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The final publication is available at: www.springerlink.comThis paper discusses variation in reasoning strategies among expert mathematicians,\udwith a particular focus on the degree to which they use examples to reason about\udgeneral conjectures. We first discuss literature on the use of examples in understanding and\udreasoning about abstract mathematics, relating this to a conceptualisation of syntactic and\udsemantic reasoning strategies relative to a representation system of proof. We then use this\udconceptualisation as a basis for contrasting the behaviour of two successful mathematics\udresearch students whilst they evaluated and proved number theory conjectures. We observe\udthat the students exhibited strikingly different degrees of example use, and argue that\udpreviously observed individual differences in reasoning strategies may exist at the expert\udlevel. We conclude by discussing implications for pedagogy and for future research

Doctoral students’ use of examples in evaluating and proving conjectures