The Students' Take on the Epsilon-Delta Definition of a Limit

Promoting Students' Ability to Think Conceptually in Calculus

“…This lesson was very closely modeled on a similar lesson described by [5]. Student outcomes from this fourth lesson were positive, and very similar to those reported by [5].…”

Reinventing the formal definition of limit: The case of Amy and Mike

“…I felt, then, that I might learn a great deal about students' reasoning about the limit concept if I engaged them in activities designed to foster their reinvention of the formal definition. In this sense, the research reported here was unique -while other studies (e.g., Larsen, 2001;Fernandez, 2004) have sought to describe how students reason about limit as they interpret the conventional ε-ı definition of limit, my research focused on how students reason about limit in the context of reinventing a definition which captures the intended meaning of the conventional ε-ı definition. To ensure such a setting, students selected for the study had no prior experience with the conventional ε-ı definition.…”

“…In addition to offering insight into how students might reason as they reinvent such a definition, Amy and Mike's experience also serves as an existence proof that students can reinvent a coherent definition of limit. While other studies (e.g., Fernandez, 2004;Larsen, 2001) have sought to describe how students interpret the formal definition of limit, the study reported here is unique in that the students who participated in the teaching experiment were posed the challenge of reinventing the formal definition. Larsen (2009), as well as Zandieh and Rasmussen (2010), has reported the potential students have for reinventing formal definitions of other mathematical concepts.…”

Calculus limits involving infinity: the role of students’ informal dynamic reasoning

“…Some recent studies which consider informal and formal reasoning appear to take informal, dynamic thinking as a starting point for leading students to the 'gold standard' of the formal definition of the limit (see [14][15][16][17][18]). This study, by contrast, explicitly moves away from the assumption that the formal definition of the limit must be an end-goal objective for first-year calculus students at all, since many are intending on majors outside of pure mathematics.…”

“…Another side to the research literature has focused more explicitly on students' understanding of the formal definition of the limit and how to help students advance to this understanding. [14][15][16][17][18][19] In reviewing the literature, most of the research is dedicated to student understanding of the specific limit structures lim x→a f (x) = L or lim n→∞ a n = L. In other words, when discussing real-valued functions, f(x), the studies tend to focus on f(x) approaching a finite limit L as x approaches a finite number a (e.g. [4,9,13,17,19]).…”