A Semiotic-Conceptual Analysis of Conceptual Learning

While learning mathematics or computer science, beginning students often encounter significant problems with abstract concepts. In both subjects there tend to be large numbers of students failing the class or dropping out during the first semesters. There is a substantial existing body of literature on this topic from a didactic perspective, but in our opinion an investigation from a semioticconceptual perspective could provide further insights and specifically analyse the difficulties encountered when learning abstract concepts. This means that both the complexities of the representations of abstract concepts and the conceptual content itself are modelled and investigated separately and in combination with each other. In our opinion a semiotic analysis of the representations is often missing from didactic theories. And in particular, as far as we know, there are not yet any formal mathematical approaches to modelling learning difficulties with respect to semiotic and conceptual structures. Semiotic-Conceptual Analysis (SCA) as presented in this paper aims to fill that niche.