The role of physical representations in solving number problems: A comparison of young children’s use of physical and virtual materials

This research aims to explore the role of physical representations in young children’s numerical learning then identify the benefits of using a graphical interface in order to understand the potential for developing interactive technologies in this domain. Three studies are reported that examined the effect of using physical representations (blocks) on children’s (aged 4–8 years) strategies in a numerical partitioning task. The first study describes the role of certain perceptual and manipulative properties of the physical materials, comparing performance with paper and no materials conditions. The study demonstrated an advantage for physical materials and identified a key property reflecting strategies: whether blocks were moved individually or as a group. This finding was investigated in the second study by comparing strategies when children were asked to constrain movements to one block at a time. Significant differences were found in strategies used although differences were reduced by children moving individual blocks quickly in succession using both hands. The final study examined the effect of constraining manipulation using a graphical user interface, where on screen squares could only be moved individually. As predicted, significant differences were found for strategies used between physical and virtual conditions. The findings suggest that differences in the manipulative properties of interfaces may affect children’s numerical strategies and are discussed with respect to the design of effective interactive technologies in this domain.