The influence of teachers’ dispositions on their use of mathematical problem-solving tasks: a Qualitative Comparative Analysis based on teachers’ pedagogical content knowledge and beliefs

Abstract

Mathematical tasks play a central role in shaping students’ opportunities to engage in complex cognitive processes such as mathematical problem solving. While previous research has highlighted the importance of teachers’ professional competence for instructional quality, less is known about how different facets of teachers’ dispositions jointly relate to the selection of tasks with high problem-solving potential. This study investigates how combinations of teachers’ mathematical pedagogical content knowledge and beliefs about mathematics and mathematics teaching are associated with the use of problem-solving tasks in lower secondary classrooms. Drawing on data from a German follow-up study of the international Teacher Education and Development Study, the analysis is based on a subsample of 31 in-service teachers whose classroom tasks were systematically collected and analyzed with respect to their problem-solving potential. Teachers’ knowledge and beliefs were assessed using established instruments. To account for the assumed complexity and interdependence of teachers’ dispositions, a Qualitative Comparative Analysis was conducted. The results show that no single facet of teachers’ dispositions is necessary or sufficient for the use of tasks with high problem-solving potential. Instead, configurations combining high levels of mathematical pedagogical content knowledge with either dynamic views of mathematics or constructivist beliefs about teaching and learning emerge as sufficient conditions. These findings underscore the importance of considering the interplay of cognitive and affective-motivational facets of teacher competence when studying task selection in mathematics education.