Complex Systems in Education: Questions, Methods and Implications for Practice

Organizers: Dimitrios Stamovlasis, Aristotle University of Thessaloniki; Matthijs Koopmans, Mercy College, USA: Hiroki Sayama, Binghamton University, USA

Objectives and Scope of Coverage: As a field of inquiry, education has been slower to catch on to complex dynamical systems (CDS) approaches than some other disciplines (e.g. biology). In educational research, there continues to be a heavy reliance on conventional paradigms and the limited range of questions they permit for investigation. Up to very recently, work on complexity in education has been largely theoretical and exploratory, without having the level of conceptual and methodological specificity that is required to capture the dynamical processes hypothesized in the dynamical literature, such as emergence, second order change, and sensitive dependence on initial conditions, nor does it speak to the specific gaps in our knowledge that result from the relative absence of dynamical perspectives in empirical research. Recent progress in dynamical systems research includes significant and path-breaking theoretical and empirical work to study the dynamical underpinnings of the educational process that are largely overlooked by conventional research paradigms.

A second major area of concern is the lack of integration of CDS into secondary school curricula and instruction. To date, the key concepts of CDS remain mostly excluded from the major content areas of science, technology, engineering and mathematics (STEM), which continue to be dominated by an empirical approach that reduces complex problems to their component pieces, and the presumption of linear models of cause and effect. The recent development of accessible materials for secondary school


Thursday September 27, 2018, Time: 9:00 – 18:30




9:00 -9:45

Fractality and power law distributions: Shifting perspectives in educational research

-Matthijs KoopmansMercy College, USA



9:45 – 10:30

The degree of readiness of teachers to change: The evaluation in Greek educational system through the lens of complexity theory

-Eugenia TsiouplisMinistry of education & Aristotle University of Thessaloniki, Greece



10:30 – 11:00

Coffee Break



11:00 – 11:40

Complexity understanding in the classroom: Case study of a novel approach

- Shae Brown – Southern Cross University, NSW Australia.



11:40 – 12:20

Complexity literacy: A progress report

-Manlio De Domenico, Hiroki Sayama et al.State University of New York, Binghamton, USA



12:20 – 13:00



13:00 – 14:30

Complexity Education and Research at C3

-Carlos Gershenson, Universidad Nacional Autónoma de México (UNAM)





14:30 – 15:15


Creativity as an emergent property of complex educational system

-Ashwin VaidyaMontclair State University, USA



15:15 – 16:00



Being in uncertainties: An inquiry-based model leveraging
complexity in teaching-learning

-Diane RosenState University of New York, Suffern, USA



16:00 – 16:30

Tea Break



16:30– 17:15

Training ability to dynamically create skillful behavior

-Martin Gardiner Brown University, Providence, R.I., U.S.A.



17:15 – 18:00

Modeling revolutionary changes: A review on bifurcations and sudden transitions in educational research

-Dimitrios StamovlasisAristotle University of Thessaloniki, Greece



9:00 – 18:00

Poster presentation – Probing complexity in educational settings: Learning, metacognition and creativity pursuit

Dimitris Stamovlasis, Georgia Stavropoulou, Lena Karastergiou & Maria GkevrouAristotle University of Thessaloniki






Abstracts (Alphabetically)


Complexity understanding in the classroom: Case study of a novel approach

Shae Brown, Southern Cross University, NSW Australia.

A central challenge for education in the new millennium is to support students to gain the skills to conceive and then articulate and organize, information of the multidimensional and the complex. Complexity thinking and understanding, towards creative engagement with complex phenomena, are vital skills for young people in these times of uncertainty and change; such skills contribute to resilience and adaptive capacity. Within my teaching practice I found students to be aware of complex dynamics, uncertainty and change, in their lives and in the world, however the current curriculum lacks language and process to conceptualize, articulate and develop complexity understanding. To address this problem a patterns-based design was developed and introduced to students, comprising flow form patterning and metaphors forming a conceptual language and practical mapping and tracking process to think about, understand and engage with complex phenomena and change. The design is developed to creatively correspond with complexity principles, to provide a material process that engages the spatial and temporal understanding of students’ embodied cognition, thereby having a low cognitive load and broad age suitability. Moving from mapping and tracking the experience of identity as a complex phenomenon, this approach integrates the social and the material in terms of complicity within any complex phenomena of interest. Early implementation with secondary students demonstrated the design’s capacity as a relational and identity development approach to learning, contributing to positive classroom culture through respect for difference, and the indeterminate as well as the determinate, as integral within the complexity of the learning environment and learning itself. In more recent research workshops with undergraduate liberal arts students the design showed to be effective for understanding complexity generally and indicated the design’s capacity as a process for engaging in collaborative projects in complex situations of difference, change and uncertainty.



