Instrumental and documentational approaches: from technology use to documentation systems in university mathematics education

In this article we present an instrumental approach in mathematics education, which focuses on the interactions between students, teachers, and artefacts. This approach analyses mediations attached to the use of a given artefact and instruments developed by the subjects from this artefact along instrumental geneses. We draw on three Research Cases at university to illustrate the use of this approach: the first is about students' geneses with a programming technology; the second about students' and teachers' geneses with a virtual learning environment; and the third about textbooks and teachers professional development. We also introduce the documentational approach, which draws on the instrumental approach, but takes into account the broader range of available resources. It distinguishes resources and documents developed by teachers from these resources, and studies teachers' documentation systems. We present a fourth Research Case concerning the documentation system of a mathematics teacher, and focusing on the place of technologies within this system.