| Summary: | Using a qualitative, exploratory, microgenetic research design, this research study examines the strategies that children who had only been taught the part-whole fraction sub-construct used for finding the fraction associated with solving partitive quotient problems over a sequence of tasks. Additionally, a key feature of the Pirie-Kieren theory for growth of mathematical understanding, which has not been previously extended empirically, is elaborated. Nine Year 5 children, who engaged in eight individual task-based interviews, over a six-week period, provide the data for this study. The research found that the research participants used four strategies for finding the fraction related to solving the partitive quotient problems. Further to this, one strategy appeared to resemble the conceptualisation for the part-whole relation. This finding suggests that previous part-whole learning impacts partitive quotient development. Another key contribution of this research is that it shows several ways in which part-whole knowledge impacted children's partitive quotient development. Regarding the theoretical contribution made by the current study, one of the significant findings challenges one aspect of the current Pirie-Kieren model, and therefore, an amendment to the existing model is proposed. An implication of this study for teachers of mathematics is that there should be a greater focus on the concept of a unit when teaching the different fraction sub-construct contexts. In addition, to help learners grow in their understanding of mathematical concepts, it is suggested that there is an increased emphasis on assisting them to develop robust and thorough ideas of concepts when working in local contexts.
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