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.

[1]  D. Stamovlasis.  The nonlinear dynamical hypothesis in science education problem solving: a catastrophe theory approach. , 2016, Nonlinear dynamics, psychology, and life sciences.

[2]  S. Guastello,et al.  Origins of Coordination and Team Effectiveness: A Perspective From Game Theory and Nonlinear Dynamics , 1998 .

[3]  Stephen J. Guastello,et al.  A butterfly catastrophe model of motivation in organization: Academic performance. , 1987 .

[4]  T. Gelder,et al.  It's about time: an overview of the dynamical approach to cognition , 1996 .

[5]  Donald G. Saari,et al.  A qualitative model for the dynamics of cognitive processes , 1977 .

[6]  Tim van Gelder,et al.  Defining ‘Distributed Representation’ , 1992 .

[7]  S. Guastello.  Nonlinear Dynamics in Psychology , 2001 .

[8]  Dimitrios Stamovlasis,et al.  Application of Complexity Theory to an Information Processing Model in Science Education , 2001 .

[9]  R. Thom.  Structural stability and morphogenesis , 1977, Pattern Recognition.

[10]  Hermann Haken.  Intelligent Behavior: a Synergetic View , 2003 .

[11]  Dimitris Psillos.  Science education research in the knowledge-based society , 2003 .

[12]  Mansoor Niaz,et al.  Progressive Transitions from Algorithmic to Conceptual Understanding in Student Ability To Solve Chemistry Problems: A Lakatosian Interpretation. , 1995 .

[13]  D. Stamovlasis,et al.  Conceptual Understanding Versus Algorithmic Problem Solving , 2004 .

[14]  J. Barkley Rosser,et al.  From Catastrophe to Chaos: A General Theory of Economic Discontinuities , 1991 .

[15]  J. Abraham.  Dynamical Systems Theory: Application to Pedagogy , 2003 .

[16]  J. S. Baker,et al.  A cusp catastrophe: Hysteresis, bimodality, and inaccessibility in rabbit eyelid conditioning , 1979 .

[17]  D. Lewkowicz,et al.  A dynamic systems approach to the development of cognition and action. , 2007, Journal of cognitive neuroscience.

[18]  H.L.J. van der Maas,et al.  Stagewise cognitive development: an application of catastrophe theory. , 1992, Psychological review.

[19]  S. Zacks,et al.  Applications of Catastrophe Theory for Statistical Modeling in the Biosciences , 1985 .

[20]  J. Nicolis,et al.  Chaos and information processing , 1991 .

[21]  Markus F. Peschl,et al.  The Representational Relation Between Environmental Structures and Neural Systems: Autonomy and Environmental Dependency in Neural Knowledge Representation , 1997 .

[22]  Juan Pascual-Leone,et al.  A mathematical model for the transition rule in Piaget's developmental stages , 1970 .

[23]  P. Preece.  A Geometrical Model of Piagetian Conservation , 1980 .

[24]  Christine Hardy.  Networks of Meaning: A Bridge Between Mind and Matter , 1998 .

[25]  J. Nathan Swift,et al.  Research in Science Education , 1969 .

[26]  Wolfgang Tschacher,et al.  The Dynamical Systems Approach to Cognition , 2003 .

[27]  S. Guastello.  Moderator regression and the cusp catastrophe: Application of two‐stage personnel selection, training, therapy, and policy evaluation , 1982 .

[28]  S. Guastello.  Managing Emergent Phenomena: Nonlinear Dynamics in Work Organizations , 2001 .

[29]  D. Stamovlasis,et al.  Conceptual understanding versus algorithmic problem solving: Further evidence from a national chemistry examination , 2005 .

[30]  Georgios Tsaparlis,et al.  A Model of Problem Solving: Its Operation, Validity, and Usefulness in the Case of Organic-Synthesis Problems. , 2000 .

[31]  J. Nicolis,et al.  Chaotic dynamics applied to information processing , 1986 .

[32]  D. Stamovlasis,et al.  Cognitive Variables in Problem Solving: A Nonlinear Approach , 2005 .

[33]  A. Opstal.  Dynamic Patterns: The Self-Organization of Brain and Behavior , 1995 .

[34]  D. Stamovlasis,et al.  Nonlinear Analysis of the Effect of Working Memory Capacity on Student Performance in Problem Solving , 2003 .

[35]  Marc D. Lewis,et al.  The promise of dynamic systems approaches for an integrated account of human development. , 2000, Child development.

[36]  M. Deakin.  Catastrophe theory. , 1977, Science.

[37]  Herman A. Witkin,et al.  Cognitive styles in personal and cultural adaptation , 1977 .

[38]  A. Newell.  Unified Theories of Cognition , 1990 .

[39]  Geoffrey E. Hinton,et al.  Distributed Representations , 1986, The Philosophy of Artificial Intelligence.

[40]  G. Ermentrout.  Dynamic patterns: The self-organization of brain and behavior , 1997 .