The main purpose of this thesis was to explore if there existed one single underlying semiotic function for representation. The problem was examined from both a theoretical and an empirical point of view. In the first part of this thesis the theoretical considerations about Piaget's hypothesis of a single semiotic function are described and compared with a number of alternative approaches. The hypothesis is critically analyzed and its limitations are pointed out. In the second part of this thesis the empirical studies are reported. One of the guiding lines for the experiments performed was the distinction made by Piaget between figurative and operative aspects of representation. The main conclusions to be drawn from the four studies were that they all supported, however tentatively, Piagets hypothesis of a single underlying semiotic function. In terms of figurative and operative aspects of cognition it was concluded that the underlying form (the operative aspect) at different ages is constant across the different representation modes. The differences found in the figurative aspect of representation were bound to the representation media, and could vary as a function of media, task demands and individual differences. In the third part of this thesis problems with representation media and task demands are discussed together with research in related areas of the semiotic function. The general conclusions drawns from this thesis were that there might exist a single underlying semiotic function for representation. The issue is neither simple nor uncomplicated. The distinction made between the figurative and operative aspect of representation is considered as one attempt to narrow down the generality of the hypothesis, and to distinguish between what is expected to be a universal aspect of the semiotic function and what varies as a function of media, task demands and individual-, social- , and cultural differences. / digitalisering@umu

Symboler har alltid varit en viktig del av matematik, därför är det inte konstigt att kunskaperom symbolspråket behövs för att uppnå en full förståelse av ämnet. Den här studiensyftar därför på att utreda användningen av det symboliska språket i den svenska gymnasialaundervisningen ur ett språkvetenskapligt perspektiv. Empirin till det här arbetetbestår av 52 elevlösningar till ett test i matematik samt transkribering av en parintervju.Det insamlade materialet har analyserats utifrån teorier om den metalingvistiska medvetenhetensamt symbolernas semiotiska och epistemologiska funktioner. Det matematiskasymbolspråkets roll i styrdokumenten har också belysts i det här arbetet. Från elevernasfel i testet var det möjligt att åskådliggöra vikten av den metalingvistiska medvetenhetenoch den semiotiska medlingen i algebrainlärningen. Slutligen blev det även tydligt att detmatematiska symbolspråket behöver en mer explicit roll i den svenska matematikundervisningen. / Symbols have always been an important part of mathematics, which is why learning thesymbolic language is necessary in order to acquire a full understanding of the subject.This study aims to investigate the use of the symbolic language in the Swedish uppersecondary school from a linguistic perspective. The data for this study consists of samplesfrom 52 student solutions from a mathematical test, together with one transcribed groupinterview, where two students participated. The analysis is based on theories about themetalinguistic awareness and symbols’ semiotic and epistemological functions. The roleof the mathematical symbolic language described in the steering documents has also beenconsidered in the study. From the mistakes made in the test, it was possible to visualisethe importance of the metalinguistic awareness and the semiotic mediation in algebralearning. In the end, it also became clear that the mathematical symbolic language needsa more explicit role in the Swedish mathematics education.