This book presents the state-of-the-art research on the teaching and learning of linear algebra in the first year of university, in an international perspective. It provides university teachers in charge of linear algebra courses with a wide range of information from works including theoretical and experimental issues.

To a large extent, it lies, no doubt, in what is presented in this work under the title of meta lever, a method which it is certainly interesting to develop and further refine. There exists in mathematics courses a strange prudery which forbids one to ask questions such as, Why are we doing this? -, At what is the objective aimed? -, whereas it is usually easy to reply to such questions, to keep them in mind, and to show that one can challenge these questions and modify the objectives to be more productive or more useful. If we don t do this we give a false impression of a gratuitous or arbitrary interpretation of a discipline whose rules are far from being unmotivated or unfounded. One must also consider the time aspect. Simple ideas take a long time to be conceived. Should we not therefore allow the students time to familiarize themselves with new notions? And must we not also recognize that this length of time is generally longer than that ofthe official length of time accorded to this teaching and that we should be counting in years? When the rudiments of linear algebra were taught at the level of the lycee (college level), the task of first year university teachers was certainly easier: for sure the student's knowledge was not very deep, however it was not negligible and it allowed them to reach a deeper understanding more quickly."