Complexity Literacy: A Progress Report

Manlio De Domenico, Massimo Stella, Thomas Schmickl, Josh Brandoff, Sabine Jeschonnek, Carlos Gershenson, José R. Nicolás Carlock, Stefano Nichele, Ángel José Martínez Salinas, Daniel Goldsmith, and Hiroki Sayama

State University of New York, Binghamton, USA

Due to the growth of Complex Systems as a research field, many courses and programs are now offered on this subject. However, teaching/learning Complex Systems poses unique challenges because its concepts, methodologies, and applications have diversified dramatically over the last several decades. Currently, no agreed-upon curricular structure exists for teaching/learning this subject. This calls for "Complexity Literacy", a concise summary and structured curricular material for teaching/learning Complex Systems. Our initiative uses two approaches: (1) a small-scale online survey collecting ideas from scholars, and (2) a large-scale text analysis of a corpus created from abstracts posted on Approach (1) focused on main take-home messages and keywords of Complex Systems. Concepts most frequently mentioned in the survey responses were (in descending frequency): emergence, networks, non-linearity, interactions, adaptability, self-organization, chaos, dynamics, non-equilibrium, scaling. Syntactic analysis additionally revealed importance of scientific understanding of interaction, structure, and dynamics. Approach (2) focused on papers on whose title/abstract contained the word “complex” and at least one more keyword relevant to Complex Systems. A multidimensional concept embedding via the word2vec method revealed the network structure of keywords, in which society related concepts occupied central positions, surrounded by other concept clusters such as networks, cognition, evolution, dynamics, and criticality. These results constitute a promising starting point and also highlight the need for further data collection, analysis, and synthesis. Our next steps will include: improving both scale and quality of the corpus via community-driven curation of a complexity literature repository and utilization of past CCS abstracts; conducting higher-order concept analysis to detect significant keyword couplings, phrases and sentences; conducting longitudinal text analysis to reveal temporal dynamics of topics and their clusters in the literature; developing an organized curricular structure for Complex Systems in higher education; and producing an easy-to-understand brochure for school children, teachers, and the general public.


Training ability to dynamically create skillful behavior

Martin F. Gardiner, Brown University, Providence, R.I., U.S.A.

In Gardiner, 2018, in press, I consider that our human brains integrate two basic strategies for producing skillful behavior. With Reproductive Strategy the brain prepares important details of needed behavior to be retrieved and reproduced when needed.  With Creational Strategy the brain creates brain engagement non-linearly and dynamically to meet the specific combinations of demands from moment to moment to which skill must adjust.  Reproductive Strategy then provides stability, Creational Strategy flexibility at behaving skillfully. Our experience and training affects the specific integration of these strategies each of us develops and uses in each way that we learn to behave skillfully.  Routine components of skill profit from Reproductive Strategy, but Creational Strategy becomes increasingly important as we move forward at any skill or wish to advance in any skill demanding profession.  And yet today training for skill through Reproductive Strategy still dominates much of formal education. That musical skill training appears to interact with skill learning more generally is of both theoretical and practical interest, for musical skill is much admired, and so many adults and most children will work hard to achieve such skill if shown how. Here I will discuss evidence from longitudinal studies (Gardiner et al, 1996, Gardiner, 2000, 2008, 2018) that involve a form of musical singing skill training (Kodaly method) that when begun by First Grade was found accelerating academic progress first in Math and then in Reading, the impact especially significant for students at highest risk for poor academic progress. I propose that an essential part of this broader impact comes from features of the Kodaly method that trains capability for Creational Strategy at singing and at the same time prepares the students to apply Creational Strategy more effectively to math and reading as well.  


Complexity Education and Research at the C3

Carlos Gershenson, Universidad Nacional Autónoma de México (UNAM)

The Centro de Ciencias de la Complejidad (C3, Center for Complexity Sciences) at the Universidad Nacional Autónoma de México (UNAM) has been active for ten years developing research and education programs related to the scientific study of complex systems. Through the experience gained from these programs, we have gained some understanding about the nature of complexity as a scientific endeavor. After sharing some insights, we will explore the possibility of applying them to education and research in general.


