GENERALIZATION PROCESSES IN A LEARNING SITUATIONRELATED TO THE TRIGONOMETRIC FOURIER SERIES

Resumen

This research deals with the processes of mathematical generalization when constructing the Trigonometric Fourier Series, since, from its epistemology, the importance of these processes for its adequate construction is evidenced. This approach responds to the Theory of Operative Generalization, which allows glimpsing the generalization processes from the students' actions. The analysis of the students' productions and interactions were based on the consideration of analytical questions resulting
from the theoretical position to characterize their actions, what they do and how they do it, the elements of the actions and the relationships between these elements, what they do it on, and their symbolization, by means of how they do it. Three organizing categories of the actions and their invariants in the process of generalization emerged from the analysis: 1) those related to fixing the causes that provoke the behaviour of the system, 2) those concerning the recognition that the phenomenon is susceptible to
reach a stable, or stationary, state, 3) those related to the relation between the convergence of the series with the stability of the system, and 4) those concerning the calculation of the Fourier coefficients. In addition, relationships are established between these categories that allow the identification of extensional generalizations.