This paper discusses variation in reasoning strategies among expert mathematicians, with a particular focus on the degree to which they use examples to reason about general conjectures. We first discuss literature on the use of examples in understanding and reasoning about abstract mathematics, relating this to a conceptualisation of syntactic and semantic reasoning strategies relative to a representation system of proof. We then use this conceptualisation as a basis for contrasting the behaviour of two successful mathematics research students whilst they evaluated and proved number theory conjectures. We observe that the students exhibited strikingly different degrees of example use, and argue that previously observed individual differences in reasoning strategies may exist at the expert level. We conclude by discussing implications for pedagogy and for future research.
- RT @MatthewMaddux: Developing mathematical knowledge for teaching teachers: potentials of history of mathematics in teacher educator traini… 4 months ago
- RT @CERME11_2019: In preparation for the conference, we kindly ask you to send questions about ERME research, questions about ERME itself,… 4 months ago
- Developing mathematical knowledge for teaching teachers: potentials of history of mathematics in teacher educator t… twitter.com/i/web/status/1… 4 months ago
- Looking forward to last day (for me) of the EML 2018 with @deborah_ball. What a wonderful opportunity to study, dis… twitter.com/i/web/status/1… 9 months ago
- RT @A2SchoolsSuper: We ❤️ #TreeTown @A2schools #InspireA2 #A2gether Ann Arbor named best place to live in America - again https://t.co/yRrH… 1 year ago