Using computer resources in teaching and learning advanced mathematics Claire Cazes * , Magali Hersant * , Ghislaine Gueudet ** , Fabrice Vandebrouck * The use of computer resources in the teaching of mathematics at the university in France has been institutionally promoted for several years. It lead to the production of several softwares and associated teaching designs. However, using computers to teach mathematics for undergraduates is still far from being widespread in France yet. Several researches in various countries studied the use of CAS and of dynamic technological environments at university level. We will not consider such tools here; our study is dedicated to softwares that allow drill and practice for undergraduate mathematics (in fact most of them allow much more than that, as we will see later on). The research presented here aims at studying the effective use, and the possible uses of such softwares. The objectives displayed by the promoters of these products are mostly of two kinds: Encourage self-directed work by the students; Allow activities suiting each student’s personal pace. Are these objectives fulfilled? Moreover, we wanted to investigate how such products could contribute to enhance a rich mathematical activity for the student. More generally, how does the use of such a software affect the traditional teaching-learning patterns? We will present here elements of answers to such questions. 1. Related works and analysis levels In the last decade, many research works have examined the use of technology to teach mathematics. However, only a small amount of them (14 % of the articles about mathematics education and technology published between1994 and 1998 according to Lagrange&al 2003) are dedicated to drill and practice programs, or e-learning. General surveys about computers in mathematics education mention them, and sometimes state very interesting results about their use. Ruthven and Henessy (2002) introduce the term “courseware” for such softwares, and we are going to do the same here. Because we aim at studying different products in various settings, a first objective for us has been to design a common analysis frame and process. It appeared necessary to consider three levels of analysis. Level 1: General description of the courseware: mathematical content, structure, public… Level 2: Setting associated: frequency and length of the sessions, articulation with ordinary lessons, role of the teacher, presence of a logbook…the planned setting and the effective one must be both analysed and compared. Level 3: Didactic analysis: for a given topic, detailed a priori analysis of the exercises proposed, and analysis of the students activity. We will refer here to didactic research specialised in the concerned topic, and to Robert’s classification of mathematics exercises texts (2003). These three levels are obviously strongly related to each other. However, they are helpful to clarify our observations. We use them to present the results we state. These results stem from five studies that we will briefly describe. 2. Five cases studies The five studies correspond to three different coursewares, and three settings. For the sake of brevity, we will not give here a full description of the softwares, but only their main features. Further details will be presented along with the results. The first teaching design observed used UEL 1 (which stands for “on-line university”), a courseware designed to permit distance learning for university students. UEL covers the whole mathematics * Equipe Didirem, Université Paris 7. ** Equipe DidmaR, Université Rennes 1.