Reducing abstraction: The case of constructing an operation table for a group

Abstract This paper describes students' mental processes while constructing an operation table for a group. More specifically, undergraduate students' approaches are analyzed as the students fill in an operation table for four elements—a, b, c, and d—in such a way that it represents a group of order four. The data are analyzed from the perspective of reducing abstraction, which aims to explain students' conceptions of abstract algebra concepts. From this perspective, most students' responses and conceptions can be attributed to their tendency to work on a lower level of abstraction than the level on which concepts are introduced in class.