Commognitive analyses of the learning and teaching of mathematics at university level: the case of discursive shifts in the study of Calculus

Abstract

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

Where form and substance meet: using the narrative approach of re-storying to generate research findings and community rapprochement in (university) mathematics education

“…In addition to this use of the term, a further notion of story emerged in the course of the study which aligns well with discursive approaches to the study of mathematics teaching and learning (generally: Sfard, 2008; specifically to university mathematics: Nardi, Ryve, Stadler & Viirman, 2014): the mathematicians have their own 'stories', their own ways of articulating how they make sense of their students' learning and their own pedagogical practices, and how they relate to the colloquial and literate discourses (Sfard, 2008, p. 299) of mathematics education as a discipline. The term discourses here covers both ways of speaking about and the practices of mathematics education.…”

Research on Teaching and Learning Mathematics at the Tertiary Level: State-of-the-Art and Looking Ahead

“…Very recently, there has been increasing interest in discursive approaches into research, with a significant influence being made by the publication of Sfard's (2008) book on the Commognitive framework (see also Nardi et al 2014b). Our review identified recent studies using the Commognitive framework for the analysis of university teachers' discursive practices in calculus courses (Park 2015;Viirman 2014Viirman , 2015; and of Calculus textbooks (Park 2016).…”

Transition from School to University Mathematics: Manifestations of Unresolved Commognitive Conflict in First Year Students’ Examination Scripts

“…The theory of commognition has become a widely used discursive approach in mathematics education (Tabach and Nachlieli 2016) and is also now used more and more in studies at university level (Nardi et al 2014). In this theory, discourses are defined as Bdifferent types of communication, set apart by their objects, the kinds of mediators used, and the rules followed by participants and thus defining different communities of communicating actors^ (Sfard 2008, p. 93).…”