Perceiving the derivative: the case of Susanna

This paper is a report of a study on how a less successful student perceives the derivative from the graph of a function. A task-based interview of a grade 11 student was analyzed to find how she perceived the derivative from a graph of a function and what kind of representations she used for this. The results show how she used representations of the increase, the steepness, and the horizontalness of the graph to perceive the derivative. Gestures were an integral part of her thinking. This case shows that with appropriate representations students can perceive essential aspects of the derivative from the graph of the function, and that students can consider the derivative as an object at the very beginning of the acquisition process.