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.
-
Recent Posts
@rmosvold on twitter
- RT @shankerinst: We are devastated to report the death of David K. Cohen, a founding member of the Albert Shanker Institute’s board of dire… 3 months ago
- Check this out! twitter.com/SLSingh/status… 3 months ago
- I really appreciated the keynote by @deborah_ball #TWSummerInstitute To quote some of her closing words: "It's coll… twitter.com/i/web/status/1… 6 months ago
- RT @TeachingWorks: Today is the day! If you signed up to join us, the link to view our #TWSummerInstitute keynote address today is waiting… 6 months ago
- Looking forward to the lecture by @deborah_ball at #TWSummerInstitute 6 months ago
Archives
Meta