Topic specificity of students' conceptual and procedural fraction knowledge and its impact on errors

Abstract

When learning about fractions, teaching usually follows certain topics - e.g. part of the whole, fraction equivalence, and size comparison. Not yet answered is whether students’ conceptual and procedural knowledge of fractions is coherent between those topics. To answer this question, we performed a latent profile analysis of data from N=1005 six-grade students regarding their conceptual and procedural knowledge in the three above-mentioned topics. Our results confirmed that the level of conceptual and procedural fraction knowledge can vary within students between topics. Furthermore, the analysis of students’ errors showed that conceptual knowledge of fractions within a specific topic is related to topic-specific error types - with conceptual errors (compared to non-conceptual errors) being demonstrated relatively more often by students with low conceptual knowledge. This indicates that to derive adequate support strategies for individual students, differentiated consideration of their topic-specific conceptual and procedural knowledge should be considered.