Abstract

ABSTRACT. Research in mathematics education and anecdotal data suggest that undergraduate students often find their introductory courses to group theory particularly difficult. Research in this area, however, is scarce. In this thesis, I consider students’ difficulties in their first group theory course and conjecture that they have two distinct sources. The first source of difficulties would pertain to a conceptual understanding of what group theory is and what it studies. The second would relate to the modern abstract formulation of the topics learned in a group theory course and the need to interpret and write meaningful statements in modern algebra. To support this hypothesis, the group concept is explored through a historical perspective which examines the motivations behind developing group theory and its practical uses. Modern algebra is also viewed in a historical context in terms of three defining characteristics of algebra; namely, symbolism, justifications and the study of objects versus relationships. Finally, a pilot study was conducted with 4 students who had recently completed a group theory course and their responses are analysed in terms of their conceptual understanding of group theory and modern algebra. The analysis supports the hypothesis of the two sources. Based on the results, I propose a remediation strategy and point in the direction of future research.