Abstract
This article reports on a qualitative, interpretivist study that focused on the use of visualisation and analytic strategies by Grade 12 learners when working with problems based on transformation geometry. The research was conducted with 40 learners from a Grade 12 class at one high school in the north Durban area of Kwazulu-Natal. Participants completed a written task and a smaller sample of the participants engaged in investigative semi-structured interviews with the researchers. The framework for the study was based on transformations of semiotic representations as well as the visualiser/analyser model. The findings revealed that most learners performed treatments in the analytic mode when responding to the tasks, and showed limited movement across the two modes which are essential for a deepening of understanding. The study identified one learner, however, who was able to move flexibly between the modes and who displayed a deep understanding of the concepts. The article concludes by recommending that opportunities need to be created for learners to engage in transformation geometry activities which emphasise conversion. Keywords: analysis; conversions; transformation geometry; transformations; treatments; visualisation
Highlights
Within the current (2011) South African curriculum, school mathematics incorporates transformation geometry, which was introduced in the Further Education and Training (FET) band in 2006
This article reports on a qualitative, interpretivist study focusing on the use of visualisation and analytic strategies by Grade 12 learners when working with problems based on transformation geometry
From the interview responses it was evident that some learners reduced the transformation exercise (Q4) to a treatment activity without any visualisation activities
Summary
Within the current (2011) South African curriculum, school mathematics incorporates transformation geometry, which was introduced in the Further Education and Training (FET) band in 2006 This strand allows learners to make connections across other geometries within the space, shape and measurement learning outcome, as well as with algebra and trigonometry. These connections are intended to create a more integrated, holistic knowledge of mathematics (DoE, 2003) and to allow for novel interpretations of the mathematics learnt in the other strands. The strand remains in the curriculum for Grades R to 9, and will still provide rich learning opportunities for the learners in these grades
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