Catastrophe theory: Methodology, epistemology, and applications in learning science

Abstract

Traditional research methodologies in education have been proved inadequate to provide sufficient explanations to certain phenomena, such as learning and problem solving which are predominantly considered and treated as linear processes. In the last decade, complexity theory and nonlinear dynamics (NDS) had provided the concepts and tools to advance hypotheses testing and theory building. In the area of science education a series of investigations using constructs and variables from neo-Piagetian theories and information processing models showed that in certain cases nonlinear models were superior to the linear counterparts and demonstrated the applicability of NDS framework in educational research. This chapter provides a historical evolution of catastrophe theory (CT) in social sciences; a clear presentation of the related concepts, such as bifurcation, hysteresis, and behavioral attractors; and a lucid review of its applications in learning and problem solving along with theoretical and practical issues of CT modeling. In addition, statistical analyses with various approaches are presented and mathematical issues are highlighted. In this chapter important philosophical-ontological and epistemological-issues arising from fostering the nonlinear framework are also analyzed along with their implication for educational sciences. Finally, the directions for future research and the crucial contribution of NDS to theory development in educational research are discussed.