Transitions between conceptual and procedural knowledge profiles. Patterns in understanding fractions and indicators for individual differences

Knowledge profiles in conceptual and procedural fraction knowledge can vary among students. Given the crosssectional design of previous studies, it is unclear whether these profiles can be altered or remain stable. Accordingly, we investigated (1) profiles of conceptual and procedural fraction knowledge, (2) their longitudinal transitions, and (3) the underlying factors. Data from N = 166 grade 7 students who participated in an intervention study with a pre-posttest design were analyzed. A latent transition analysis revealed six distinct profiles characterized by equal strength or weakness and varying conceptual and procedural knowledge levels, replicating individual differences in fraction knowledge. The longitudinal analysis showed that the knowledge profiles tended to be stable. Moreover, the profile transitions indicated gradual differences in the two types of knowledge rather than students catching up in one type of knowledge. Furthermore, the results suggest that basic arithmetic competence, and mathematics anxiety are related to profile membership. Educational relevance statement: Studying individual differences in conceptual and procedural fraction knowledge is highly important in education. It helps educators gain valuable insights into how students grasp this fundamental mathematical concept, as they can identify diverse knowledge profiles and underlying factors. By understanding these differences, teachers can develop tailored instruction to meet the specific needs of each learner, ultimately enhancing their understanding and mastery of fractions. This research deepens the understanding of fraction learning and offers valuable guidance for creating more effective and personalized teaching approaches.