A group as a 'special set'? Implications of ignoring the role of the binary operation in the definition of a group

This paper builds on a developing area of research in mathematics education that focuses on students' learning of abstract mathematical concepts such as Groups in Abstract Algebra. It draws on a Nuffield study of Year 2 mathematics undergraduates' written responses to Group Theory problems and its analysis indicates students' problematic perceptions of Groups. For example, students do not see a group as a pair (a set with a binary operation) but merely as a 'special set' whose elements hold certain properties as determined by the group axioms. The paper focuses on implications of such problematic perceptions: for example, seeing a group as a special set' implies that students occasionally omit checking for Associativity (especially when the group is presented in the form of a table) and neglect elements of its inner structure. This paper was peer-reviewed and presented at an international conference with a 60% contribution by Iannone.