Fractality and Power Law Distributions: Shifting Perspectives in Educational Research

Matthijs Koopmans, Mercy College, Dobbs Ferry, USA

The dynamical character of education and the complexity of its constituent relationships have long been recognized (e.g., Dewey, Vygotsky), but the full appreciation of the implications of these insights for educational research is recent. Most educational research to this day tends to focus on outcomes rather than process, and rely on conventional cross-sectional designs and statistical inference methods that do not capture this complexity. In dynamical circles, this dominant research paradigm is often referred to as the linear model and among its essential features are the following:

  1. Causality is a sequentially ordered relationship between antecedents and consequences;
  2. Every sample in a temporal string of observations is equally representative of behavior across the entire time range of interest (the ergodic assumption);
  3. Outcomes change gradually as input conditions vary (first order change), and
  4. A focus on normally distributed outcomes.

This presentation focuses on two related aspects not well accommodated within this model, namely fractality (self-similarity, scale invariance) and power law distributions (an inverse relationship between frequency of occurrence and strength of response). Fractality suggests complex adaptive behavior in the system (Beran, 1994). Power law distributions point to an underlying dynamical process irrespective of scale. A prototypical example is the earthquake statistics reported by Bak (1996), in which the magnitude of earthquakes is inversely and asymmetrically related to the frequency with which quakes of such magnitude are reported. Examples are presented for both phenomena based on my empirical work on of daily high school attendance rates over time. We will discuss how the statistical indicators (e.g., Hurst exponent) are generated and interpreted and what they reveal about the underlying dynamics of school attendance behavior.


Bak, P. (1996). How nature works: The science of self-organized criticality. New York: Springer. 

Beran, J. (1994). Statistics for long-memory processes. New York: Chapman-Hall.


Being in uncertainties: An inquiry-based model leveraging complexity in teaching-learning

Diane Rosen, State University of New York, Suffern, USA

Despite the fact that linear mechanics subvert the flourishing of nonlinear minds, pedagogy historically privileges the control, predictability and outcome-driven methods of closed systems. In recent decades the discourse on education policy and practice has shifted, with Complex Dynamical Systems (CDS) theory a significant factor as increasingly applied to dynamics of educational processes. Drawing on a systems perspective of teaching-learning as complex, open and dynamic, this discussion focuses on the Methods of Inquiry (MoI) Language Arts curriculum I designed and taught as a Consultant for Columbia University, in partnership with a New York City high school. Inquiry-based learning itself is not new; transactional/constructivist theories reach back to Vygotsky and Dewey, among others. MoI, however, is specifically grounded in basic CDS concepts, e.g. dynamic interaction, self-organization, critical instability. Instructional "perturbations," aimed at heightening the potentiating force of uncertainty, include: cultivating curiosity, challenging assumptions, exploring multiple viewpoints, and valuing dis-order as a generative modality-- a fundamental paradox of creative process described by John Keats as the "Negative Capability of being in uncertainties, mysteries, doubts, without reaching after fact & reason." Inquiry stimulates a similar kind of productive disequilibrium, fostering open-ended conditions that facilitate critical and creative thinking. Student work and process-reflections illustrate this complexivist framework in action. The notion of "being in uncertainties" is here the conceptual link between inquiry and principles of emergent phenomena, notably that complex systems operate in transitional space between order and disorder where a measure of instability spurs change. Implementation of such flexible practices, at varieties of scale and scope, is crucial for learning-to-learn within boundaries that guide but do not stifle, and teaching not just for information but transformation.


Probing complexity in educational settings: Learning, metacognition and creativity pursuit

