Structural Reasoning

Abstract

In this paper we give a general definition of structural reasoning, followed by a typology that instantiates the definition in mathematical practices. Five major categories of structural reasoning, some with subcategories, are offered: (a) pattern generalization, (b) reduction of an unfamiliar structure into a familiar one, (c) recognizing and operating with structure in thought, (d) epistemological justification and (e) reasoning in term of general structures. The first four categories of this typology are illustrated by field-based events of secondary mathematics teachers’ mathematical behaviors. The potential contribution of the typology to research in mathematics education is that its elements can be used as indicators and conceptual labels of empirical observations. The potential contribution of the illustrative field-based events is that they can serve as initial models for structural reasoning phenomena to be examined by researchers.