An investigation of middle school students' proficiency levels in transformation between representations in fractions

In this study, the competency levels of middle school students in transforming representations in fractions were investigated using a quantitative research approach with a descriptive survey model. The study consists of six representation types: "Real-Life", "Visual/Number Line", "Visual/Model", "Symbolic", "Linguistic", and "Manipulative". The analyses revealed that fifth and sixth grade students performed better in questions requiring visual/model and real-life input representations compared to other representation types. Conversely, they showed significantly lower performance in questions requiring linguistic input representation. Seventh and eighth grade students, on the other hand, demonstrated higher performance in questions requiring manipulative and symbolic input representations, but faced challenges in questions requiring linguistic input representation. Upon examining input and output representation types, it was found that fifth and sixth grade students struggled most in transforming from linguistic representation to manipulative representation, whereas seventh and eighth grade students faced difficulties in transforming from linguistic to real life representation. Furthermore, as grade level increased, there was an observed improvement in students' performance in questions involving visual/number line, symbolic, linguistic, and manipulative representation types. The more abstract and complex nature of these representation types compared to others may contribute to lower performance among younger students. As students progress through grade levels, their cognitive development and accumulated experience in instructional processes related to these types of representations may facilitate higher performance. Presenting fractions with different representation types during the instructional process can support students' cognitive development.