Nonlinearity, Thresholds and Bifurcations in Knowledge Acquisition and Problem Solving: towards a Paradigm Shift in Educational Research

The present paper addresses the nonlinear dynamical hypothesis in knowledge acquisition and problem solving. These cognitive phenomena are processes of change or imply changes, which might be trivial, smooth or discontinuous. The usual linear approaches do not capture the dynamics of these processes. This work attempts first, to build theoretical bridges between the nonlinear dynamical systems (NDS) framework and the above cognitive processes, and second, to introduce nonlinear research methodologies. A Catastrophe Theory approach is proposed for testing nonlinear hypotheses in educational and pedagogical research. The data analysis involves dynamic difference equations and statistical regression techniques. Two examples from science education problem solving are provided, which implement cusp catastrophe models, accounting for discontinuities in students’ performance. The meaning and the implications of the nonlinear model are discussed. Moreover, the perspectives for a potential paradigm shift in educational research methodologies are addressed.