Conceptualization of the directional derivative from the slope of a line in space

Abstract

A proposal was planned based on an instructional sequence of activities, articulated with two- and three-dimensional dynamic objects created using the GeoGebra software, for the learning of the notion of a slope on a straight line in space, as a pre-requirement for the understanding of the concept of directional derivative. The design of the activities is centered on presenting in a dynamically and explicitly the conceptual elements immersed in this notion, like vector position, direction, and horizontal and vertical variations on the plane and on space. A group consisting of 10 students who recently began their studies of multivariate calculus is tested. Taking in consideration the technological concept used, the Instrumental Approach was chosen as framework for the results analysis. The results show that presenting in an explicit and graphic way this concept, along with dynamic elements that enable exploring it from different perspectives, encourages the understanding and conceptualization of the derivative on space.