Abstraction in mathematics: A dialectical perspective

Abstract

In the classical Aristotelian empiricist view, abstraction is associated with an ascending developmental process from the concrete to the abstract. In this paper, however, I argue that the development coming about in the formation of mathematical abstraction can be best portrayed as a dialectical development to and fro between the concrete and abstract. This argument is exemplified on the basis of the verbal protocols of two students working together on a task connected to sketching the graphs of absolute value linear functions