Analysis of Errors in the Semiotic Representation of Fractions among Elementary School Students

Khadijah Khadijah

doi:10.35877/454RI.eduline4475

Authors

Khadijah Universitas Negeri Makassar, A.P. Pettarani, Makassar 90224, Indonesia

DOI:

https://doi.org/10.35877/454RI.eduline4475

Keywords:

Semiotic Representation, Fractions, Student Errors, Numerator–Denominator, Representation Analysis

Abstract

This study aims to analyze elementary students’ semiotic representation errors in fractions through tasks requiring the conversion of area diagrams into symbolic fraction forms. Using a qualitative case study design, two students were selected as participants. Data were collected through fraction worksheets consisting of five sets of circular area diagrams with shaded parts, supplemented by written documentation of students’ responses. Data analysis was conducted through four stages: (1) identifying students’ answers, (2) coding error types based on semiotic representation theory, (3) examining unit coherence and fraction structure, and (4) determining error patterns for each subject. The findings show that both students experienced difficulties in identifying the whole and in understanding the relationship between shaded parts and the total number of equal parts. The first subject (S1) correctly identified the numerator but assigned the denominator as the total number of small segments across the entire row of diagrams, resulting in fractions less than one although the context represented improper fractions. The second subject (S2) displayed more complex errors by using different units for the numerator and denominator, leading to fractions that lacked valid mathematical meaning. These errors stem from misconceptions of units, confusion in the roles of numerator and denominator, and challenges in converting visual representations into symbolic forms. The results highlight the need for instructional approaches that strengthen students’ understanding of units, fraction structures, and representational flexibility.

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