Individual differences in conceptual and procedural knowledge when learning fractions.

Abstract

Previous research on children's conceptual and procedural understanding of fractions, and other arithmetic skills, has led to contradictory conclusions. Some research suggests that children learn conceptual knowledge before procedural knowledge, some suggests that they learn procedural knowledge before conceptual knowledge, and other research suggests that they learn conceptual knowledge and procedural knowledge in tandem. We propose that these contradictory findings may be explained by considering individual differences in the way that children combine conceptual and procedural knowledge. A total of 318 Grade 4 and 5 students in the United Kingdom (mean age = 9.0 years) completed a measure of fractions understanding, which included subscales of conceptual and procedural knowledge. A cluster analysis identified 5 distinct clusters that differed from each other in terms of their relative success with conceptual and procedural problems. The existence of these clusters suggests that there may be more than one way in which children draw on conceptual and procedural knowledge. Some children rely more on procedural knowledge and others more on conceptual knowledge, but these differences may not be related to developmental processes. The children in the 5 clusters differed in their total fractions performance and in their understanding of intensive quantities. These differences suggest that children who rely on conceptual knowledge may have an advantage compared to those who rely more exclusively on procedural knowledge.