PROCEEDINGS OF THE 17TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2014
Denver, Colorado
Perceptions in Abstract Algebra: Identifying Major Concepts and Concept Connections Within AbstractAlgebra
Page: 274
Abstract algebra is recognized as a highly problematic course for most undergraduate students. Despite these difficulties, most mathematicians and mathematics educators affirm its importance to undergraduate mathematical learning. The purpose of this research was to formulate a list of the important concepts in abstract algebra as perceived by graduate students in mathematics, understand how they define these concepts, and recognize any relationships or connections between these concepts perceived by the students. The theoretical perspective of concept images and concept definitions as described by Tall and Vinner (1981) and Vinner (1983) was used to investigate participants’ understanding of abstract algebra concepts. Through an interview study, the students’ perceptions were analyzed through the creation of concept maps. The results revealed the participants had great difficulty articulating their concept images and concept definitions. In addition, they had differing views of major concepts and relationships within the course.