n Learning and Teaching Mathematics - Generalising Some Geometrical Theorems and Objects

Volume 2016, Issue 21
  • ISSN : 1990-6811


Generalisation is an important mathematical process, one that lies at the very heart of mathematical thinking. Not only does generalisation expand knowledge, but it often contributes to increasing our understanding by revealing relationships between different mathematical concepts and topics. With this in mind it is unfortunate that most formal school systems around the world tend to focus largely on 'routine' problems and the 'drill and practice' of mathematical techniques. Little opportunity is typically left to stretch and challenge more able learners. Given the pivotal role that generalisation plays in mathematics, it seems educationally necessary to design suitable activities for engaging talented mathematical learners (as well as prospective Mathematics teachers) in the process of generalisation that goes beyond the normal curriculum, and can possibly stimulate them to explore generalisations of their own. This article presents two possible examples of appropriate generalisation activities. The first is the generalisation of a familiar theorem for cyclic quadrilaterals to cyclic polygons, while the second is the generalisation of the concept of a rectangle to a higher order polygons.

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