Making Connections in Math: Activating a Prior Knowledge Analogue Matters for Learning

This study investigated analogical transfer of conceptual structure from a prior-knowledge domain to support learning in a new domain of mathematics: division by fractions. Before a procedural lesson on division by fractions, fifth and sixth graders practiced with a surface analogue (other operations on fractions) or a structural analogue (whole number division). During the lesson, half of the children were also asked to link the prior-knowledge analogue they had practiced to fraction division. As expected, participants learned the taught procedure for fraction division equally well, regardless of condition. However, among those who were not asked to link during the lesson, participants who practiced with the structurally similar analogue gained more conceptual knowledge of fraction division than did those who practiced with the surface-similar analogue. There was no difference in conceptual learning between the two groups of participants who were asked to link; both groups performed less well than did participants who practiced with the structural analogue and were not asked to link. These findings suggest that learning is supported by activating a conceptually relevant prior-knowledge analogue. However, unguided linking to previously learned problems may result in negative transfer and misconceptions about the structure of the target domain. This experiment has practical implications for mathematics instruction and curricular sequencing.