RUME 26
2024
Omaha, Nebraska
Moving Between Abstraction Levels by Linking Recursion and Induction
Page: 81
The relationship between mathematical induction (MI) and recursion compels us to ask how we could leverage recursive functions to bolster students’ understanding of MI. We describe task- based interviews that utilized concurrent interactions with MI tasks and recursive functions that mirrored those induction tasks via a character-based user-interface. To gain insights into how students’ conceptions of MI and recursion co-evolved as they interacted with these tasks, it was necessary to accommodate these multiple concurrent contexts by extending Hazzan's (1999) Reducing Abstraction framework. Our extended framework, called the Navigating Abstraction framework, documents ascending, descending, and transferring abstraction levels across contexts. Viewing the data through this lens allowed us to illustrate the way in which these three mechanisms together play a crucial role in students joint development of their understandings of both recursion and induction.