Recognizing the roles of mathematics in society is an important goal for the teaching and learning of mathematical modelling. The Likert-scales method is a simple and effective tool to assess student appreciation about the utility of mathematics; however, it does not reveal the detailed aspects of student perceptions of the roles of mathematics in society. This study aimed to answer the following research question: how can we assess the detailed aspects of student perceptions of the roles of mathematics in society? An analytical tool consisting of three viewpoints, namely, (1) personal-societal perspectives, (2) clarity of role statements, and (3) specific-general contexts, was developed. It was revealed that students' perceptions of the roles of mathematics in society significantly changed between the phases before and after an experimental teaching program. Namely, the analytical tool developed and used in this study enabled, at least partially, the clarification of the states or changes of students' perceptions of the roles of mathematics in society. Although further attention is required to improve the validity and reliability of the analytical tool, the present study encourages future research on this important topic.