PROCEEDINGS OF THE 23RD ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2020
Boston, Massachusetts
A proposed framework of student thinking around substitution equivalence: Structural versus operationalviews
Page: 762
This theoretical paper explores one way in which student conceptions of substitution equivalence might be classified along a spectrum between operational and structural thinking, which we generalize from Sfard’s theories of the Genesis of Mathematical Objects and research on student conceptions of the equals sign. We provide some sample student work that illustrates different ways in which students may exhibit structural or operational thinking about substitution equivalence. The aim of this paper is to provide an initial testable framework of student thinking around substitution equivalence that could be used as a basis for future studies that confirm, refute, or refine this framework, or use the framework to explore the relationship of different kinds of student thinking around equivalence to other mathematical conceptions and skills.