Gap reasoning is an inappropriate strategy for comparing fractions. In this article, Patrick Sullivan and Joann Barnett look at the persistence of this misconception amongst students and the insights teachers can draw about students' reasoning.

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…

Described is an exercise that will help college-level psychology students learn abstract and relational thinking skills. The exercise will provide students with a new way to handle compare-and-contrast questions. (RM)