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This article reports on results from a design research project that implements a formative assessment practice with support from a classroom response system (CRS). Cumulatively building on earlier research and drawing on iteratively generated data from secondary schools in Sweden, the article elaborates on design principles and task types for constructing CRS tasks aimed at generating mathematical classroom discussions. The study generated three design principles, six task types and 31 empirically evaluated tasks useful for developing and using CRS tasks in classroom practices. The results are discussed in relation to earlier research, methodological considerations and the cultural context of Sweden.

In recent decades, research has stressed the prominence of mathematics classroom discussions in productive instructional practices in mathematics instruction. In this context, problem-solving activities have been a common focus of research. Research shows that teachers need to deal with prerequisites and challenges such as norms, design of tasks, activating students, and leading students' discussion to achieve a productive whole-class discussion. However, another promising activity for achieving productive discussions involves using a classroom response system and implementing different task types in a multiple-choice format. There is little knowledge about whole-class discussions using this approach. To meet this need, this paper presents results from a mixed-method approach that characterizes whole-class discussions to explore the potential of multiple-choice tasks supported by a classroom response system to achieve productive whole-class discussions. Three types of multiple-choice tasks were implemented in the classrooms of twelve mathematics teachers at secondary schools. The lessons, including 35 whole-class discussions, were video-recorded, transcribed, and analyzed. The results summarize the characteristics of these whole-class discussions, including measures of students' opportunities to talk and teacher and student actions. These results can help us develop a more profound understanding of whether and how multiple-choice tasks supported by a classroom response system can support teachers in achieving productive whole-class discussions.

Leading whole-class discussions in mathematics in a productive way is identified as a core practice in mathematics instruction. At the same time, productive discussions are rarely seen in classrooms. Thus, we need more knowledge about how different teacher actions in response to students’ comments can affect the students’ learning in these discussions. If research is to be able to produce such knowledge, detailed analytical frameworks and concepts are required in order to describe, analyse and better understand teachers’ actions in whole-class discussions. However, an extensive literature review has identified a lack of such frameworks. Thus, this study sought to propose concepts and refine definitions of existing categories of teacher actions to help develop an analytical framework. This was done by investigating Drageset’s (2014) redirecting, progressing and focusing framework’s potential for conceptualising teachers’ actions during mathematical whole-class discussions generated from multiple-choice tasks supported by classroom response system technology. The analysed data consisted of 35 mathematical whole-class discussions in secondary schools (students aged 13-17 years) in Sweden and the UK. The results suggest five new categories of teacher actions and enrichments of two existing categories in the explored framework.

The aim of this paper is to investigate the potential of Ruthven's (2009) framework the Structuring Features of Classroom Practice (SFCP) as a tool to analyze empirical data to conceptualize and analyze teachers' reasoning about technology integration in the mathematics classroom. The framework is tested on interview data from a Swedish design research project seeking to develop design principles for Classroom Response System (CRS) tasks. The results show that the framework captures a large part of teachers' ways of reasoning, while the parts it does not capture are related to students' attitudes and behaviors. If the SFCP framework aims at capturing key features of classroom practice, and is to be built on a system of constructs closer to the 'lived world' of teacher experience and classroom practice, it would benefit from an extension.