Analyzing students’ fraction strategies: a case study of high-achieving middle school learners

Year 2025, Volume: 6 Issue: 2, 77 - 91, 26.12.2025

Aygül Kartal , Niymet Demirci

https://doi.org/10.5281/zenodo.17995307

Abstract

The aim of this study is to examine the cognitive strategies that academically successful middle school students employ when solving problems involving fractions, and to explore how these strategies influence their mathematical thinking and problem-solving processes. Adopting a qualitative case study design, the research involved students from 5th to 8th grades who demonstrated high achievement in mathematics. Data were gathered through a semi-structured interview form that focused on key components associated with reasoning about fractions—such as estimation, operational understanding, reference benchmarks, magnitude comparison, and equivalence. Content analysis and thematic coding techniques were used to analyze the data. The findings suggest that students' strategy use is closely related to their conceptual and procedural understanding of fractions. Students who employed intuitive, flexible strategies demonstrated deeper mathematical reasoning, while those who relied on rule-based methods produced more procedural and limited responses. These cognitive patterns were directly reflected in the nature and effectiveness of their mathematical thinking. The study also suggests that reasoning about fractions develops through instruction and can be observed at varying levels—basic, intermediate, and advanced. Accordingly, number sense should be approached as a foundational competence in mathematics education. Instructional practices should integrate visual models, estimation activities, conceptual tools, and strategy-based tasks to better support students’ mathematical development.

Keywords

fractionalnumbersense , mathematiceducation , qualitativeresearch , middileschoolstudents , problemsolvingstrategies

Ethical Statement

This study was conducted in compliance with ethical research principles. The data were collected in 2024 through voluntary participation of students, without collecting any identifying personal information. Since the research did not involve any clinical procedures, sensitive data, or intervention with human physiology, and was conducted in an educational setting, ethical approval was not required under the national regulations. Informed consent was obtained from all participants and their legal guardians.

Supporting Institution

This research was independently conducted by the author without the support of any specific funding agency or institutional grant. The study is not affiliated with any thesis project or funded research.

Thanks

The author would like to express sincere thanks to the students who participated in the interviews, as well as their families for allowing their involvement in this study. The author also appreciates the support of colleagues who provided feedback during the development of the data collection tools.

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