Case Study on Intra-mathematical Connections when Solving Tasks Associated with the Classification of Groups of Prime Order

Abstract

In Abstract Algebra, isomorphism is a difficult concept to understand for undergraduate students. However, Mathematics Education suggests that it is necessary to promote mathematical connections in students to foster their understanding, that is, to help them establish relationships between two or more ideas, concepts, definitions, theorems, procedures, representations, or meanings, with other disciplines and with real life situations. This paper presents some intra-mathematical connections on the classification of groups of prime order that emerged during task solving, which were based on a historical and epistemological analysis of the concept of isomorphic groups. This research is a case study, where an interview was applied for data collection, and qualitative text analysis was performed. As a result, fourteen connections associated with the concepts of group, subgroup, cyclic groups, isomorphism, isomorphic groups, and the Lagrange theorem were identified, involved in the classification of prime order groups. We concluded that the tasks designed with a historical foundation enhance a deep understanding from the connected appreciation of concepts, theorems, methods, and algorithms.