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High-Attaining Year 10 pupils’ conceptions and learning of proof: A critical analysis.

Christopher Payne

Secondary PGCE ( Mathematics) 2010-2011



For most mathematicians, proof is seen as an integral part of the subject; it ensures absolute certainty and separates this subject from other sciences. Yet my own experience suggests that proof is not incorporated into the mathematics curriculum and therefore pupils are being deprived of this essential, and fascinating, cornerstone of mathematics. This study will outline the findings of a small-scale case study conducted mainly with high attaining year 10 pupils from a rural 11 – 16 comprehensive community college. Year 7 and year 10 pupils were initially given a diagnostic questionnaire. A short lesson sequence was then taught to the year 10 group and a concluding questionnaire administered. The main conclusion of the study is that the pupils taking part in this research do indeed have very little interaction with proof throughout their compulsory mathematics career. Even after changes to the mathematics curriculum that explicitly incorporate proof at all ages and levels, pupils have very little conception of proof and struggle with proof related tasks. To combat these difficulties, I argue that proof needs to be the heart of mathematics education and outline further research that can investigate the best methods to achieve this.

Copyright: © 2011. This paper is copyright of the author. (Please read the Journal's copyright information page by using the menu to the left of this page.)

The full paper is available for download as a pdf file: 093-158-paynec

Citation: Payne, C. (2011) High-Attaining Year 10 pupils’ conceptions and learning of proof: A critical analysis.Journal of Trainee Teacher Educational Research, Volume 3, pp.93-158. (Downloaded from, [date of access])