Nonlinear learning of linear algebra

Abstract

Students find difficulty in learning linear algebra because of the abstraction and formalism associated with concepts such as vector space, linear independence, rank and invertible matrices. Learning the necessary procedures becomes insufficient, and imitating worked examples does not guarantee the maturity level necessary for understanding these concepts. Instructors who seriously consider education reform look for teaching modes that induce active learning; the author resorted to journal writing in the particular context of coordinating between the different definitions and theorems related to the invertibility of a matrix: students were required to write about the various modes of representing invertible matrices, trying to guide them so as not to confuse the object with its representation, a notion referred to by Dorier as cognitive flexibility. As an auxiliary result, learners were observed in the process of building the construct of invertible matrices. The topic of invertible matrices was chosen because it appears that it weaves through the material, and plays the role of a unifier concept. In their final draft, many journals culminated into a student personal paper, entitled ‘Many ways to show invertibility: how to choose the most fit method?' Above all, the project helped students reclaim their intuition and common sense about mathematics.