Exploring preservice teachers’ PCK on fractions: Insights from the fraction-as-operator sub-construct

Teachers’ understanding of fractions—especially the fraction-as-operator interpretation—is essential for students’ learning of rational numbers, yet research shows persistent weaknesses in this area. This study presents an empirical analysis of Spanish preservice primary teachers’ pedagogical content knowledge (PCK) regarding the fraction-as-operator, using a content representation aligned with the mathematical knowledge for teaching framework. A total of 263 third- and fourth-year students of different specialization completed six fraction-focused items. Through directed content analysis, 53 indicators linked to PCK subdomains were generated. The results show low PCK, with limited identification of teaching and learning difficulties. The operator interpretation appeared in fewer than 15% of responses, despite being explicitly included in the task. Differences between academic years and specializations were minimal, indicating limited PCK development. These findings point to program-level challenges in initial teacher education within a European generalist-teacher model and highlight the need to strengthen opportunities for developing deeper, more diagnostically oriented PCK.