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 TIMSS 2003 Mathematics achievement Constructivism

3 TIMSS 2003

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

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

7 Mathematics achievement

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 Math achievement Basic statistics NMeanSD A-stream (0.4)8.3 B-stream (0.7)7.2 Variance Components % pupil% class% school A-stream69%17%15% B-stream80%2%18%

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

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% Deviance

12 Constructivist learning environment

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

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

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 ‘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 ‘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 ‘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 ‘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 ‘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 ‘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 Scales, pupils’ questionnaire Basic statistics ScaleNMeanSD Activation Clarity Authentic Motivation Feedback Cooperation CP

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

26 Class level constructivism variables Basic statistics in A-stream ScaleNMeanSD Activation Clarity Authentic Motivation Feedback Cooperation CP CT

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 Class level constructivism variables Correlations in A-stream CLARAUTHMOTIVFEEDBCOOPCPCT ACTIV CLAR AUTH MOTIV FEEDB COOP CP 0.19

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

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) Deviance

31 Single predictor models Summary VariableNCoeff.p-value Activation (1.7)9% Clarity (0.9)6% Authentic (1.0)14% Motivation (0.9)89% Feedback (0.9)25% Cooperation (0.9)39% CP (1.1)10% CT (0.5)9%

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