Introduction : Education is a Dynamical System

Pre-post testing is a commonly used method in physics education community for evaluating students' achievement and or the effectiveness of teaching through a specific period of instruction. A popular method to analyze pre-post testing results is the normalized gain first brought to the physics education community in wide use by R.R. Hake. This paper presents a measurement based probabilistic model of the dynamic process of learning that explains the experimentally observed features of the normalized gain. In Hake's study with thousands of students' pre-post testing results, he observed that on average 48 courses employing " interactive engagement " types of instruction achieved average normalized gains about two standard deviations greater than did 14 courses subjected to traditional instruction. For all courses the average normalized gains had a very low correlation +0.02 with average pretest scores. This feature of the normalized gain has allowed researchers to investigate the effectiveness of instruction using data collected from classes with widely different average pretest scores. However, the question of why the average normalized gain has this feature and to what extent this feature is generally present is not well understood. In addition, there have been debates as to what the normalized gain actually measures, and concerns that it lacks a probability framework that undergirds psychometric methods such as Item Response Theory (IRT). The present model leads to an explanation of the observed features of the normalized gain, connects to other models such as IRT, and shows that the normalized gain does have a probability framework but one different from that emphasized by IRT.

Complicity: An International Journal of Complexity and Education

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.

This text aims to try to open a discussion about the school in the age of information, technology and the rapid changes that societies and their protagonists are going through, and to instigate the following reflection, as proposed by Gadotti (2000): what is the role of education in the information age? What perspectives can we point to education in this Third Millennium? Where are we going? In this way, we seek to raise new interpretations of natural and social phenomena, with the aim of studying and recognizing these phenomena, without the intention of reducing and minimizing the multiple interferences and correlations that make up these dynamics. It is noteworthy that ethical, political and educational phenomena are included in the social phenomena, which are fruits and products of the dynamics of processes that occur in societies and are provoked by social subjects in their multirelationships. These subjects act as agents and recipients of these actions, thus creating a feedback process.

Nonlinear dynamics, psychology, and life sciences, 2013

In this article we shall focus on learning-teaching trajectories ='successful' as well as 'unsuccessful' ones - as emergent and dynamic phenomena resulting from the interactions in the entire educational context, in particular the interaction between students and teachers viewed as processes of intertwining self-, other- and co-regulation. The article provides a review of the educational research literature on action regulation in learning and teaching, and interprets this literature in light of the theory of complex dynamic systems. Based on this reinterpretation of the literature, two dynamic models are proposed, one focusing on the short-term dynamics of learning-teaching interactions as they take place in classrooms, the other focusing on the long-term dynamics of interactions in a network of variables encompassing concerns, evaluations, actions and action effects (such as learning) students and teachers. The aim of presenting these models is to demonstrate, firs...

Linear Relationships in Education

Identifying linear and non-chaotic relationships within complex systems like education can provide valuable insights. The interrelation of the educational community (parents, teachers, librarians, cultural centers, etc.) and students belonging to schools of all levels and modalities, particularly the homeschooling modality.

Educational Researcher, 2019

Mind, Brain, and Education, 2014

The general aim of the article is to teach the reader how to transform conceptual models of change, development, and learning into mathematical expressions and how to use these equations to build dynamic models by means of the widely used spreadsheet program Excel. The explanation is supported by a number of Excel files, which the reader can download at www.paulvangeert.nl/articles_appendices.htm. The article begins with a discussion of how to define variables in the context of modeling and the difference with the context of measurement. It proceeds with a simple dynamic model to give the reader a general idea, and continues with an explanation of the extended logistic model, which can be conceived of as a building block of more complex growth models pertaining to learning and development. The final section discusses the building of a concrete developmental model, answering the question of why girls like pink. The issue of dynamic modeling of developmental and educational processes can be approached from two different sides. Abraham (forthcoming) approaches modeling from the general theory of dynamical systems, working his way down to the actual empirical phenomena and the theories that explain them. In this article the opposite approach will be followed. I will start from processes of learning and development and the conceptual theories or principles aimed at explaining them, and will then go on with the question of how these conceptual principles can be transformed into mathematical equations. Finally, a concrete tutorial will be given on how dynamic models can be constructed by means of standard spreadsheet software (Microsoft Excel).

Developmental Science, 1998

Classical developmental theories, like those of Piaget, Werner and Vygotsky, were on the verge of developmental science, the study of phenomena from the point of view of development. Methodological and theoretical shifts in the 1960s changed the original goals and questions and turned developmental psychology into a discipline that is, on the whole, more like a subservient than a leading branch of psychology. Dynamic systems theory, which has its roots in mathematics and physics, can help developmental theory out of its current blind alley by providing the general theoretical frameworks and methods for bringing the dynamic aspects of change back to the fore. By doing so, it will help turn the scientific course back in the direction of developmental science.

Learning, design, and technology: An international compendium of theory, research, practice, and policy, 2019

Chaos theory and the sciences of complexity are branches of systems theory that were developed to help understand highly complex systems. This chapter begins with a summary of some key features of these theories that are particularly relevant to understanding educational systems: coevolution, disequilibrium, positive feedback, perturbation, transformation, fractals, strange attractors, self-organization, and dynamic complexity. Then it explores two major ways that these theories can inform systemic transformation (paradigm change) in K-12 education in the United States and other parts of the world. One way is to help people understand their present systems of education, how each islikely to respond to changes that people try to make, and the effects of those changes, to determine when a system is ready for transformation and identify the system dynamics that are likely to influence both the attempted changes and the effects of those changes. The other way is to help people understand and improve the transformation process, which is itself a complex system that educational systems can use to transform themselves. Strange attractors and leverage points are two particularly powerful tools for influencing the success of the transformation process.

It is designed to be read by individuals who are involved in career developmentrelated work in a wide range of settings including information,