Bifurcation and Hysteresis Effects in Student Performance: The Signature of Complexity and Chaos in Educational Research

Abstract

This paper addresses some methodological issues concerning traditional linear approaches and shows the need for a paradigm shift in education research towards the Complexity and Nonlinear Dynamical Systems (NDS) framework. It presents a quantitative piece of research aiming to test the nonlinear dynamical hypothesis in education. It applies catastrophe theory and demonstrates that students’ achievements in science education could be described by a cusp model, where two cognitive variables are implemented as controls - the logical thinking as the asymmetry and the field dependence/independence as the bifurcation respectively. The results support the nonlinear hypothesis by providing the empirical evidence for bifurcation and hysteresis effects in students’ performance. Interpretation of the model is provided and implications and fundamental epistemological issues are discussed.

Perspectives on Complexity, Its Definition and Applications in the Field

“…The other is between normal science and complexity, as expressed by Principles 3, 4, 5, 6 and 7. While inductive reasoning, as stated in Principle 1 has been productively used in work on complexity (e.g., Laidlaw, Makovichuck, & Wong, 2013), it is not necessarily a defining characteristic of the perspective, which also accommodates the productive use of deductive methods to confirm hypotheses about complexity (e.g., Stamovlasis, 2014). Likewise, the complexity angle does not require the use of qualitative research approaches.…”

Exploring Links between Complexity Constructs and Children’s Knowledge Formation: Implications for Science Learning

“…Here again there is evidence that these concepts are applicable to cognitive processes [124]. Stamovlasis [125], for example, has demonstrated hysteresis in students' science learning, modulated by parameters such as logical thinking ability. Thus, it is possible that context effects seen during learning might be the result of the inherent complexity of knowledge formation.…”