Dimitris Stamovlasis, Georgia Stavropoulou, Lena Karastergiou & Maria Gkevrou, 

Aristotle University of Thessaloniki

Following the new paradigm of Complexity and Nonlinear Dynamics in educational research three independent studies add to the current literature by presenting catastrophe theory models  explaining learning, metacognitive skills and quest for creativity. The first study was a long term teaching intervention in Ancient Greek language, aiming to investigate the effect of students’ achievement goals orientations and the perceived-class-structure goals on students’ achievement and classroom involvement. The intervention applied to seventh grade junior high school students and lasted one academic year. One of the main hypotheses was to test whether students’ achievement goals orientations and the corresponding class structure goals can act synergetically to enhance outcomes. Cusp catastrophe analysis showed that examining students’ efficacy as the state variable, the mastery goals orientation acted as asymmetry factor predicting linearly the dependent variable, while class-structure goals acted as bifurcation factor. The implications for teaching are farther discussed. The second study was a research investigated the socialization of university students.  Achievement goal theory was also used to explore students’ perceptions and views about their future careers. One of the dimensions considered was the creativity quest in career development, which was associated with motivational constructs. Cusp catastrophe analysis revealed that the quest of creativity predicted by mastery goals orientations in the role of asymmetry factor, while both performance approach and performance avoidance goal orientations acted as bifurcation factors. The findings are in line with previous results reported within achievement goal theory demonstrated the detrimental and maladaptive role of performance orientation goals. The third study aimed to associate achievement goal orientations with learning strategies and meta-cognitive skills in university students. Learning strategies predicted meta-cognitive skills via a cusp catastrophe structure. Persistence acted as the asymmetry factor, while confidence proved to be the splitting parameter. The nonlinear models explained better the empirical data demonstrating ones more the ubiquitous nonlinearity in psychological constructs involves in educational research. Last, it is important to stress that nonlinear dynamics and complexity opens new avenues of inquiry, by offering new methodological approaches and ways of looking at encountered findings.


Modeling revolutionary changes: A review on bifurcations and sudden transitions in educational research

Dimitrios Stamovlasis, Aristotle University of Thessaloniki, Greece

The growth of Complex Dynamical Systems (CDS) perspective, along the development of nonlinear methodologies, over the last decades instigated a considerable number of investigations, which has advanced Theory in social and behavioral sciences. Besides evolutionary and gradual changes, human systems often undergo sudden transitions between states, which are overlooked by traditional linear methodological approaches. Such revolutionary changes are properly investigated via stochastic catastrophe theory. In this presentation, a lucid review of the empirical endeavors aiming in probing discontinuous changes is provided. The agenda includes applications within various domains, such as decision-making, motivational and achievement goal theories, and research on psychometric constructs operationalizing brain/mental resources involved in cognitive tasks. The common attainment in all these endeavors is revealing the crucial control variables, which under certain conditions induce nonlinear phenomena. The so called asymmetry factors are those maintaining linear relationships with state variables, which however are destroyed when a threshold value is reached in the bifurcation factor. Beyond that crucial value the system enters the bifurcation area, where transitions are possible to occur between states. This unfamiliar for the traditional paradigm phenomenology is due to the complexity of the underlying processes and the dynamics of the system. The CDS perspective has already been established in the above-mentioned areas of educational research, and has contributed to our understanding how discontinuities can occur in the systems under investigation. The nonlinear phenomena in question concern academic and social behaviors and are probed via cusp catastrophe models. Indicatively, destructive and illicit behaviors, achievement and school improvement, carrier decision making, conceptual change and creativity are phenomena for which catastrophe theory has provided superior rational explanations. The following list of variables: cognitive styles, divergent /convergent thinking, performance-approach and performance-avoidance achievement goals, emotional factors and dysfunctional beliefs are factors with the characteristic role of bifurcation. Implication for theories and practices are discussed. Moreover, methodological and statistical issues are highlighted along with philosophical question ascended from the CDS paradigm shift.



Cobb, L., & Watson, B. (1980). Statistical catastrophe theory: An overview. Mathematical Modelling, 1(4), 311–317.

Thom, R. (1975). Structural stability and morphogenesis. New York: Benjamin-Addison-Wesley.

Stamovlasis, D. (2011). Nonlinear dynamics and Neo-Piagetian Theories in Problem solving:  Perspectives on a new Epistemology and Theory Development. Nonlinear Dynamics, Psychology and Life Science, 15, 145-173.

Stamovlasis, D. & Sideridis, G. (2014). Ought approach -ought avoidance: Nonlinear effects under achievement situations. Nonlinear Dynamics, Psychology & Life Sciences, 18(1), 67-90.

Stamovlasis, D. & Vaiopoulou, J. (2017). The Role of Dysfunctional Myths in a Decision-Making Process under Bounded Rationality: A Complex Dynamical Systems Perspective. Nonlinear Dynamics, Psychology, and Life Sciences, 3, 267-288.335-358.

Stamovlasis, D., & Gonida, E. (2018). Dynamic effects of Performance-Avoidance Goal Orientation on Student Achievement in Language and Mathematics. Nonlinear Dynamics, Psychology, and Life Sciences, 22(3), 335-358.


