1. 4 September 20051 The effect of students’ perceptions of the learning environment on mathematics achievement Explaining the variance in Flemish TIMSS 2003 data J. Van Damme, A. Van den Broeck, W. Schelfhout & G. Van Landeghem, K.U.Leuven

2. 4 September 20052 TIMSS 2003 Mathematics achievement Constructivism

3. 4 September 20053 TIMSS 2003

4. 4 September 2005TIMSS 20034 TIMSS 2003 international Flanders: 5213 8th grade pupils in 276 classes in 148 schools Math and science achievement Pupils’, teachers’ and principals’ questionnaires

5. 4 September 2005TIMSS 20035 TIMSS 2003 Flemish extras Parents’ questionnaire Additional questions in pupils’, teachers’ and principals’ questionnaires Spatial and numerical intelligence test Two classes per school

6. 4 September 2005TIMSS 20036 A-stream vs. B-stream ClassesNumber of schools Two A109 One A10 One B10 Two B19 Total148 A = general B = vocational

7. 4 September 20057 Mathematics achievement

8. 4 September 2005Math achievement8 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. 4 September 2005Math achievement9 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. 4 September 2005Math achievement10 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. 4 September 2005Math achievement11 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% Deviance29023.6729428.04

12. 4 September 200512 Constructivist learning environment

13. 4 September 2005Constructivist learning environment 13 Measurements Pupils’ questionnaire (Flemish part): 33 (4- point) items Teachers’ questionnaire (Flemish part): 6 (5-point) items

14. 4 September 2005Constructivist learning environment 14 Scales, pupils’ questionnaire Activation (ACTIV) Clarity (CLAR) Authentic (AUTH) Motivation (MOTIV) Feedback (FEEDB) Cooperation (COOP) Constructivism (TIMSS 1999) (CP)

15. 4 September 2005Constructivist learning environment 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. 4 September 2005Constructivist learning environment 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. 4 September 2005Constructivist learning environment 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. 4 September 2005Constructivist learning environment 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. 4 September 2005Constructivist learning environment 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. 4 September 2005Constructivist learning environment 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. 4 September 2005Constructivist learning environment 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. 4 September 2005Constructivist learning environment 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. 4 September 2005Constructivist learning environment 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. 4 September 2005Constructivist learning environment 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. 4 September 2005Constructivist learning environment 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. 4 September 2005Constructivist learning environment 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. 4 September 2005Constructivist learning environment 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. 4 September 2005Constructivist learning environment 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. 4 September 2005Constructivist learning environment 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. 4 September 2005Constructivist learning environment 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. 4 September 2005Constructivist learning environment 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. 4 September 2005Conclusion32 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