PROCEEDINGS OF THE 19TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2016
Pittsburgh, Pennsylvania
On the axiomatic formalization of mathematical understanding
Page: 633
This study adopts a property-based perspective to investigate the forms of abstraction, instantiation, and representation used by undergraduate topology students when acting to understand and use the concept of a continuous function as it is defined axiomatically. Based on a series of task-based interviews, profile cases are being developed to compare and contrast the distinct ways of thinking and processes of understanding observed by students undergoing this transition. A framework has been established to interpret the participants’ interactions with the underlying mathematical properties of continuous functions while they reconstructed their concept images to reflect a topological (axiomatic) structure. This will provide insight into how such properties can be successfully incorporated into students’ concept images and accessed; and which obstacles prevent this. Preliminary results reveal several coherent categories of participants’ progression of understanding. This report will outline these profiles and seek critical feedback on the direction of the described research.