CoRe as a tool to evaluate the pedagogical knowledge of future teachers about the fraction as an operator

Diana Herreros-Torres Maria T. Sanz ^* Carlos B. Gómez-Ferragud

• University of Valencia, Valencia, Valencian Community, Spain

Numerous studies have shown that one of the fundamental factors for effective teaching is the possession of an adequate Pedagogical Content Knowledge (PCK). This knowledge enables teachers to effectively translate specific topics for their students and requires strong support during teacher training, as it is developed throughout the professionalization process. This study aims to determine whether the Content Representation (CoRe) instrument, widely used in international research, aligns with the three components defined by the Mathematical Knowledge for Teaching model for assessing PCK: students learning, teaching and curriculum. To this end, the instrument focuses on a specific mathematical concept, the construct fraction as an operator, and was administered to 263 prospective teachers at a Spanish university. The results reveal the reliability of the scale scores in the sample, and confirmatory factor analysis demonstrate a stable underlying structure, showing that the CoRe questions aligns satisfactorily with the three associated components. However, the findings also highlight notable deficiencies in the participants’ PCK, especially in understanding students’ difficulties and planning effective teaching methodologies. These results emphasize the need to integrate tools like CoRe into teacher education programs to address these gaps and better prepare future teachers to teach complex mathematical concepts, such as fractions as operators.