Fractal descriptions of inferential processes in children during the creation of hypotheses aimed at solving problems

Abstract

This work is a descriptive approach, from the dynamic point of view, to synthetic inferential thought processes. We assume as a working hypothesis that thought is a particular type of nonlinear dynamic system and we define this conjecture through a particular system of postulates. Based on Piaget's cognitive psychology and on the theory of chaos and fractals, we build a specific experimental paradigm that allows us to study the inferential dynamics during problem solving (a strategy game known as Naval Combat). The instrument used to describe the inferential dynamics was the fractal dimension. The problem task was presented to the children. The results obtained, using the fractal dimension, have allowed a) to describe the inferential dynamics of the subjects while they were solving the problem. b) characterize, through a model (in terms of a mathematical function) the dynamic form of the inferential procedure of each subject in the sample. Our results suggest that each child has a personal and characteristic dynamic unit during the generation of hypotheses.