Students' problems in the identification of subspaces in Linear Algebra

International audienceThe goal of the study presented in this paper is the investigation of students' problems with exercises concerning central topics of linear algebra courses at university level. We present the results of our analysis of students' work on an exercise about subspaces of . We evaluated the written solutions of the task as well as transcripts based on videos taken of student groups working on the problem. We identified and classified descriptions of vector spaces and subspaces that varied widely and demonstrated highly different skills in working with geometric or formal algebraic objects. We analyzed how far students could progress in a complex reasoning process, and identified those steps in the reasoning process on which students needed support to continue