Índice de Tablas y Figuras
CUESTIONARIO DE EVALUACIÓN DE RIESGOS PSICOSOCIALES
Concerning computational speed, the Laplacian method was faster than all conditions in SAS, except the least accurate non-adaptive Gaussian setting with 1 quadrature point. The difference between the defaults in computational speed is in favor of R, which was approximately a factor 20 times faster.
4.3. Limitations
It is important to look at limitations of the current research to see the results and conclusion in a correct perspective. The current research performed analyses completely on material that was collected for national assessment purposes without the current research questions in mind. The teacher questionnaire was a self-report instrument. We do not know if all the answers are really true. Especially, the question concerning the students’ home support,
it could be that the teacher had a wrong perception of the student while answering this question. Wrong answers of the teachers can lead to wrong conclusions in the current study.
For missing variables, mean and mode imputation was used instead of (multiple) imputation techniques, because of the complexity of the current analyses. Donders, van der Heijden, Stijnen and Moons (2006) showed that mean and mode imputation provide biased results in all missing conditions. Bias in the estimates can lead to problems. First, the sizes of the true parameter values are different than the results in the analysis. A simulation study of Donders et al. (2006) showed differences of 0.45 with a true parameter value of 1 with mean imputation. It could be the true values in our research were higher or lower. This leads to the second problem, a negative value in our research, for example -0.20 for home support could be in real positive. This would change the perspective considering home support to the opposite, which would have major impact on our educational implications and conclusions. The other significant teacher parameter values in the current research were -0.15 for differentiation and 0.21 for school support. They could also be incorrect, as a consequence results, implications and conclusions in the present study should be considered carefully. Running the same analysis with multiple imputation techniques is in this context interesting for future research.
Finally, the current research is based on associations and as a consequence, conclusions about cause and result are incorrect.
4.4. Educational implications
The finding of the present study that school support has a positive effect on accuracy has consequences for education. School support seems to play an important role in learning mathematic skills. It may also be important for learning (all) other topics at school. In this context it is important that schools develop their school support system. School support can be individual, at the group level, but for example also at the level of personal problems. This, together with the current development of the so-called ‘tailored education’ in the Netherlands, where the schools in a district are together responsible for education for every child (with or without learning problems or handicap) makes school support an interesting topic for future
study. Which factors in school support are successive and which not and for which goal? Psychological support with a wider scope of school support or just a focus on school topics?
With regard to the first research question of the present study, concerning teacher practices that can explain the mathematics ability at the end of primary school, three conclusions can be made. First, the grade 6 teacher does play a role in the mathematical performance of the students, because of model comparisons, as described in section 3.1. Second, school support plays a positive role (in comparison with no school support) and third, differentiation and home support (in comparison with no home support) have a negative effect on the mathematics ability of the students. The other teacher variables in the current research did not play a significant role. With regard to section 1.4, less aspects of teaching than expected have an effect on accuracy.
4.5. Methodological implications
Concerning the parameter values, under the condition that the adaptive Gaussian setting with 5 quadrature points is the most accurate, it seems that, in the context of section 4.2, unbiased and accurate values are obtained with the non-adaptive Gaussians setting with 20 quadrature points or more. However, it may be that the non-adaptive Gaussian setting with 20 quadrature points is not sufficient in providing accurate parameter values when the sample size is lower than the sample size of the current study, since Pinheiro and Chao (2006) found biased estimates of variance components and fixed effects in both data configurations of their research. Pinheiro and Chao (2006) had three different random effects in their study, whereas the present study had 1 random (student) effect. How the accuracy of the parameter values under different Gaussian settings relates to sample size and number of random effects is in this context an interesting topic for a future (simulation) study.
