Errors in the Study of the Variational Behavior of Functions in the University Engineering Students

The study of the variational behavior of functions constitutes an important element in the understanding of the change of phenomena in real life. His understanding is an essential axis in the mathematical training of university students, especially those who pursue engineering careers. This article presents the results of a study whose objective was to determine the mistakes made by engineering students about the variational behavior of functions. The Duval Semiotics Records Theory was taken as a reference and a questionnaire was prepared with questions about identification of regions of variability for "x" and "y"; regions of growth, decrease, stability, extreme values and, analysis and description of the behavior of the function. The evaluation of the answers was done in a quantitative-qualitative way, from an exploratory and descriptive perspective, with 100 students participating in the civil engineering career. The results indicate that students do not make a real reflection on the variational behavior in intervals of the variables or in a global way. They have difficulty discriminating between the behavior of the function and the location of the function. They present cognitive difficulties that do not allow them to make an adequate conversion from one register to the other. Errors related to mathematical language were found, to the limitations to obtain spatial information, to establish erroneous inferences and to the inadequate development of previous knowledge, which does not allow them to properly evaluate the variational behavior of the functions. [For full proceedings, see ED621941.]