Analytical Framework

The underlying idea of the study is that the teacher factors and teachers’ instructional practices both have an effect on students’ learn- ing. The teacher factors could have both a direct and indirect effect on students’ learning and instructional factors could have a direct effect on students’ learning. The analytical model of the current study has been developed on the basis of the evidence provided from the theoretical models and previous research. While there are other important factors of teacher effectiveness mentioned in the previous research e.g. classroom management, pedagogical knowledge, teacher-student relationship, classroom environment etc. these have not been included in the study as these factors could not be examined using NEPS data. The analytical model given in the figure 1 shows the teacher factors and instructional factors that were analyzed in this study in order to measure the relation- ship between teachers’ effectiveness and students’ mathematics compe- tence. Teacher factors are the distal indicators of teacher effectiveness and instructional factors are the proximal indicators of teacher effective- ness as teacher factors are distal to the teaching-learning process and instructional indicators are proximal to the teaching-learning process. The definition of distal and proximal indicators is adopted from Seidel and Shavelson (2007). The expectations of the current study from each distal and proximal indicator are as follows.

The first teacher factor in the model is teacher belief. On the ba- sis of the theoretical background and empirical evidence provided about

teacher beliefs, it is expected that teacher belief could affect teacher’ prac-

tices and hence student learning. The study has investigated the follow- ing aspects of teacher beliefs; deep learning, transmissive instruction and

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constructivist instruction. The second teacher factor is teacher professional competence. As explained earlier, the teachers significantly differ in their

professional skills mainly because of the different types of teacher train- ing in Germany; the current study has explored if the students in certain school tracks disadvantaged in relation to students from other school tracks due to their teachers’ different types of training. Although, it is better to measure teacher professional competence by proximal indicators, the current study has measured it distally because NEPS study has measured it only in this way. NEPS has followed the TALIS method of measuring teacher’s professional competence i.e. professional training attended by teachers and their participation in the activities of profes- sional development. NEPS has followed the same pattern. Moreover, the COACTIV study has recently investigated professional competence of teachers through proximal indicators and provided detailed findings. Therefore, the current study examined the effect of teacher’s profession- al competence on students’ mathematics competence through distal indicators. The third teacher factor being investigated is teachers’ plan-

ning which includes lesson planning, considering individual needs of stu- dents while planning and creating interest in learning. On the basis of the

theoretical background it is expected that teachers’ planning has a posi- tive effect on student learning. The fourth teacher factor is cooperation

among teachers. The current study has followed the TALIS study pattern

and has investigated two aspects of teacher cooperation; exchange and

coordination for teaching and professional collaboration. The current study

investigates how often mathematics teachers cooperate with each other and what are the effects of their cooperation on student mathematics competence. The fifth teacher factor is job satisfaction. The current study has investigated three dimensions of job satisfaction; missing identification

with job, job stress, and extrinsic motivation as the determinants of job satisfaction. Missing identification with job addresses factors like how hap-

py and unhappy teachers are with their job and how successfully they are coping with the challenges involved at workplace. Job stress tests the factors that stress teachers for instance missing appreciation, lack in

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opportunities and competition among colleagues. Extrinsic motivation explored the factors that keep teachers motivated for their job. On the basis of previous research, it can be expected that teachers’ level of satis- faction with their job might affect their practices and hence their stu- dents’ learning. The sixth and final teacher factor is stress in planning and

classroom. The current study expected to have a negative effect of stress in planning and classroom on student mathematics competence.

Teacher instructional factors include five factors that are related to teachers’ instruction in the classroom. Learning in general and math- ematics learning in particular, require active student participation in the process of learning. Therefore, all the instructional factors revolved around active student participation. The first is cooperative learning which is measured through the usage of social groups in learning, peer- tutoring, project-based learning, partner work and discussions. Coopera-

tive learning showed positive effect on student learning in previous re-

search, however, the previous research has shown that the success of

cooperative learning depends on the competence of teachers to apply this

method successfully. It is expected that there will be a positive effect of

cooperative learning on student mathematics competence. The second

instructional factor is student engagement in learning. This construct is measured through discussion among teachers and students and stu- dents presenting to the classroom. It is assumed that the more the teachers use these two instructional methods, the higher the student achievement. The third instructional factor is cognitive activation. The construct is rather new and as such more research is needed, however, it has thus far shown a positive effect on student learning particularly in mathematics instruction. The fourth instructional factor is cognitively

challenging tasks. Although very little past research is found on this con-

struct, and weak but positive effect were found on student outcomes. The current study also expected a positive effect of cognitively challenging

tasks on student. The last instructional factor is differentiation. It is

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dents’ abilities. Previous research has shown mixed results regarding the effectiveness of differentiation.

In the present study, the data about teacher factors was collected on a teacher self-report questionnaire and data about teacher instruction in the classroom was collected on instructional questionnaire. Both questionnaires were self-report questionnaires. The data from students was collected on standardized mathematics competence tests.