Children engaging with partitive quotient tasks: elucidating qualitative heterogeneity within the Image Having layer of the Pirie–Kieren model

AbstractThe paper presents findings from a study that examined, through the lens of the Image Having layer of the Pirie–Kieren model, the qualitative characteristics of the images that different children formed when engaging with eight, novel partitive quotient tasks. The Image Having layer is the first point of abstraction within the Pirie–Kieren model. Therefore, this research is significant in aiming to advance theoretical insight into how the notion of child-created images relates to the development of children’s mathematical understanding, in the context of novel for them tasks. This study adopted a qualitative, microgenetic research design and involved nine Year 5 (aged 9–10 years) children. Data based on children’s verbal responses and jottings were collected through multiple trials over eight individual sessions with each child. Analysis of 72 interview transcripts showed that children formed and used a range of different images that varied across tasks but also within the same task. This study provides a nuanced description of qualitative distinctions in the nature of child-created images. It thus reveals varied dimensions of a dynamic process of knowledge development and sense-making. This highlights, for educators, the need to be aware of and adaptive to the varied and dynamic dimensions of knowledge that children draw from, when dealing with novel tasks, and which change as children’s understanding of new mathematical content develops.