Combining different theoretical perspectives for analyzing students’ difficulties in vector spaces theory

Abstract

This paper originates from our doctorate research project, in which we investigated graduate and undergraduate students’ errors and difficulties in vector space theory (VST). After a brief account of the whole study, we will focus on the analyses carried out through the lenses of two different theoretical frameworks: Fischbein’s Theory of Tacit Models and Sfard’s process/object duality theory. We also propose a retrospective reflection concerning the reasons why we chose to carry out our analysis according to more than one theoretical framework and why we chose those specific theoretical frameworks as well. Hence this contribution has a double focus: on the one hand it reports on the results drawn from our study on students’ difficulties in VST; on the other hand it presents a personal retrospective reflection on the use of theoretical frames within that study.