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International Journal of Educational Studies in Mathematics






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This study examined 32 second-grade children’s interactions with six virtual manipulative mathematics apps on the iPad using a novel analysis approach called heatmap analysis. Mathematical topics of the six apps focused on understanding skip counting and place value concepts. Children interacted individually with the apps under the guidance of an interviewer during 30-40 minute clinical interviews. The heatmap analysis revealed patterns in children’s performance on the tasks and suggested individual cases for further analysis. For example, clusters of children showed high or low performance during the skip counting sequence. In the high-performing cluster, one child still struggled to monitor the skip counting process. In the low-performing cluster, one child showed growth on learning tasks but struggled on the assessments, which contained a different representation of the mathematical content and involved greater target numbers than in the learning app. There were fewer variations in place value task performance, but application of interaction techniques influenced children’s growth on one learning app. Although some children showed varying performance when encountering challenging mathematics content in the higher levels of one app, other children inefficiently interacted with the app and did not reach the more challenging content.



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