Visualisation as a metacognitive strategy in learning multiplicative concepts : a design research intervention

Abstract

At the primary school level, the understanding of multiplication and division is critical, and division is a particularly challenging concept for most learners. I argue that the concept of division can be grasped more readily if learners learn to regulate their own mental processes intentionally; and that metacognitive strategies can be cultivated. Learners’ cognitive development and their propensity for visual imagery at age 11 to 12 years provide an opportunity to mediate such a strategy while learning mathematics concepts. Visualisation gives learners access to what I call “the virtual space of the mind”, where they can reconstruct an external life situation as an internal reality, upon which they can act mathematically. Based on a review of the relevant literature, the use of visualisation in problem solving (division in particular) at this developmental age was found to be under-explored, which gave rise to the need to develop a useful and feasible instructional design. Design Research was applied, as its iterative, cyclic nature allows the researcher to work through phases while developing various prototypes of the design. The fourth prototype of this design was tested with sixteen Grade 6 participants in the classroom setting of an English-medium primary school in Gauteng Province, South Africa, where the strategy was mediated for division in money-, area- and rate contexts. The research enabled the identification of specific design principles to underpin a final design for the mediation of visualisation as a metacognitive strategy in learning multiplicative concepts.