Remarks on (dis)connectivities across institutional, sociocultural and discursive approaches to research in university mathematics education

In this paper we present the work generated during and after a Working Group session at the BSRLM conference of March 1st 2014 entitled Institutional, sociocultural and discursive approaches to research in (university) mathematics education: (Dis)connectivities, challenges and potentialities. In the session we organised a discussion based on highlights from a Special Issue (SI) for Research in Mathematics Education (entitled Institutional, sociocultural and discursive approaches to research in university mathematics education, 16(2)) which we had just finished writing and editing, together with 20 other colleagues from 11 countries. The approaches covered by the SI papers are: Anthropological Theory of the Didactic; Theory of Didactic Situations; Instrumental and Documentational Approaches; Communities of Practice and Inquiry; and, Theory of Commognition. The papers present recent cutting edge research on several aspects of university mathematics education: institutional practices, analysis of teaching sequences, teacher practices and perspectives, mathematical and pedagogical discourses, resources and communities of practice. In the WG session we invited participants to generate university mathematics education research questions in a small group discussion, and then address these to the whole group in order to discuss how different issues could be dealt with by the different approaches covered by the SI. Our overall aim was to explore how these approaches may offer complementary, overlapping and in some cases diverging or even incommensurable points of departure for dealing with such questions. The participant small groups generated the following list of questions:
(1) How can issues of equity and gender be explored by the frameworks presented in the SI?
(2) What are the praxis and logos in different courses (e.g. in pure and applied mathematics)?
(3) What are the distinct differences of the didactic contract in different courses (including those other disciplines with a strong mathematical component)?
(4) What communication practices can we discern in students’ writing?
In this paper we present short answers from each framework to a (slightly amended version of) one of the research questions asked by the WG participants, namely (4). To this purpose we first outline how we developed a more detailed question based on (4), which, for the purposes of this paper, will act as a common Research Question. We then use this as a platform on which to illustrate the potentialities of the frameworks presented in the SI. We conclude with a few thoughts on ways forward of this work.