Individual differences in conceptual and procedural fraction understanding: the role of abilities and school experience.

Recent research on children's conceptual and procedural knowledge has suggested that there are individual differences in the ways that children combine these two types of knowledge across a number of mathematical topics. Cluster analyses have demonstrated that some children have more conceptual knowledge, some children have more procedural knowledge, and some children have an equal level of both. The current study investigated whether similar individual differences exist in children's understanding of fractions and searches for explanations for these differences. Grade 6 students (n=119) and Grade 8 students (n=114) were given measures of conceptual and procedural knowledge of fractions as well as measures of general fraction knowledge, general conceptual ability, and general procedural ability. Grade 6 children demonstrated a four-cluster solution reflecting those who do poorly on procedural and conceptual fraction knowledge, those who do well on both, those whose strength is procedural knowledge, and those whose strength is conceptual knowledge. Grade 8 children demonstrated a two-cluster solution reflecting those whose strength is procedural knowledge and those whose strength is conceptual knowledge. Cluster in either grade, however, did not vary in distribution across schools and was not related to general conceptual ability or general procedural ability. Overall, these results provide a more detailed picture of individual differences in conceptual and procedural knowledge in mathematical cognition.