Examining mathematical reasoning through enacted visualisation

Abstract

This study sets out to analyse the co-emergence of visualisation and reasoning processes when selected learners engaged in solving word problems. The study argues that visualisation processes and mathematical reasoning processes are closely interlinked in the process of engaging in any mathematical activity. This qualitative research project adopted a case study methodology embedded within a broader interpretative orientation. The research participants were a cohort of 17 mixedgender and mixed-ability Grade 11 learners from a private school in southern Namibia. Data was collected in three phases and comprised of one-on-one task-based interviews in the first phase, focus group task-based interviews in the second, and semi-structured reflective interviews in the third. The analytical framework was informed by elements of enactivism and consisted of a hybrid of observable visualisation and mathematical reasoning indicators. The study was framed by an enactivist perspective that served as a linking mediator to bring visualisation and reasoning processes together, and as a lens through which the coemergence of these processes was observed and analysed. The key enactivist concepts of structural coupling and co-emergence were the two mediating ideas that enabled me to discuss the links between visualisation and reasoning that emerged whilst my participants solved the set word problems. The study argues that the visualisation processes enacted by the participants when solving these problems are inseparable from the reasoning processes that the participants brought to bear; that is, they co-emerged.