Cambio cognitivo en problemas de proporcionalidad modelado bajo autómatas finitos: Estudio de casos

This paper presents the development of the research that aimed to characterize the cognitive changes in the process of solving three problems of simple proportionality. Cognitive change is characterized in terms of the forms of variable control, the different states and emergent transitions between the attempts, and the generated paths and trajectories. The problems were presented using the Uranus web application (version 2) and the data was modeled and analyzed under the finite automata technique using the Auros system (version 1). Two case studies were conducted with two schoolgirls regarding cognitive changes, with a microgenetic methodological approach, which assumes that the subject's behavior is not linear and that it shows specific ascents, descents, and equilibria, in the context of a probabilistic epigenesis. The results confirm that the novelty arises in a space of related tensions, non-sequential, as a systemic scenario of opposing forces that do not obey the passage between the simple and the complex; the emergence of change is imposed at some point, when a force of a conquered state determines the following in a certain direction, in a non-ergodic development process, which shows variation and difference, inter and intra subject. The study has its limitations in respect to the sample selected as well as the calculated likelihoods of following or not following a specific route, a theme that should be dealt in the next research.