Learning to ‘deal’: A microgenetic case study of a struggling student’s representational strategies for partitive division

Abstract

International audienceThis paper focuses on the arithmetical understandings and behaviours of one fifteen-year old student with very low attainment in mathematics, as she worked on a sequence of scenario-based partitive division (sharing) tasks with individually-tailored verbal and visuospatial support. The student’s independent and co-created visuospatial representations of arithmetical structures, along with her verbal comments, were analysed qualitatively using a multimodal microgenetic approach. This paper focuses on three particular excerpts which illustrate the fundamentally componential nature of the concept and practice of division, some difficulties that may be experienced when modelling ‘sharing’ tasks, and the pedagogical importance of spatial structuring when a learner is moving between different kinds of representation