id: 06388985
dt: j
an: 2015a.00687
au: Grenier-Boley, Nicolas
ti: Some issues about the introduction of first concepts in linear algebra
during tutorial sessions at the beginning of university.
so: Educ. Stud. Math. 87, No. 3, 439-461 (2014).
py: 2014
pu: Springer Netherlands, Dordrecht
la: EN
cc: H65 D75 D20
ut: linear algebra; FUG concept; methodology; students’ activity; teacher’s
activity
ci:
li: doi:10.1007/s10649-014-9564-0
ab: 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. Pariès}, {\it
A. Robert} and {\it J. Rogalski} [“Comment l’enseignant de
mathématiques, en classe, met ses élèves sur le chemin des
connaissances: un point de vue méthodologique en didactique des
mathématiques”, Trav. Apprentiss., No. 3, 95‒123 (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.
rv: