Advanced college-level students' categorization and use of mathematical definitions

Abstract

This qualitative study of five undergraduate mathematics majors found that some students, (even students at an advanced level of undergraduate mathematical study) have a mathematician’s perspective neither on the concept of mathematical definition nor on the structure of mathematics as a whole. Participants in this study were likely to reason from incomplete concept images rather than from concept definitions and were likely to perceive that definitions (like theorems) need to be verified. The results of this study have implications for college-level mathematics instruction.