A Study on Middle School Students’ Perceptions of Repeating Decimal Representations of Rational Numbers

This study aims to examine how the achievement standards, teaching and learning methods, and considerations related to the representation of rational numbers as repeating decimals—outlined in the national mathematics curriculum—are implemented in textbooks, and how students perceive them. To this end, pre-tasks and interviews were conducted with ninth-grade students who had studied repeating decimals. The study revealed that some students understood the relationship between terminating and repeating decimals differently from how it is described in the textbook. While some students distinguished between “fractions that can be expressed as repeating decimals” and “fractions that can only be expressed as repeating decimals,” they often only recognized the linguistic distinction without understanding the mathematical differences or the reasons behind these expressions. Additionally, some students stated that they would follow the intent of the textbook or test-maker even when it conflicted with their own reasoning, and expressed views that there could be ambiguous aspects in mathematics, as well as opinions that the textbook’s definition of repeating decimals needs to be revised. These findings suggest the need to critically reconsider the pedagogical validity of classifying terminating decimals as fractions that cannot be expressed as repeating decimals. As new textbooks are being developed under the 2022 revised curriculum, it is essential to reflect students' perspectives and problem-solving processes, and to interpret the meaning of the curriculum’s achievement standard explanations with greater precision.