n Learning and Teaching Mathematics - A dynamic investigation of geometric properties with "proofs without words"

Volume 2016, Issue 21
  • ISSN : 1990-6811


Dynamic geometry environments are a powerful way of engaging students in real-time mathematical exploration. Students are able to investigate mathematical properties through dynamic engagement by dragging objects and observing the effect immediately. Through this process it is possible not only to investigate geometric properties but to form conjectures and hypotheses relating to additional properties. Although it may be easy enough to establish that a conjecture is not true, we need to be a little more careful with establishing its veracity. Although the dynamic geometry environment can lead us to suspect that a conjecture is true, to verify that it is indeed true still requires a formal geometric proof. In this article we present a series of progressive tasks that are ideally suited to exploration in a dynamic geometry environment. The tasks are gradually developed through 'what if' question posing (Brown & Walter, 1990, 1993). Rather than getting students to attempt to prove various conjectures on their own (which they could of course do if they wanted), 'Proofs Without Words' (PWWs) are presented as a route to this verification process (Katz, Segal & Stupel, 2016; Nelsen, 2001; Sigler, Segal & Stupel, 2016). The idea is for students to engage with each PWW diagram, attempt to make sense of it, and then to articulate a formal geometric proof of the conjecture based on the PWW diagram.

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