The role of children’s analogies in the transfer of their knowledge in mathematical modelling processes

The difficulty of transferring mathematical and/or extra-mathematical knowledge from one real-world context to another and the lack of established strategies to facilitate student knowledge transfer have long been a gap in educational research involving mathematical modelling. To address this gap, we developed a framework that shows the relationship between types of analogy and the typology dealing with the context of mathematical modelling and conducted mathematical modelling lessons that elicit various analogies that promote the transfer of children’s personal contextual knowledge. This study aims to empirically clarify what types of analogy contribute to the transfer of mathematical and/or extra-mathematical knowledge when children engage in structurally similar mathematical modelling in real-world contexts. We conducted lessons with two mathematical modelling tasks using similar geometric structures of an ordinary helix on a cylinder, involving 33 grade 5 children in Japan and 22 grade 6 children in Australia. A qualitative analysis of children’s approaches to real-world contexts and their use of analogy in transfers between contexts was conducted using the coded content of target problem solutions described by Japanese and Australian children on their worksheets. These results show that the various analogies elicited in this lesson contribute to the subjectivity of children’s personal contextual knowledge that is evoked when interpreting the task context, as well as dynamics of their contextual knowledge (previously learned mathematical knowledge, manipulative knowledge using 3D miniature, knowledge from physical experience) that is generated, developed, and changed in the process of tackling the task.