Characterization of practices related with prediction facing the erratic: a socioepistemological study - Hernández Zavaleta , M. Sc. Jesús Enrique; Cantoral Uriza, Dr. Ricardo (Transformación, 2024)
This paper shows the results of a historical-epistemological analysis that points out the practices performed by Poincaré (1890), Lorenz (1963) and May (1974) in their encounter with chaotic dynamics, we are interested in their argumentations against the erratic (coming from unexpected events), in the transit between the predictable and unpredictable; we assume that the way to act in this kind of situations indicates a way to build specialized mathematical knowledge. Socioepistemological approach methods were applied to search the practices associated with mathematical concepts processing: temporal recurrence, sensitivity to initial conditions and parameter graphics. The findings show that searching the circular, comparing solutions over time and classifying behaviors are practices that give meaning to this kind of situations and are part of an a priori analysis that provides elements for the characterization of a form of variational thinking to face the unexpected. This study provides elements for the construction of a situation that presents unexpected cases, facilitates to study cases of actions in pre-university students and will serve as a guide for the creation of specific examples that allow their integration at school.
Keywords: mathematics instruction; educational sciences history; prediction; knowledge; social studies; mathematical concepts