Support for productive whole-class discussions in mathematics. Developing and exploring frameworks in the context of classroom response systems

Abstract in English

In recent decades, research has stressed the importance of productive classroom discussions in high-quality mathematical instruction for all learners. However, after decades of attempts by professional development programs to support teachers in achieving these discussions, they are rarely reported on in the classroom context. Thus, there is still a need for support for teachers’ establishment of these discussions. One promising activity for achieving productive discussions involves using a classroom response system and implementing tasks in a multiple-choice format. However, there is little knowledge about whole-class discussions in secondary school mathematics using this approach. This thesis responds to this lack by contributing to knowledge about support for achieving productive whole-class discussions in mathematics using classroom response systems and multiple-choice tasks. The thesis particularly addresses knowledge about the key practices of constructing multiple-choice tasks and leading whole-class discussions. This is operationalized by applying an educational design research approach to 1) develop design principles for constructing tasks and a supplementary task type framework and further evaluate the potential of these design principles by characterizing whole-class discussions, and 2) explore frameworks for analyzing teachers’ leading of whole-class discussions and technology integration. In this work, data from interviews with teachers, reflection notes, and observations were used. The main results cover: characteristics of useful tasks in a multiple-choice format aiming at supporting teachers in achieving productive discussions; characteristics of whole-class discussions in the context of classroom response system in secondary school mathematics; the potential of applying the Structuring Features of Classroom Practice framework as an analytic tool to conceptualize and analyze teachers’ reasoning about classroom response system; and the suggestion of five new categories of teacher actions and enrichments of two existing categories in the redirecting, progressing and focusing framework. In the kappa of this thesis, these results are merged and discussed in relation to theories of ambitious mathematics instruction. The focus is on examining whether and how classroom response systems and multiple-choice tasks can support teachers in establishing this instruction. In summary, the main contributions of this thesis are: a tool for constructing multiple-choice tasks aimed at generating productive discussions in mathematics; an examination of analytical tools for analyzing teachers’ leading of whole-class discussions and technology integration; and suggestions for the development of these tools.