How do secondary students develop the meaning of fractions? A hermeneutic phenomenological study

Understanding various meanings of fractions is a foundation to learn related fractions topics. However, students are struggling with this essential topic. This hermeneutic phenomenological study aims to further investigate the meaning of fractions developed by secondary school students, the process of constructing the meaning using models, and factors that hinder the development of the meaning. It involved twenty-two students given fractions tasks, and some students of the different categories of mathematics ability were selected to be interviewed. A thematic analysis using NVivo-12 found that some students interpret fractions as a tool and integers. Most of the students in all categories tend to espouse fractions as ratio and quotient. However, they cannot use the models to represent the meanings. This study reveals that the students’ developed meanings of fractions are limited and different from what primary students have. In addition, there is an inconsistency between the espoused meanings and the use of models. The limitation and inconsistency are considered to be affected by teachers’ lack of content knowledge on the topic and less attention to using models in teaching fractions. This study implies that (mathematics) teachers education should pay more attention to the meaning of fractions and their related models in learning.