On the origin, characteristics, and usefulness of instrumental and relational understanding

Abstract

In this paper, the aim is to make a theoretical contribution by focusing on the origin, characteristics, and potential values of the concepts of instrumental and relational understanding. Five characteristics are identified to make it easier to operationalise the concepts and use them as an analytical framework. There is also a focus on how the concepts are closely related to two rationales for learning, the instrumental and the social rationale. The potential values of the concepts and their rationales are shown by using them to suggest a revision of the van Hiele framework and to analyse three empirical examples concerning young students’ understanding of triangles and a cylinder.