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

Abstract

Knowledge profiles in conceptual and procedural fraction knowledge can vary among students. Given the cross-sectional 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.