Abstract
Undergraduate students’ engagement with mathematical discourse when defining geometric solids is analysed and compared with what their lecturers expect them to do. The theory of commognition is adopted as the theoretical framework, which permits the characterisation and comparison of their discursive activities, and may lead to the identification of potential commognitive conflicts. The participants were forty-five undergraduate students (primary pre-service teachers) and their lecturers. A worksheet with questions about defining geometric solids was used as a data collection instrument. The students, in small groups, had to discuss and write their answers, and the lecturers were asked what they expected from their students. Results show three main areas of mismatch between students’ engagement in mathematical discourse and what their lecturers expected from them. There is no clear consensus across the students on how to define or on what a definition is or on which criterion to use when selecting a definition.
Highlights
Research at university level in the field of mathematics education has been the focus of interest of many studies and it has increased its presence in specific journals like the International Journal of Research in Undergraduate Mathematics Education (IJRUME) and the journal Problems, Resources, and Issues in Mathematics Undergraduate Studies (PRIMUS)
In order to design the questions of the worksheet, it was taken into account that, for us, the process of defining is the one that begins with the identification and description of the characteristics of objects and ends with the construction of a formal mathematical definition
For us, the process of defining is the one that begins with the identification and description of the characteristics of objects, continues with the construction of several preliminary definitions and ends with the selection of one of them, which will become the formal mathematical definition, the results have been organized around three themes: how students describe the solids, how they construct definitions for them and how they choose what they consider the best definition
Summary
Research at university level in the field of mathematics education has been the focus of interest of many studies and it has increased its presence in specific journals like the International Journal of Research in Undergraduate Mathematics Education (IJRUME) and the journal Problems, Resources, and Issues in Mathematics Undergraduate Studies (PRIMUS). Following this characterization of defining as a sociocultural practice, a sociocultural approach is adopted in this work when studying how undergraduate students construct definitions: Sfard’s (2008) theory of commognition This theory ( called commognitive framework) considers the discourse as the principal object of attention, which “sets this approach apart from other types of participationists’ research” Cooper and Karsenty (2018) state that these four discursive properties permit them to compare the patterns of communication of different communities (in their study, lecturers and mathematicians) In this paper, those properties are used in the characterisation of students’ discursive activity when defining geometric solids, and in the discursive activity that their lecturers expect from them. This permits their comparison in order to identify similarities and differences, which could indicate potential commognitive conflicts
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