Empirical reconstruction of mathematics teaching practices in problem-solving lessons: a multi-method case study

In this exploratory case study, the teaching practices of two secondary level mathematics teachers are examined within the framework of a sequential multi-method design. To this end, data on the teachers’ recurrent patterns of action were collected using video-based classroom observations in problem-solving lessons, semi-structured interviews and video-stimulated recalls. The qualitative analyses of the respective data allowed a differentiated description of the self-reported, observable, and articulable elements of their teaching practices. This includes the requirement situations to which the teachers respond with recurrent patterns of actions, their cognitive and affective dispositions on which they rely, and their situation-specific skills that enable them to adaptively orchestrate their problem-solving lessons. An empirical reconstruction of a selected practice, including a description of its constitutive elements, followed from a superordinate integration of the data by triangulation. This study contributes to the discourse on mathematics teacher education by providing an innovative study design for the empirical reconstruction of teaching practices. Moreover, its findings validate the theoretical assumption that teaching practices are an expression of mathematics teachers’ professional competence and expertise.