Derivada/reta tangente: imagem conceitual e definição conceitual

Abstract

This is a diagnostic research. The objective of this research is to investigate elements of the concept image and concept definition related to the concept of derivative while interpreted geometrically. It is based on the David Tall and Shlomo Vinner theory about concept image and concept definition. The investigated persons are students of the Formation Course for Mathematic Teachers in a private university of the State of São Paulo, who already had attended classes of Calculus I e II. Two kind of methodological instruments were used: questionnaire and interview. Among the conclusions we detach: the interpretation of the equation of the tangent straight line to the graph of function f as being the function derived from f; the interpretation of the derivative of function f in the point of absciss x = a, as being the y coordinate b of the point (a,b) in which the straight line is tangent to the graph of function f; the existence of persons that verbalize a concept definition related to the derivative concept whose elements are related of a coherent form with the geometric definition of this concept, which is ignored by them at the moment of the elaboration of the answers to the proposed questions