
06388985
j
2015a.00687
GrenierBoley, Nicolas
Some issues about the introduction of first concepts in linear algebra during tutorial sessions at the beginning of university.
Educ. Stud. Math. 87, No. 3, 439461 (2014).
2014
Springer Netherlands, Dordrecht
EN
H65
D75
D20
linear algebra
FUG concept
methodology
students' activity
teacher's activity
doi:10.1007/s1064901495640
Summary: Certain mathematical concepts were not introduced to solve a specific open problem but rather to solve different problems with the same tools in an economic formal way or to unify several approaches: such concepts, as some of those of linear algebra, are presumably difficult to introduce to students as they are potentially interwoven with many types of difficulties as formal ones and far away from the actual knowledge of the students. The purpose of this paper is to propose a methodology for studying the introduction of such concepts in linear algebra during tutorial sessions at the beginning of university, the wording of the concepts being yet presented during lectures. For this purpose, we amend a general methodology of {\it M. Pari\`es}, {\it A. Robert} and {\it J. Rogalski} [``Comment l'enseignant de math\'ematiques, en classe, met ses \'el\`eves sur le chemin des connaissances: un point de vue m\'ethodologique en didactique des math\'ematiques'', Trav. Apprentiss., No. 3, 95123 (2009)] inside the general framework of activity theory. This methodology lets us take into account several specificities of these concepts and studies the mathematical activity the teacher organises for students and the way he manages the relationship between students' actual activities and mathematical tasks. We also present an implementation of this methodology based on a French university course to illustrate our approach and discuss its possibilities.