1. 1 The effect of students’ perceptions of the learning environment on mathematics achievement Explaining the variance in Flemish TIMSS 2003 data W. Schelfhout, G. Van Landeghem, A. Van den Broeck, & J. Van Damme, K.U.Leuven 2nd IEA International Research Conference

2. 2 TIMSS 2003 Mathematics achievement Constructivism

3. 3 TIMSS 2003

4. 4 TIMSS 2003 international Flanders: 5213 pupils 8th grade pupils in 276 classes in 148 schools Math and science achievement Pupils’, teachers’ and principals’ questionnaires

5. 5 TIMSS 2003 Flemish extras Parents’ questionnaire Additional questions in pupils’, teachers’ and principals’ questionnaires Spatial and numerical intelligence test Two classes per school

6. 6 A-stream vs. B-stream ClassesNumber of schools Two A109 One A10 One B10 Two B19 Total148 A = general B = vocational

7. 7 Mathematics achievement

8. 8 Math achievement TIMSS 2003 Rasch score 8th grade math achievement in Flanders 4908 pupils in 268 classes in 144 schools A-stream: 4328 pupils in 224 classes in 119 schools B-stream: 580 pupils in 44 classes in 25 schools

9. 9 Math achievement Basic statistics NMeanSD A-stream4328152.8 (0.4)8.3 B-stream580137.0 (0.7)7.2 Variance Components % pupil% class% school A-stream69%17%15% B-stream80%2%18%

10. 10 Intelligence (A-stream) Basic statistics NMeanSD A-stream437452.0 (0.5)11.6 Variance Components % pupil% class% school A-stream72%12%16% Correlation with math achievement: 0.62

11. 11 Intelligence as a predictor of math achievement (A-stream) Dependent variable: MathN = 4266 A-stream pupils Model 1Model 2 FixedIntercept152.8(0.4)152.0(0.2) Explained variance INT0.37(0.01) Random  2 school 9.9(2.5)3.1(0.9)68%  2 class 11.6(1.9)4.0(0.8)66%  2 pupil 47.1(1.0)35.9(0.8)24% Deviance29023.6727714.97

12. 12 Constructivist learning environment

13. 13 Measurements Pupils’ questionnaire (Flemish part): 33 (4- point) items Teachers’ questionnaire (Flemish part): 6 (5-point) items

14. 14 Scales, pupils’ questionnaire Activation (ACTIV) Clarity (CLAR) Authentic (AUTH) Motivation (MOTIV) Feedback (FEEDB) Cooperation (COOP) Constructivism (TIMSS 1999) (CP)

15. 15 ‘Activation’ scale (11 items,  = 0.76) In the math class …  … the teacher asks about relationships between different parts of the subject material during tasks. (8)  …  … the teacher gives small clues that help us to find solutions by ourselves. (22)  …  … during team work or when I am working on my own, the teacher inquires after the time I need to solve a problem. (33)

16. 16 ‘Clarity’ scale (7 items,  = 0.82) In the math class …  … the teacher bears in mind pupils’ remarks when searching for suitable assignments or practice materials. (3)  …  … the teacher keeps the class under control. (9)  …  … it’s thanks to the teacher’s approach that I understand the subject matter well. (29)

17. 17 ‘Authentic’ scale (3 items,  = 0.74) In the math class …  … the teacher gives examples of situations in daily life where the subject matter can be applied. (1)  … each new chapter starts with examples from daily life that clarify the new subject. (5)  …situations are described that can happen in the real world and that need a mathematical solution. (14)

18. 18 ‘Motivation’ scale (4 items,  = 0.76) In the math class …  … the teacher makes sure that I get interested in the subject matter. (2)  … the teacher uses an agreeable diversity of approaches in his/her teaching. (4)  … we work in a pleasant manner. (12)  … I feel that the subject matter will be useful to me later. (21)

19. 19 ‘Feedback’ scale (3 items,  = 0.70) In the math class …  … the teacher explains the solution after an exercise. (18)  … the teacher repeats the subject matter when it is not properly understood by some pupils. (26)  … the teacher clarifies errors in tests. (28)

20. 20 ‘Cooperation’ scale (2 items,  = 0.74) In the math class …  … we have the opportunity to ask other pupils to explain their way of solving a problem. (27)  … we have the opportunity to discuss our approach to math problems with other pupils. (32)

21. 21 ‘Constructivism’ scale (6 items,  = 0.73) Combines items from the scales  Activation (2 items) (15) (33)  Clarity (1 item) (3)  Authentic (1 item) (5)  Cooperation (both items) (27) (32)

22. 22 Scales, pupils’ questionnaire Basic statistics ScaleNMeanSD Activation46202.560.48 Clarity46902.990.62 Authentic48292.160.74 Motivation47152.380.71 Feedback48553.210.69 Cooperation48342.220.85 CP47382.210.63

23. 23 Scales, pupils’ questionnaire Variance components Scale% pupil% class% school Activation87%6%7% Clarity72%19%9% Authentic79%9%12% Motivation79%17%4% Feedback78%14%9% Cooperation85%10%5% CP79%12%9%

24. 24 Scale teachers’ questionnaire 6 item scale (CT),  = 0.74 Items closely related to CP items Range 1 to 5; mean = 3.16; SD = 0.64; N = 256 classes Variance components: class 48%, school 52%

25. 25 Class level constructivism variables 8 class level indicators of ‘constructivism’: Class means of 7 scales from pupils’ questionnaire Scale CT from teachers’ questionnaire

26. 26 Class level constructivism variables Basic statistics in A-stream ScaleNMeanSD Activation2272.560.19 Clarity2273.010.35 Authentic2272.080.33 Motivation2272.340.34 Feedback2273.240.35 Cooperation2272.150.36 CP2272.150.28 CT2163.150.65

27. 27 Class level constructivism variables Variance components in A-stream Scale% class% school Activation67%33% Clarity69%31% Authentic69%31% Motivation95%5% Feedback65%35% Cooperation91%9% CP86%14% CT47%53%

28. 28 Class level constructivism variables Correlations in A-stream CLARAUTHMOTIVFEEDBCOOPCPCT ACTIV 0.800.560.720.770.570.780.16 CLAR 0.470.750.880.550.710.16 AUTH 0.590.410.400.690.14 MOTIV 0.670.600.760.14 FEEDB 0.520.660.12 COOP 0.850.19 CP 0.19

29. 29 Class level constructivism variables Correlations with class mean math achievement (A-stream) ACTIV 0.12 CLAR 0.14 AUTH -0.16 MOTIV 0.00 FEEDB 0.09 COOP -0.04 CP -0.14 CT 0.12

30. 30 Single predictor models Example Dependent variable: MathN = 4328 A-stream pupils Model 1Model 2 FixedIntercept152.8(0.4)152.8(0.4) ACTIV2.9(1.7) Random  2 school 9.9(2.5)9.6(2.4)  2 class 11.6(1.9)11.5(1.9)  2 pupil 47.0(1.0)47.0(1.0) Deviance29431.0229428.04

31. 31 Single predictor models Summary VariableNCoeff.p-value Activation43282.9(1.7)9% Clarity43281.8(0.9)6% Authentic4328-1.5(1.0)14% Motivation4328-0.1(0.9)89% Feedback43281.1(0.9)25% Cooperation 4328-0.8(0.9)39% CP4328-1.9(1.1)10% CT40880.9(0.5)9%

32. 32 Conclusion Major intake differences between classes and schools (cf. intelligence) Indications of marginally significant effects of some aspects of teaching as perceived by the students: activation and clarity