Types of mathematical tasks in lower secondary classrooms in Germany: Statistical findings from a latent class analysis based on general mathematical competencies

Abstract

Tasks play an important role in mathematics education, as they provide opportunities for students to develop their competencies and to cognitively engage with the mathematical content. The potential for cognitive activation as a central feature of a mathematical task has been considered in numerous studies, mostly as a didactical analysis by means of existing classification systems. In this study, which has been carried out in the frame of the TEDS research program, a different approach is taken by which we aim to identify the cognitive demand level of tasks used in ordinary mathematics lessons. Thus, the correlation between general mathematical competencies and the cognitive mathematical activities required to solve the task was analyzed and common properties of groupings of tasks were empirically extracted. In detail, 2490 tasks from mathematics lessons in Germany were analyzed by means of a rational task analysis with regard to their potential for fostering general mathematical competencies, namely modelling, problem solving, reasoning and argumentation, use of representations, use of symbols and operations, and communication. Latent class analysis revealed six classes of mathematical tasks with varying potential for the different competencies. In accordance with previous studies on mathematical tasks in Germany, the biggest class focused solely on the use of symbols and operations, while other classes showed different foci. Post hoc analyses revealed that the classes of tasks differ with regard to the level of cognitive activity they require. The results of the study highlight that the potential for cognitive activation of the tasks used in the classrooms of this more recent study has not improved in the last decades, despite many reform activities in German mathematics education, and that many mathematical tasks used are still more or less calculation oriented.