Semiotic Representations in The Learning of Rational Numbers by 2nd Grade Portuguese Students

The use of different registers to represent mathematical concepts improves their understanding. For example, rational numbers can be represented by symbolic or pictorial representations and by natural language, and this kind of transformation between them improves learning. Based on these assumptions, a teaching experiment for the learning of rational numbers by 2nd grade students were conducted to understand the contribution of semiotic representations in the learning of rational numbers, in particular in the topic of unit fractions. Using a qualitative methodology and a content analysis of the students' written productions, the study shows a greater use of the pictorial representation register compared to the other representation types. Students' main difficulties in learning rational numbers relate to the pictorial representation of unit fractions and to understanding the concept of fraction itself. Some of these difficulties are the result of errors such as the misrepresentation of unit fractions by the pictorial register, the association of the concept "half" with multiple unit fractions, the absence of the fraction bar when they use the symbolic register, the use of everyday terms to represent fractions when students use the natural language register, and the misrepresentation of rational numbers when they use the graphic register.