Abstract
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 semiotic-conceptual 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.
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Notes
- 1.
Because Formal Concept Analysis (FCA) has been presented many times at this conference, this paper does not provide an introduction to FCA but there is an example with some explanation in Sect. 5. Further information about FCA can be found, for example, on-line (http://www.fcahome.org.uk) and in the main FCA textbook by Ganter and Wille (1999).
- 2.
‘Interpretation’ in SCA is an anonymous sign and refers to a function. ‘Having a different interpretation’ in SCA means using a different function. Different interpretations can still lead to the same denotation. This is different to how ‘interpretation’ is used in ordinary language.
- 3.
A tolerance relation is symmetric and reflexive. An equivalence relation is also transitive.
- 4.
A reader who is unfamiliar with FCA could read Sect. 5 first because it contains an example of a concept lattice.
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Priss, U. (2016). A Semiotic-Conceptual Analysis of Conceptual Learning. In: Haemmerlé, O., Stapleton, G., Faron Zucker, C. (eds) Graph-Based Representation and Reasoning. ICCS 2016. Lecture Notes in Computer Science(), vol 9717. Springer, Cham. https://doi.org/10.1007/978-3-319-40985-6_10
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