Evaluating fraction understanding among higher secondary students in Mexico: a cross-sectional analysis

Abstract Fractions are essential for students’ success in higher mathematics, yet many learners struggle to develop robust conceptual understanding in this domain. This study investigates fraction-related “mental objects” among a convenience sample of 292 first- (15–16 years old) and second-year (16–17 years old) higher secondary students from five public schools in Mexico City. Drawing on Freudenthal’s phenomenological ideas and more recent frameworks for fraction understanding (e.g., part-whole, operator), we developed a pencil-and-paper test comprising six tasks: four involving graphic or pictorial representations (discrete and continuous), one focusing on fraction arithmetic, and one requiring problem-solving with fractions. Results indicate that while students in both grades displayed basic competence with standard fraction operations and certain representations, they had significant difficulties with tasks requiring redefinition of the whole (“parts of parts”) or “what is left” scenarios. Notably, second-year students did not consistently outperform first-year students on fraction arithmetic, suggesting a reliance on memorized rules that may erode over time. Although these findings cannot be generalized to the entire Mexican education system, they highlight areas in which fraction teaching—particularly with varied representations and conceptual connections—might be strengthened. Future research with larger, more diverse samples could further clarify the implications for curriculum and instructional practices at the national level.