Beata Dongwi


Beata completed her Master’s and PhD Degree in Mathematics Education at Rhodes University in South Africa. She taught Mathematics in government High schools before she went to teach at Oranjemund Private School in Oranjemund, Southern Namibia where the Namib Desert, the Orange River and the Atlantic Ocean all meet at one point. She has presented at numerous national and international mathematics conferences and congresses. She is very passionate about teaching and learning mathematics for conceptualisation. Her research interests are visualisation and reasoning in mathematics within an enactivist context.

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PhD thesis

Examining mathematical reasoning through enacted visualisation


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 mixed-gender 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 co-emergence 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.

Last Modified: Thu, 13 Feb 2020 08:46:23 SAST