| Tóm tắt: | This research analyzed the semiotic representations that students handle in the conceptualization of rational numbers; it was carried out with seventh grade students of a private school in the city of Tunja (Boyacá), who presented difficulty in the conceptual apprehension of the mathematical object, since sometimes they did not use at least one of the three cognitive actions related to semiosis denominated by Duval (2004) as identification, treatment and conversion; that is, they did not find the adequate semiosis to reach the noesis (Duval, 2006). The study was conducted from a qualitative approach, based on action research, following the spiral of Carr and Kemmis (1983) and the theory on which it was based was Duval's Semiotic Representations (2004), where cognitive actions were observed, described and interpreted. The results show that the register of semiotic representation most handled by the students corresponds to the graphic scheme where the representation in the form of a cake predominates from the part-whole meaning, an interpretation that generated obstacles and artificiality in the conceptualization, in addition to establishing treatments in the arithmetic register and conversions between the registers of common language, the arithmetic and the graphic.
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