Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 10, Iss. 1, January, 2006, pp. 37-70
@2006 Society for Chaos Theory in Psychology & Life Sciences

 
 
 

The Nonlinear Dynamical Hypothesis in Science Education Problem Solving: A Catastrophe Theory Approach

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 studentsí 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