From ‘proofs without words’ to ‘proofs that explain’ in secondary mathematics
The original publication is available at http://www.pythagoras.org.za
CITATION: Gierdien, F. 2007. From ‘proofs without words’ to ‘proofs that explain’ in secondary mathematics. Pythagoras, 65: 53-62, doi: 10.4102/pythagoras.v0i65.92.
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. 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. The proofs without words chosen are those that show analytic and visual representations of series and sequences. In the secondary curriculum series and sequences are mainly represented analytically. 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). There is more mathematics embedded and ‘unseen’ in these proofs without words.