Technology in University Mathematics Education

We present a new classification of technologies and their didactic functions, based on the anthropological theory of the didactic and, in particular, on the media-milieu dialectic. Drawing on this framework, we examine how research on university mathematics education (UME) has focused on different aspects of technology use, while other aspects remain to be considered more closely. We observe, in particular, that a large part of the existing research literature has focused on small-scale experiments with ready-made tools (such as computer algebra systems) and more recently also on the use of online platforms for teaching and disseminating mathematics. Adopting largely the viewpoint of university mathematics teachers, such research explores new possibilities for undergraduate mathematics teaching, taking into account its great heterogeneity of audiences. Research has so far been much less attentive to the institutional forces that drive or inhibit the use of technology in universities, as well as to the changes in mathematical contents which such use often implies, locally (e.g., certain mathematical methods cease to be taught) and more globally (e.g., certain mathematical domains become more or less privileged). Some parts of the research object are intensively investigated, most notably the use of CAS in basic university mathematics teaching, while others – such as programming as a tool for learning and doing mathematics – are only emerging as phenomena to be studied.