RUME 26
2024
Omaha, Nebraska
Analogical Quotient Structure Sense in Abstract Algebra: An Expansion of University Structure Sense
Page: 232
Despite existing research describing students’ understanding of group concepts, little research in undergraduate mathematics education has attended to students’ understanding of ring concepts. In this paper, we present an analysis of four students engaged in task-based interviews that provided insights into their understanding of quotient ring when constructed as an analogy to quotient group. Using university structure sense (Novotná & Hoch, 2008) as a foundation, we propose an expansion of structure sense to include attention to various structures (e.g., subgroups and quotient groups), and attention to analogous structure across different contexts (e.g., attending to quotient structure across group theory and ring theory.) Findings suggest that while students uniformly attended to similar structural components when creating the concept of quotient ring, there was variation in the depth of their reasoning about why certain structures exist.