Girls_Classical/Languages Girls_Economical/Languages Girls_Economical/Sciences Girls_Mixed/Social SES_Classical/Languages SES_Economical/Languages ** ** SES_Economical/Sciences ** ** SES_Mixed/Social ** ** Self-concept4_Classical/Languages Self-concept4_Economical/Languages Self-concept4_Economical/Sciences Self-concept4_Mixed/Social ** ** Presentation Earli Sig Interest Group 18 (Leuven) 2010

6. Results (Grade 11 - Continued) Parameter βS.E.Exp (β) FIXED EFFECTS (student level) Achievement Dutch4_Classical/Languages ** ** Achievement Dutch4_Economical/Languages ** ** Achievement Dutch4_Economical/Sciences ** ** Achievement Dutch4_Mixed/Social ** ** Achievement Math4_Classical/Languages ** ** Achievement Math4_Economical/Languages ** ** Achievement Math4_Economical/Sciences Achievement Math4_Mixed/Social ** ** Verbal Intelligence_Classical/Languages Verbal Intelligence_Economical/Languages ** ** Verbal Intelligence_Economical/Sciences ** ** Verbal Intelligence_Mixed/Social ** ** Numeric Intelligence_Classical/Languages ** ** Numeric Intelligence_Economical/Languages ** ** Numeric Intelligence_Economical/Sciences ** ** Numeric Intelligence_Mixed/Social ** ** Presentation Earli Sig Interest Group 18 (Leuven) 2010

6. Results (Grade 11 - Continued) Parameter βS.E.Exp (β) FIXED EFFECTS (student level) Interest Business6_Classical/Languages ** ** Interest Business6_Economical/Languages ** ** Interest Business6_Economical/Sciences ** ** Interest Business6_Mixed/Social Interest Sciences6_Classical/Languages ** ** Interest Sciences6_Economical/Languages ** ** Interest Sciences6_Economical/Sciences ** ** Interest Sciences6_Mixed/Social ** ** Interest Social6_Classical/Languages Interest Social6_Economical/Languages ** ** Interest Social6_Economical/Sciences ** ** Interest Social6_Mixed/Social Interest Literature6_Classical/Languages ** ** Interest Literature6_Economical/Languages ** ** Interest Literature6_Economical/Sciences Interest Literature6_Mixed/Social ** ** Presentation Earli Sig Interest Group 18 (Leuven) 2010

6. Results (Grade 11 - Continued) Parameter βS.E.Exp (β) FIXED EFFECTS (school level) SES-composition_Classical/Languages SES-composition_Economical/Languages SES-composition_Economical/Sciences SES-composition_Mixed/Social Girls school_Classical/Languages Girls school_Economical/Languages Girls school_Economical/Sciences Girls school_Mixed/Social Mixed school_Classical/Languages Mixed school_Economical/Languages Mixed school_Economical/Sciences Mixed school_Mixed/Social Math composition_Classical/Languages Math composition_Economical/Languages Math composition_Economical/Sciences Math composition_Mixed/Social Presentation Earli Sig Interest Group 18 (Leuven) 2010

6. Results (Grade 11 - Continued) S.E. RANDOM EFFECTS Level 3 – School level Cons_Classical/Languages.Cons_Classical/Languages Cons_Economical/Languages.Cons_Economical/Languages Cons_Economical/Sciences.Cons_Economical/Sciences Cons_Mixed/Social.Cons_Mixed/Social Cons_Classical/Languages.Cons_Economical/Languages Cons_Classical/Languages.Cons_Economical/Sciences Cons_Economical/Sciences.Cons_Economical/Languages Cons_Mixed/Social.Cons_Classical/Languages Cons_Mixed/Social.Cons_Economical/Languages Cons_Mixed/Social.Cons_Economical/Sciences Level 2 – Student Level Level 1 – Multinomial Variance Presentation Earli Sig Interest Group 18 (Leuven) 2010

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

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

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

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, 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, Smyth, E., & Hannan, C. (2006). School Effects and Subject Choice: The uptake of scientific subjects in Ireland. School Effectiveness and School Improvement,17, Stokking, K. M. (2000). Predicting the choice of physics in secondary education. International Journal of Science Education, 22, 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, 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, Presentation Earli Sig Interest Group 18 (Leuven) 2010

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