Multimodal Production of Signs in the Appropriation of Relations Between a Function and Its Derivative (original) (raw)

In this paper we describe a study in which we investigated the way in which linguistic and extralinguistic resources that employ students, facing with a sequence of activities, are important for the emergence and appropriation of mathematical notions. In the research, 65 students of about 18 years participated in a course of University Mathematics for Engineering that took place in 2013 at a private institution in northern Mexico. During the teaching sequence addressing qualitative relations between the graph of a function and the graph of its derivative is promoted. These notions are being interpreted by the change of position of an object that moves over a straight line and its velocity, respectively. For this, the SimCalc MathWorlds ® software is used, a dynamic environment in which students can explore mathematics of change and variation in the context of movement. In it, various representations (graphs, tables, algebraic expressions) are dynamically linked and in its design infrastructure resides the Fundamental Theorem of Calculus.