Abstract
To follow
Highlights
From the mid 1970s onwards in almost every issue of the undergraduate mathematics journals Mathematics Magazine and College Mathematics Journal there is at least one ‘proof without words’ (Nelsen, 1993)
The purpose of this paper is to explore an epistemic role for visualisation with respect to proofs without words in secondary mathematics in the current South African education policy context
In classrooms, teaching and explaining a proof becomes a form of discourse in which visualisation as process and product can lead to insight and connections among mathematical ideas
Summary
From the mid 1970s onwards in almost every issue of the undergraduate mathematics journals Mathematics Magazine and College Mathematics Journal there is at least one ‘proof without words’ (Nelsen, 1993). Writing explanations for and discussing a suitable proof without words can present opportunities to develop insights about and connections between different mathematical ideas These are ways to popularise proof in general in the secondary mathematics curriculum (De Villiers, 1990; Volmink, 1990). Visualisation as process and product can be a means to examining proofs without words by turning them into proofs that explain In this way students can develop insights and explanations for the mathematics they encounter in the secondary curriculum. It will be shown that a thoughtful interpretation and explanation through visualisation of such proofs without words connects different strands in the bureaucratically stated secondary curriculum found in the policy document (Department of Education, 2003). Visualisation as product can include explanatory notes that result from interpretation of and reflection on a proof without words, in addition to the final picture or proof without words
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