The role of metaphors in interpreting students’ difficulties in operating with percentages: A mixed method study based on large scale assessment

The issue of students’ difficulties in processing operations with percentages has been addressed in several international research studies from a qualitative perspective. In this study, we analyze students’ difficulties on this topic, focusing on the transition from middle school to high school with a mixed methods research design. We focus on students’ responses in a specific task belonging to the Italian large-scale assessment analyzed through the Rasch model, and we deepen the task analysis thanks to interviews, which enlightened image schemas and metaphors underlying students’ reasoning. From the qualitative point of view, the Rasch model shows that students’ difficulties in dealing with percentages is a macrophenomenon that involves the higher levels of competences. From the qualitative point of view, the metaphoric approach outlines the image schemas that foster the correct conceptualization of percentage and those that hinder their correct learning and can be one of the possible causes of the emerging aforementioned macrophenomenon.