PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2015
Pittsburgh, Pennsylvania
Opportunity to learn the concept of group in a first class meeting on abstract algebra
Page: 529
This paper is a case study of the teaching of an undergraduate abstract algebra course; in particular, it examines the opportunity that the students had during the first class meeting to learn about the concept of a mathematical group and how much intellectual responsibility for the definition they were given. The paper offers a description of the classroom teaching and discussion an inquiry-oriented abstract algebra course. It focuses on the mathematical tasks that the professor used to introduce the concept of a group, the student solutions and classroom presentation of those tasks, and the professor's activities. It analyzes the class in terms of providing students the opportunity to learn the concept of a mathematical group and about the mathematical process of defining. It also analyzes the professor's activities in terms of devolving intellectual responsibility for writing the definition of a group. Finally, the analysis suggests ways that the professor's actions failed to devolve mathematical authority and limited opportunities to learn.