Tentativeness is often framed as a deficit, synonymous with timidity or a lack of confidence. In this article, I situate the notion of tentativeness in an enactivist framework and describe its role as both a strategy and affordance in a spatial visualization exercise. Drawing on insights from mathematics education and ecological psychology, I…

This article explores the inter-relationship between the embodied processes of pattern generalisation and the visualisation of pictorial cues. A research framework is established for analysing pupils' multiple visualisations of figural cues in the context of pattern generalisation. The research framework centres on a novel combination of three…

A well-documented experience of students of elementary Euclidean geometry is "seeing" a geometric result and being sure about its truth; this sort of experience gives rise to the notion of geometrical visualisation that is developed here. In this essay a philosophical argument for the epistemic potential of geometrical visualisation is reviewed,…

Investigates the mathematical practices used by a home designer and builder. Points out the existence not only of diverse forms of mathematics, or ethnomathematics, but also of diverse ways of doing mathematics. Argues that these idiosyncratic ways of mathematizing, whether pertaining to individuals or to entire cultural groups, should be…

Presents a case study that aimed to obtain information on students' mathematical comprehension levels and on whether students may or may not make use of visualization processes in solving mathematical problems. Discovers students' beliefs about teaching and learning processes in general, and mathematics in particular. (Contains 25 references.)…

Reports on a case study of a student who constructs formalism not from processes of quantification, but from his own visuospatial imagery. Rather than construct new objects from cognitive processes, the student reflects on mental objects already in mind and refines them to build an interpretation of the formal theory. This example leads to…

Identifying the strengths of visual processing in high school mathematics is considered. The development of an instrument to assess mathematical processing is described. Then the kinds of visual imagery found in children in England and Natal are presented, along with difficulties and benefits experienced by visualizers. (MNS)

Reports a study designed to identify 9 and 11 year olds' ways of drawing nets of solids and to provide opportunities for them to reflect on their models in whole class discussions. Results indicated that children's views of solids' nets progressed from more global and holistic to more quantitative and analytic. (MDH)