Resumen de Is the derivative a function? If so, how do students talk about it?
This study explores how calculus students talk about the derivative as a function based on the concepts of function at a point and function on an interval. Twelve Calculus I students took a survey and explained their solution process during interviews. The analysis of students� discourse with the commognitive lens focusing on their use of words and visuals showed that most students did not appreciate the derivative at a point as a number and the derivative function as a function. Moreover, one of the common descriptions of the derivative as a tangent line implies that they considered the �derivative� as a point-specific object but also a (linear) function defined on an interval. This description was closely related to their use of the word, �derivative� for both �the derivative function� and �the derivative at a point.
