Construction of the vector space concept from the viewpoint of APOS theory

We apply APOS theory to propose a possible way that students might follow in order to construct the vector space concept. We describe the mental mechanisms and constructions that might take place when students are learning this concept. We then report on a study that we performed with 10 undergraduate mathematics students through the application of a questionnaire and an interview. In this paper we focus on the coordination between the two operations that form part of the vector space structure and the relation of the vector space schema to other concepts such as linear independence and binary operations.