The nonlinear dynamical hypothesis in science education problem solving: a catastrophe theory approach

The current study tests the nonlinear dynamical hypothesis in science education problem solving by applying catastrophe theory. Within 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 relevant information and the inhibitory process of dis-embedding 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 (R(2)=0.77) comparing to the pre-post linear counterpart (R(2)=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.