Continuous analysis of one year of science students' work in linear algebra, in first year of French university

Linear algebra is one of the newest fields students discover in their first year at university. Its abstract nature is often a problem for them. We wanted to know if notions in basic logic are prerequired to succeed in linear algebra, and if y es what kind of previous abilities are needed. We wanted as well to have a better appreciation of what teaching linear algebra consists of and what kind of effects it produces on students. In the following article, we describe the methodology employed to analyse results of standard first year science students in a pretest about basic logic and algebra notions, and in all the tests given to them in linear algebra during a year. Then we try to answer the questions raised above with help of this analysis and its statistical results. Finally we will propose a new organisation of teaching linear algebra according to our hypotheses