In this paper we outline the main tenets of the commognitive approach and we exemplify its application in studies that investigate the learning and teaching of mathematics at university level. Following an overview of such applications, we focus on three studies that explore fundamental discursive shifts often occurring in the early stages of studying Calculus. These shifts concern the lecturers' and students' communicative practices, routines of constructing mathematical objects and ways of resolving commognitive conflicts. We then propose that commognitive constructs such as subjectification can be deployed towards ‘scaling-up’ the hitherto fine-grained focus of commognitive analyses. Finally, we conclude with observing how the commognitive approach relates to constructs from other sociocultural approaches to research in university mathematics education, such as “legitimate peripheral participation” from the theory of Communities of Practice and “didactic contract” from the Theory of Didactic Situations

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Can instructional quality be measured using TIMSS items on how often certain instructional practices are used in the mathematics classroom? We focused on three instructional practices that have been the topics of longstanding debates in the educational literature: memorizing formulas, listening to the teacher, and relating mathematics to daily life. In a multi-level multiple regression analysis, we examined how class-level responses to these items predicted mathematics achievement. In Sweden, across four waves of TIMSS, relating to daily life was a negative predictor of achievement, whereas memorizing formulas and listening to the teacher were positive predictors. This was also the typical pattern of results across all countries participating in two waves of the international TIMSS. Our findings are in line with certain positions on the abovementioned debates. Although conclusions are limited by the correlational nature of the data, we argue that TIMSS is a promising tool for evaluating the effectiveness of different instructional practices. We also suggest several improvements.

The aim of this article is to develop analytical tools for studying mathematical communication in collaborative activities. The theoretical construct of contextualization is elaborated methodologically in order to study diversity in individual thinking in relation to effective communication. The construct of contextualization highlights issues of diversity in collaborative activities as it emphasizes how students may struggle differently with a learning activity. The interaction of students (12 to 13 years old), playing a specifically designed dice game, is used as an example for illustration. The article shows how accounting for the focal events of the interlocutors, and the contexts in which they contextualize these events, help in organizing our thinking about mathematically effective communication in collaborative activities.

have developed a methodological framework, which aims at characterizing the students' mathematical discourses while they are working in groups. In this study, I focus on an important aspect of this methodological framework, namely the interactive flowcharts. The aim of this study is to suggest two complementary analyses for the construction of the interactive flowcharts: an additional analysis by means of the analytical construct of contextualization as well as an analysis of types of mathematical discourses. Based on data from a study of how four groups of Swedish engineering students collaboratively construct concept maps in linear algebra. I show that the two complementary analyses make the construction of the interactive flowcharts more coherent and transparent, and hence, more reliable. Furthermore, the two complementary analyses dramatically changed the picture as to whether the studied discourses were to be seen as mathematically productive or not. In the end of the article, I discuss the possibilities of performing the suggested additional analyses within the original methodological framework.

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