It is widely assumed that teachers play a key role in providing high-quality learning opportunities to students and fostering students’ learning. Yet it is still unclear how specific teacher knowledge facets as part of their professional competence contribute to classroom processes and learning outcomes. Focusing on mathematics education at the secondary level, this study investigates the links between teachers’ pedagogical competence (i.e., cognitive pedagogical facets of their professional competence), instructional quality, and students’ mathematics achievement. The sample comprises mathematics teacher and student data from 59 classrooms in Germany. Student mathematics achievement was measured across two time points (grade 7 and 8). Teachers’ pedagogical competence was tested using two tests measuring their general pedagogical knowledge (GPK) and situation-specific classroom management expertise (CME). Instructional quality was measured using observational rating data from in vivo rating in mathematics classrooms. Research questions on the relation of teachers’ competence and students’ mathematics achievement were answered using multilevel models. Results from multilevel regression analyses indicate that both GPK and CME predict instructional quality. Direct statistical effects on students’ mathematical progress were identified, whereas no indirect statistical effects via instructional quality could be identified. Although teachers’ measured pedagogical competence is not subject-specific, it serves as a significant predictor for cognitive activation as an indispensable part of quality-oriented mathematical teaching and learning processes in the lower secondary mathematics classroom, and it contributes to students’ mathematical progress.
This paper aims at identifying qualitatively different profiles of teachers' general pedagogical knowledge as a central component of their competence. We applied a mixed Rasch model (Rost 2007) to a sample of 462 in-service, mathematics and non-mathematics teachers that were tested using a short version of the TEDS-M test for general pedagogical knowledge (König et al. 2011). The analysis revealed two profiles that were characterized by (quantitative) differences in their overall GPK level as well as (qualitative) differences resulting in varying rankings of certain items' difficulties. An item-level analysis revealed that the profiles differed mainly on test items dealing with adaptivity, most notably on a set related to Bruner's modes of representation. A person-focused comparison of the profiles showed that teachers who had undergone training for teaching mathematics had a higher chance of belonging to the profile with a strength on these adaptivity items. The profiles' were validated against teacher belief and instructional quality criteria. The results showed that teachers of different GPK profiles differed significantly in their epistemological as well as teaching and learning beliefs. Moreover, teachers differed significantly in the cognitive activation level of their instruction.
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