What Skills Do Students Have in Solving Proportionality Problems?

Problem solving is a central skill in mathematics education, yet it remains a persistent challenge for many students, particularly in proportional reasoning. This concept, essential for success in mathematics and science, requires abstract thinking and the coordination of multiple quantities through multiplicative relationships.

Research shows that difficulties persist well into secondary school, with consequences for academic performance and confidence. In this exploratory study, we investigate the abilities of 13-year-old students in French-speaking Belgium to solve simple direct proportionality problems, classified according to Vergnaud’s (1990) framework. Using a specially designed diagnostic test, we aim to identify the problem types causing the greatest difficulties. The diagnostic approach, rooted in both internal and external assessment practices, allows for the early detection of conceptual obstacles and the adaptation of teaching strategies.

Our preliminary findings reveal distinct performance variations depending on problem structure, with certain categories posing significant cognitive challenges. Performance varies significantly according to this typology, with a critical rate of 59% for the fourth proportional group. Interpreted as a gap in mastery (Leclercq, 2003), this result identifies 41% of students as a target population for remediation. This study fills a gap in the francophone context and provides a basis for designing effective interventions to strengthen proportional reasoning skills in lower secondary students.