There are at least 5 different answers to this question, says a new study in Journal of Educational Psychology. Researchers say they identified 5 clusters of students that use different blends of these 2 types of knowledge. If teachers could classify their students into these 5 clusters, they would be better able to tailor instruction to children’s needs in learning fractions, the researchers write.
“The existence of these clusters suggests that there may be more than one way in which children draw on conceptual and procedural knowledge,” the researchers write. “It is possible that some children focus on learning procedures, other children focus on learning concepts, and a third group of children learns procedures and concepts in tandem.”
Previous research has drawn different conclusions about what type of knowledge students acquire first, with some studies finding that children need conceptual knowledge to solve fraction problems while other studies finding that children can work with fractions procedurally with little sign of conceptual understanding.
The reason for these conflicting results may be that students are using different combinations of these 2 types of knowledge, the researchers write. The 5 clusters identified in the study are: Lower procedural, lower conceptual, higher-procedural-lower conceptual, lower procedural-higher conceptual and higher conceptual-higher procedural.
Students who were weakest on procedural knowledge or on conceptual knowledge had the most difficulty learning fractions, according to the study. There were disproportionately more boys in the higher conceptual-lower procedural cluster. But the number of boys and girls was similar in the higher conceptual-higher procedural cluster.
Students’ individual differences may have less to do with developmental processes than with the facility and interest that different children have in learning procedures and concepts, according to the researchers. The different clusters may also be the result of different teaching practices, the researchers note.
The data for the study is from a larger intervention study on assessing the effectiveness of training programs in increasing understanding of fractions. A total of 318 Grade 4 and 5 students in the U.K. completed an assessment of fractions understanding that included subscales for conceptual and procedural knowledge. Each of the items in the 40-item measure was coded as either conceptual or procedural.
The researchers write that the 5 clusters identified in their study may be plausible profiles for math understanding in general.
Recent research has demonstrated that children learning of addition may exhibit similar kinds of differences in conceptual and procedural knowledge,” the researchers write.
Individual Differences in Conceptual and Procedural Knowledge When Learning Fractions,” by Darcy Hallett, et al., Journal of Educational Psychology, 2010, Volume 102, Number 2, pps. 395-406.