Os números racionais e suas diferentes representações na reta numérica: os erros de alunos do ensino fundamental II

Abstract

The present study aims to characterize errors made by middle school students in solving a question involving the placement of rational numbers with different representations (fractions, decimals, and percentages) on the number line. To achieve this goal, it was analyzed a question applied to 203 students (across sixth, seventh, eighth, and ninth grades) from a State School located in the West of Paraná, with Error Analysis and Content Analysis as theoretical and methodological frameworks. By conducting a detailed analysis of the students' responses, patterns were identified, and the following error categories were established: incomplete resolution, failure to recognize percentage representations and locate them on the number line, distraction, and lack of articulation between the representations of rational numbers. The study concludes that out of the 129 students who attempted the question, 70.5% answered incorrectly by using inconsistent locations on the number line, 28% partially solved the question by demonstrating an understanding of fractions as quotients, and 1.5% of the students answered correctly, albeit with occasional errors considered as distractions. The analyses revealed a lack of flexibility in converting between the different representations of rational numbers on the number line, suggesting new teaching strategies to enhance the understanding of this content throughout middle school. Thus, we emphasize the relevance of educational products for the training of Mathematics teachers in middle school, from sixth to ninth grades, with activities that can help promote the integration of concepts of different representations of rational numbers, considered fundamental for students, both in their academic and everyday lives.