Functions and graphs in dynamic digital environments

Abstract

In this paper we present a study on the formation of meanings about the notion of mathematical function and graphic representations in dynamic geometrical environment; we also describe a didactic activity on functions centered on the management of different graphics and
verbal representations of real functions of real variable. The dynamic geometry environments allow the construction of dynamic graphics (dynagraphs) and the realization of functional dependency by means of two different kinds of movement, direct and indirect, of points that represent independent and dependent variables. The continuous effort of students in describing the dynamic graphics and their observations during their dragging promoted the use of particular terms and, in general, of signs that were shared in the classroom and were linked to each other in order to formulate progressively more complex expressions and more advanced mathematical meanings.