PROCEEDINGS OF THE 17TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2014
Denver, Colorado
The Construction Of Cohomology As Objectified Action
Page: 957
The purpose of this paper is to investigate a theory about the nature of mathematical development, in which mathematics is characterized as the objectification of action. Informed by existing research on how students construct new mathematical objects, we consider as an example the psychological construction of cohomology and related objects of algebraic topology. This example extends neo-Piagetian theories of mathematical development from elementary school to graduate-level mathematics, while integrating existing research on students’ learning of abstract algebra. Results of the investigation affirm the objectification of action as a distinguishing feature of mathematics in general, while indicating the kinds of mental actions that undergird the objects of advanced mathematics.