Semiotic Representations In The Learning Of Rational Numbers By 2nd Grade Portuguese Students

Floriano Viseu,Luís Menezes,Ana Maria Costa,Ana Luísa Pires

doi:10.26822/iejee.2021.216

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 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.

Highlights

Mathematics is a human activity and one of the oldest sciences, occupying an important place in the school curriculum
Given the nature of mathematical elements, being unique with regard to teaching and learning, it implies using good and multiple representations of mathematical ideas (Duval, 1995, 2003; Ponte et al, 2007; Ponte & Quaresma, 2012). Such a claim, which is widely accepted, is shown to be even more relevant for learning in the early years of schooling, since children's thinking, at this age, relies on the manipulation of concrete ideas (Canavarro & Pinto, 2012). An example of this is the teaching of rational numbers in the Portuguese early Primary school grades (1 to 4), which represents a great challenge for teachers, especially since the last curriculum changes determine that the learning of fractions, among other topics, should start earlier, in the earlier grades (Ministério da Educação e Ciência [MEC], 2013)
When we introduced the topic 'Unit Fractions', students explored the division of the unit into equal parts, a topic already studied with natural numbers, and provided a representation of the situations covered in the tasks selected for the study of this topic

Summary

Introduction

Mathematics is a human activity and one of the oldest sciences, occupying an important place in the school curriculum This school subject is quite different from most other subjects that students have to learn in school because its object of study is of an abstract nature (Davis & Hersh, 2020; Ponte et al, 2007). Given the nature of mathematical elements, being unique with regard to teaching and learning, it implies using good and multiple representations of mathematical ideas (Duval, 1995, 2003; Ponte et al, 2007; Ponte & Quaresma, 2012) Such a claim, which is widely accepted, is shown to be even more relevant for learning in the early years of schooling, since children's thinking, at this age, relies on the manipulation of concrete ideas (Canavarro & Pinto, 2012). An example of this is the teaching of rational numbers in the Portuguese early Primary school grades (1 to 4), which represents a great challenge for teachers, especially since the last curriculum changes determine that the learning of fractions, among other topics, should start earlier, in the earlier grades (Ministério da Educação e Ciência [MEC], 2013)

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Conclusion