Understanding Learning Barriers in Fractional Multiplication: An Investigation Using Hermeneutics Phenomenology

Abstract

The multiplication of fractions was considered an easy operation, but it posed a challenge for students. The lack of previous research on this topic, especially at the tertiary level, made it an intriguing subject for investigation. This study aimed to explore the factors contributing to these difficulties and the types of learning barriers students faced. Hermeneutics phenomenology was used as the research design. Fifteen participants, aged between 18 and 25, consisting of 7 boys and 8 girls, were selected for this study. Nine students had a background in natural sciences during high school, while six were from social studies majors. The researcher served as the main instrument, employing a fraction multiplication test with two questions developed by NCTM. Additionally, a semi-structured interview guide was used as an additional instrument. The data obtained were analyzed using NVivo-12-assisted thematic analysis for a simplified coding process. The study findings indicated that students encountered more learning difficulties when dealing with non-routine fraction multiplication problems. For routine problems, the learning obstacles were primarily ontogenic and psychological in nature (carelessness). However, when dealing with non-routine problems, students faced epistemological barriers due to their limited experience with word problems. Moreover, they encountered conceptual obstacles (inability to equivalence and convert fractions to decimal form) and psychological hurdles (doubt) during the learning process.