The heuristic significance of enacted visualisation - Samson, Duncan Alistair (Rhodes University, Faculty of Education, Department of Education, 2012)
This study is centred on an analysis of pupils' lived experience while engaged in the generalisation of linear sequences/progressions presented in a pictorial context. The study is oriented within the conceptual framework of qualitative research, and is anchored within an interpretive paradigm. A case study methodological strategy was adopted, the research participants being the members of a mixed gender, high ability Grade 9 class of 23 pupils at an independent school in South Africa. The analytical framework is structured around a combination of complementary multiple perspectives provided by three theoretical ideas, enactivism, figural apprehension, and knowledge objectification. An important aspect of this analytical framework is the sensitivity it shows to the visual, phenomenological and semiotic aspects of figural pattern generalisation. It is the central thesis of this study that the combined complementary multiple perspectives of enactivism, figural apprehension and knowledge objectification provide a powerful depth of analysis to the exploration of the inter-relationship between the embodied processes of pattern generalisation and the visualisation of pictorial cues. The richly textured tapestry of activity captured through a multi-systemic semiotic analysis of participants' generalisation activity stands testament to this central thesis. Insights gleaned from this study are presented as practical strategies which support and encourage a multiple representational approach to pattern generalisation in the pedagogical context of the classroom.
Keywords: Heuristic; Visualization; Problem solving; Pattern perception; Problem solving -- Ability testing; Mathematics -- Study and teaching; Education -- Research; Interdisciplinary approach to knowledge