Proving is an essential activity in mathematics but there are serious diYculties encountered by mathematics undergraduates in engaging with proof in the intended way. This article presents an initial analysis of (i) a quantitative study of a large sample of UK mathematics undergraduates which describes their declared perceptions about proof, and (ii) a qualitative study of a subsample of these students which analyses their actual proof perceptions as well as their actual proof practices. A comparison is also made between their publicly declared perceptions of proof and their personal proclivities in proving.
Proving is an activity which occurs only implicitly in the UK school mathematics curriculum: the present advice is for pupils to engage in personal investigations and problem solving so as to promote process skills such as conjecturing, generalizing, and justifying. This article describes the proof practices of a sample of year 10 pupils. The evidence indicates that a few pupils were able to justify accessible statements using logical arguments and that the type and structure of the mathematical activities in the classroom may need to be changed in order to motivate all pupils to justify by logical reasoning rather than by empirical evidence.
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