Dimitrios Stamovlasis, Ministry of Education, Athens, Greece

Abstract: The current study tests the nonlinear dynamical hypothesis in science education problem solving by applying catastrophe theory. With in the neo-Piagetian framework a cusp catastrophe model is proposed, which accounts for discontinuities in students performance as a function of two controls: the functional M-capacity as asymmetry and the degree of field dependence/independence as bifurcation. The two controls have functional relation with two opponent processes, the processing of rele vant information and the inhibitory process of disembedding irrelevant information respectively. Data from achievement scores of freshmen at a technological college were measured at two points in time, and were analyzed using dynamic difference equations and statistical regression techniques. The cusp catastrophe model proved superior (R2=0.77) comparing to the pre-post linear counterpart (R2=0.46). Besides the empirical evidence, theoretical analyses are provided, which attempt to build bridges between NDS-theory concepts and science education problem solving and to neo-Piagetian theories as well. This study sets a framework for the application of catastrophe theory in education.

Keywords: catastrophe theory, science education, problem solving, cusp catastrophe model, neo-Piagetian theories, M-capacity, field dependence/independence