Nonlinear Dynamics and Neo-Piagetian Theories in Problem Solving: Perspectives on a New Epistemology and Theory Development

Dimitrios Stamovlasis, Aristotle University of Thessaloniki, Greece

**Abstract: **In this study, an attempt is made to integrate Nonlinear Dynamical
Systems theory and neo-Piagetian theories applied to creative mental processes,
such as problem solving. A catastrophe theory model is proposed, which
implements three neo-Piagetian constructs as controls: the functional
M-capacity as asymmetry and logical thinking and the degree of field
dependence independence as bifurcation. Data from achievement scores of
students in tenth grade physics were analyzed using dynamic difference
equations and statistical regression techniques. The cusp catastrophe
model proved superior comparing to the pre-post linear counterpart and
demonstrated nonlinearity at the behavioral level. The nonlinear phenomenology,
such as hysteresis effects and bifurcation, is explained by an analysis,
which provides a causal interpretation via the mathematical theory of
self-organization and thus building bridges between NDS-theory concepts
and neo-Piagetian theories. The contribution to theory building is made,
by also addressing the emerging philosophical, - ontological and
epistemological- questions about the processes of problem solving and
creativity.

*Keywords: *nonlinear dynamics, catastrophe theory, creativity, problem solving, neo-Piagetian theories, M-capacity, logical thinking, field dependenceindependence, science education