Defining and classifying quadrilaterals, though an established component of the school mathematics curriculum, appears to be a difficult topic for many learners. The reasons for such difficulties relate to the complexities in learning to analyse the attributes of different quadrilaterals and to distinguish between critical and non-critical aspects. Such learning, if it is to be effective, requires logical deduction, together with suitable interactions between concepts and images. This paper reports on an analysis of data from a total of 263 learners. The main purpose of the paper is to present a theoretical framing that is intended to inform further studies of this important topic within mathematics education research. This theoretical framing relates prototype phenomenon and implicit models to common cognitive paths in the understanding of the relationship between quadrilaterals
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