A Calculus Activity with Foundations in Geometric Learning

Calculus, perhaps more than other areas of mathematics, has a reputation for being steeped with procedures. In fact, through the years, it has been noticed of many students getting caught in the trap of trying to memorize algorithms and rules without developing associated concept knowledge. Specifically, students often struggle with the fundamental concept of a limit. Many textbooks motivate limits, and ultimately the definition of the derivative, by briefly presenting secant lines and tangent lines in the context of rates of change. To enhance this traditional approach, the authors created small-group activities that would gently introduce students to conceptual components of a limit in a student-centered environment. The authors consulted well-established learning theories about geometric visualization and concept development. In this article, the authors describe how they developed their concept-based activities and how their students responded.