The Interplay of Language and Objects in the Process of Abstracting

Abstract

Abstracting is an important mathematical process. Students should think and talk about abstract mathematical entities, such as mathematical objects, relations, and processes. With regard to the process of abstracting, concrete didactic material and an abstract decontextualized language are often conceptualized as opposites. In this paper, we offer a theoretical framework that allows a new perspective on the interplay of language and objects in the process of abstracting. We combine three theoretical perspectives, namely the perspectives of empirical abstracting, of recontextualization and of objects as actors to analyse data collected in mathematics lessons in primary schools and, in addition, in tutorial sessions at the university.