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

Floriano Viseu; Ana Luisa Pires; Luís Menezes; Ana Maria Costa

Vol. 13 No. 5 (2021) IEJEE

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

Floriano Viseu
Ana Luisa Pires
Luís Menezes
Ana Maria Costa

Published July 14, 2021 | Pages: 611-624 | Views: 493

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Abstract

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 2^nd 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.

<p>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 2<sup>nd</sup> 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.</p>

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Keywords

Registers of Semiotic Representation, Mathematics, Learning rational numbers, Unit fraction, Primary School

Affiliations

Floriano Viseu

Universidade do Minho

Ana Luisa Pires

Luís Menezes

Polythecnic of Viseu

Ana Maria Costa

Higher School of Education. Polytechnic of Viseu

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How to Cite

Viseu, F., Pires, A. L., Menezes, L., & Costa, A. M. (2021). Semiotic Representations in The Learning of Rational Numbers by 2nd Grade Portuguese Students. International Electronic Journal of Elementary Education, 13(5), 611–624. Retrieved from https://iejee.com/index.php/IEJEE/article/view/1453