Dynamical Systems Theory – A Powerful Tool in the Educational Sciences

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For a mathematician dynamical systems theory is thought like a branch of the mathematics, closely related with the bifurcation theory and deterministic chaos theory. This theory deals with the qualitative behavior of dynamical systems for long-term and the studies of the solutions of the motion equations of systems that are primarily mechanical in nature. The applications of dynamical system theory are many in almost all areas of human activity. Among these domains we find to those of the education sciences. In this sense, the integrative nature of education must be thought like an ecosystem where each its component influences and is influenced by every other. Dynamical systems theory provides a framework for defining and examining the critical components in complex environments with the certain evolutions in time. The quality of the teaching-learning process is essential for the integrity of learning outcomes. Moreover, the learning process itself can be thought like a self-organizing system in which, for example, new information may conduct to the conflicts with knowledge already learned, and thus a sense of disequilibrium to understand and integrate the new concept into a previously stable knowledge structure appears for the students. Our main aim is to show that using dynamical systems theory and its related theories as research tools of the entire educational process, it is possible to obtain the appropriate picture of the teaching- learning classroom process. But, first we have to understanding and describing these like a dynamical system, and then we are able to govern it in a coherent framework with an adequate policy for the students