Coming to Understand the Formal Definition of Limit: Insights Gained From Engaging Students in Reinvention

The purpose of this article is to elaborate Cottrill et al.'s (1996) conceptual framework of limit, an explanatory model of how students might come to understand the limit concept. Drawing on a retrospective analysis of 2 teaching experiments, we propose 2 theoretical constructs to account for the students' success in formulating and understanding a definition of limit. The 1st construct relates to the need for students to move away from their tendency to attend first to the input variable of the function. The 2nd construct relates to the need for students to overcome the practical impossibility of completing an infinite process. Together, these 2 theoretical constructs build on Cottrill et al.'s work, resulting in a revised conceptual framework of limit.