RUME 25
2023
Omaha, Nebraska
Explicating the Role of Abstraction During Analogical Concept Creation
Page: 806
Recent research has explored the potential for students to create new mathematical concepts by analogy with previously known concepts. However, there is more to be understood about the intricate processes of analogical reasoning that students leverage when creating new concepts. In this paper, we describe an initial theory explicating the role of abstraction during analogical concept creation. First, we introduce the abstracted domain to operationalize abstraction during analogical reasoning. We then describe two mechanisms of analogical concept creation through which abstraction may occur while reasoning about a ring-theoretic analogue to subgroups: (1) comparative analogy, and (2) inductive analogy. To broaden the interpretive scope of the theory, we further apply the mechanisms to scenarios involving meta-analogical reasoning and pedagogy. Implications for research and teaching mathematics with analogy are discussed.