Laplace in R is approximately a factor 1.7 times faster than this non-adaptive setting with 20 quadrature points and around 20 times faster than adaptive Gaussian structure with 5 quadrature points. One can conclude that Laplace in R is sufficient for explanatory IRT. Laplace in R provides estimates within one standard error of the estimates of the accurate, unbiased adaptive Gaussian with 5 quadrature points and is approximately a factor 4 times
faster than the accurate non-adaptive Gaussian with 100 quadrature points and a factor 20 times faster than the adaptive Gaussian with 5 quadrature points settings in SAS. Further, R is free available whereas SAS is part of a commercial software package.
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Appendix
Background information teacher • Personalia
1) What is your age? … Year
2) What is your gender?
□ Male
□ Female
• Education / work experience
3) Which education did you finish with a degree?
□ PABO (pedagogic academy of primary education, ± 4 years)
□ Teacher education after other work (±2 years)
□ PA (pedagogic academy, training college or toddler education)
□ Teacher education secondary education
□ Teacher education is not (yet) finished / internship
□ Other, namely ………
4) How many successive years did you teach grade 6 students at the end of this schoolyear? ……… year.
• Training
5) Did you get extra training/education in the last 5 years?
□ Yes
□ No
Students
6) How many students do you have in your class? _____ students.
7) What do you think of the number of students in your class??
□ Way too low.
□ Too low.
□ Optimal.
□ Too high.
□ Way too high.
Curriculum
• Mathematics method
8) Which mathematics textbook did you use in the class?
Write down the mathematics textbooks used in the last school years
Schoolyear Mathematics textbook Date Edition
2008-2009
2009-2010
2010-2011
9) How much time do you spend on mathematics education in an average school week? On average _______ hours (weekly)
10) How much mathematics study time do weak students get on top of the normal mathematics study time? On average _____ minutes extra per week
11) As a teacher, do you have a preferred multiplication strategy?
□ Strong preference for the whole-number-based strategy
□ Small preference for the whole-number-based strategy
□ No preference
□ Small preference for the digit-based strategy
12) As a teacher, do you have a preferred division strategy?
□ Strong preference for the whole-number-based strategy
□ Small preference for the whole-number-based strategy
□ No preference
□ Small preference for the digit-based strategy
□ Strong preference for the digit-based strategy
Calculation by head and estimation
13) How many times do you treat calculation by head and estimation in mathematics lessons?
□ Less than once a week
□ Once a week
□ Twice a week
□ More often namely, ____ times a week
14) How much time do you spend on average on calculation by head and estimation? _____ minutes
Classroom management
15) Is there differentiation in your class with regard to the skill and/or work pace of the students in the mathematics lessons?
□ Normally all students get the same instruction and exercises at the same time.
□ Instruction is normally the same for all students: when dealing with exercises there is differentiation with regard to skill and work pace.
□ There is group instruction at the skill level or by work pace with the potential of further differentiation when dealing with exercises.
□ Instruction is individual and exercises are selected for each student individually.
Student care
16) Are there possibilities at your school for extra individual support for mathematics, for example a person in school who is responsible for the development of the student care?
□ No, continue with question 49
□ Yes, by a remedial teacher
□ Yes, by an internal co-worker/mathematics specialist
□ Yes, by a remedial teacher and by an internal co-worker/mathematics specialist
17) How intensive is the support at home by parents or caretakers?
□ Not supporting
□ Little supporting
□ Regularly supporting
□ Often supporting
Acknowldegements
First, I would like to thank my supervisor msc Marije Fagginger Auer for providing me with constructive feedback and criticism during the writing of my thesis. Without her guidance I would never have finished this master. The support of my student friends Sanne Cnossen and Hans Revers was also very helpful. I enjoyed the coffee sessions in the café of the university with them. They were always inspiring. Last, but no least I want to thank my wife Hester Overmars for given me the space and time to do this study. She lived 6 years with me spending countless hours behind my computer. She was always supporting and stimulating and helped me through difficult times with her right words. I apologize for the stressed situations, difficult moods, worrying and sometimes irritable attitude I could have.