The degree of readiness of teachers to change. The evaluation in Greek educational system through the lens of complexity theory

Eugenia Tsiouplis, Ministry of Education & Aristotle University of Thessaloniki, Greece

The Greek education system had experienced a lot of reforms, most of which have failed to make the intended changes and they attenuated shortly after their implementation or they ceased at the stage of legislative planning. One of the most important reform measures of incomplete implementation, despite the multiple efforts since 1982, is the teacher's evaluation and the self-assessment of the school units. The main position of the present paper is that the failure of educational reforms in these issues is due to a great extent to the erroneous decisions of stakeholders and policy-makers expressing a top-down implementation and fostering a mechanistic view for the education system; in addition the traditional methodological approaches based on similar mechanistic view and linear thinking failed to provide rational interpretations of such failures. The present research proposes complexity theory as an alternative epistemological framework for studying the processes underlying educational reforms. Contrary to the traditional approaches, the present research considers the system as complex one, where states of stability or instability and ensuing changes are determined by the interacting components in a dynamical and nonlinear fashion. Thus, a bottom-up perspective in investigating and interpreting the educational processes is developed. It focuses on teachers' readiness for changes in their workplace and specifically how ready they are to receive the evaluation of both the educational process and the school unit.  Specifically, it examines the dimensions of the resistance to change as far as the values, attitudes, dysfunction beliefs and planed behaviors of teachers. Methodologically, the present inquiry first implemented focus group settings to reveal clues of those dimensions, emerged out of spontaneous interaction processes, which analyzed by orbital decomposition analysis (ODA). Subsequently, survey instruments were developed and implemented to measure the dimensions of resistance-to-change.  Cusp catastrophe analysis revealed discontinuities in teachers’ attitudes and pointed out the crucial role of a number of variables as bifurcation factors. The implications of these findings are discussed, while this works sets a framework for the application of complexity theory and nonlinear dynamics in organizational theory of educational change.


Creativity as an Emergent Property of Complex Educational System

Ashwin Vaidya, Department of Mathematical Sciences, Montclair State University, Montclair, NJ.

The importance of creativity in education has been discussed often in the literature in recent times. While there remains no simple definition of creativity, the psychological literature points to traits which can be related to this idea [2]. These include: the ability to think outside the box, make connections between seemingly disparate ideas, question norms etc. The literature provides several examples of classroom experiments to help foster creativity in the classroom which includes getting students to recognize mathematics and the sciences as being creative endeavors. While these attempts are noteworthy, they suffer from a fundamental, fatal flaw; they are rooted in an unstable underlying education system. In this talk, we propose that to promote creative thinking in our classrooms, we need to see our educational system as a complex system or a network of connections between different disciplines. The 20th century notion, that school and college education is rooted in discipline based reductionism and that learning amounts to specialization caters to a few, leaving a larger and larger body of students to fail out of the system. The American liberal arts educational model prides itself on giving students a holistic perspective by exposing them to various disciplines. However, merely exposing students to different ideas without having them realize the deep, underlying connections is like expecting interesting dynamics in a collection of disconnected nodes.  We propose that education system is a complex system composed of various nodes, representing different disciplines, and the edges representing the flow of unifying ideas between them. Connections between the nodes allows for flow in these paths, resulting in greater opportunity for creativity, which is an emergent property of such a network. The abstract notions discussed above are illustrated by deliberate attempts (ambitious though small) made at the author’s institution to build an educational experience focused on creativity [3-5].



  1. R.L. DeHaan, Teaching creativity and inventive problem solving in science. CBE Life Sci. Educ., 8(3), 172-181 (2011).
  2. Sternberg, R. (2006).  The nature of creativity. Creativity Research Journal, 18(1), 87-98.
  3. M.Munakata and A. Vaidya, Encouraging creativity in mathematics and science through  photography, Teaching Mathematics with Applications, 31(3): 121-13, 2012
  4. M. Munakata and A. Vaidya, Experiments in Project- and Theme-based Learning To Encourage Creativity in Science, Journal of College Science Teaching (National Science Teacher’s Association), 45 (2), 48, 2015.
  5. E. Leszczynski, Monahan, C., M. Munakata and A. Vaidya, The Windwalker Project: An Open-Ended Approach to Physics Instruction, Journal of College Science Teaching Teaching (National Science Teacher’s Association), Vol. 46, No. 6, 27-33, 2017. 






The official Hotel of the Conference is
Makedonia Palace.

Conference Organiser: NBEvents

The official travel agency of the Conference is: Air Maritime

Photo of Thessaloniki seafront courtesy of Juli Bellou
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