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 @A2SchoolsSuper: We ❤️ #TreeTown @A2schools #InspireA2 #A2gether Ann Arbor named best place to live in America - again https://t.co/yRrH… 5 months ago
- RT @SpringerEdu: Teachers’ talk about the mathematical practice of attending to precision link.springer.com/article/10.100… 5 months ago
- RT @SpringerEdu: RT @authorzone: Discover what English-language #SpringerNature books topped 2017’s list in downloads, citations, and menti… 5 months ago
- Sharing some thoughts about the process of settling down in Ann Arbor. #Sabbatical fulbright.no/grantee-experi… 9 months ago
- RT @velonews: Time trials can be a snooze, but the elite men’s ITT championship race was quite the opposite. velonews.com/2017/09/news/b… 9 months ago