Cognitive Structures of Differential Geometry and Their Implications on Undergraduate Mathematics Curriculum

Abstract

Based on similar studies using the FCI and CCI, this project aims to explore how effectively undergraduate courses prepare students for study in higher level mathematics courses. To investigate this, we choose to study the preparedness of Level III differential geometry students by developing and implementing a concept inventory that measures the cognitive structures of prerequisite undergraduate material. Using techniques in item analysis and concept mapping, we assess the cognitive structures of the incoming students, and identify areas for improvement within the Calculus and Linear Algebra course sequences based on the current literature on concept inventories. We also investigate potential relationships between cognitive structure and academic success, and attempt to measure the development of cognitive structures as a result of instruction throughout the term.