Dr. Joanna Garner's Essential Reading List
Dr. Matthijs Koopmans Essential Read List
Dr. Matthijs Koopmans Essential Read List
Our second essential reading list contributor is Dr. Joanna Garner. Dr. Garner is a Research Associate Professor and the Executive Director of The Center for Educational Partnerships at Old Dominion University. Garner is an experienced PI and scholar in the fields of applied educational psychology and human development.
Essential Readings in Complexity
Dr. Joanna K. Garner, Old Dominion University
It is an honor to be asked to share my top ten essential readings in complexity, but it was not easy to choose only ten sources! I managed to curate the following list using three criteria. The first is that the resource has been influential in my own intellectual journey of becoming dissatisfied with the linear, component-driven paradigm that was in favor when I was first a psychology student in the early 1990’s (yes, I am that old), and subsequently embracing the complexity paradigm through the mid-way point of learning about the ecological approach to perception, action, and human development. A second criterion was that each source explores one or more big, cross-cutting ideas in complexity. The third criterion is that, although the Complexity Theories in Education SIG audience is broad, I present resources that speak to my “home” discipline of educational psychology. The result of applying these criteria is that most (but not all) of the resources I chose are articles rather than books or edited volumes; that the selections offer ideas about complexity as a core feature of phenomena and as an appropriate methodological approach for studying phenomena; that the resources include reference lists to entice you into further reading; and, finally, that the theory or system being characterized originates from one of several social science disciplines.
While this last feature might make some of my choices a little controversial, my decision to include them reflects a fundamental value that I hold dear—to keep moving forward on an intellectual journey, there is much to be gained from not staying in a single lane. Like Matt Koopmans’ reflections last month, I feel it is important to acknowledge work that is highly relevant but just tangential enough to not be included in the list. I encourage you to think about Ellen Skinner and colleagues’ expansion of Bronfenbrenner’s ecological systems approach through a complexity lens (1). Consider how Waddock and colleagues use complexity to explore large scale, wicked problems (2). Revisit E.J. Gibson & Walk’s classic visual cliff experiment from an ecological perspective on learning that embraces notions of feedback loops and discontinuity (3). And, seriously consider the theoretical and empirical implications of choosing a particular unit-of-analysis by reading Aaron Fisher and colleagues’ argument that aggregate data should not be evoked to describe an individual (4).
1. Ellen A. Skinner, Nicolette P. Rickert, Justin W. Vollet & Thomas A. Kindermann (2022) The complex social ecology of academic development: A bioecological framework and illustration examining the collective effects of parents, teachers, and peers on student engagement. Educational Psychologist, 57:2, 87-113, DOI:10.1080/00461520.2022.2038603
2. Waddock, S., Meszoely, G., Waddell, S., & Dentoni, D. (2015). The complexity of wicked problems in large scale change. Journal of Organizational Change Management, 28 (6), 993-1012. DOI:10.1108/JOCM-08-2014-0146
3. Gibson, E. J., & Walk, R. D. (1960). The” visual cliff”. Scientific American, 202 (4), 64-71.
4. Fisher, A.K., Medaglia, J.D. & Jeronimus, B.F. (2015). Lack of group-to-individual generalizability is a threat to human subjects research. PNAS 115 (27) E6106-E6115 https://doi.org/10.1073/pnas.1711978115
Top Ten Essential Readings List
1. Thelen, E., & Smith, L. B. (1998). Dynamic Systems Theories. In R. M. Lerner & W.
Damon (Eds.), Handbook of child psychology: Theoretical models of human development (pp. 258–312). John Wiley & Sons, Inc.
Although this chapter focuses on complex dynamic systems (CDS) as a metatheory that can be applied to human development rather than to education, I very much appreciate the way the authors lay out key CDS principles and ideas such as self-organization, attractor landscapes, and how they call attention to mechanisms of stability and change that underpin learning and development and that are revealed when we attend to dynamics and relationships in our data. The authors summarize the perspectives of other influential scholars in human development who draw on CDS principles including Waddington, Lewin, and Lerner. The mid-section of the chapter presents a useful set of steps that can be followed to promote CDS thinking about a
phenomenon and gives empirical examples of how time-series data can reveal insights into children’s attempts to master cognitive and physical tasks. Ultimately, this chapter reminds me not to forget that developmental processes and nested time-scales are inherent in educational contexts that are often only described on the basis of short-term interventions and cross-sectional data.
2. Gibson, J. J. (1979). The ecological approach to visual perception. Boston: Houghton Mifflin.
I first came across this book as an undergraduate student in whom the reductive, modular, and computational ontological and epistemological assumptions of cognitive psychology were rapidly becoming ingrained. However, in this book, Gibson introduces ideas that represent a different approach to understanding perception—one that is holistic, situated, functional, and embodied. If we extrapolate these ideas to other human abilities and tasks, we are called to consider the agent-in-context and to characterize behavior as an emergent property of the individual and the environment. This book demonstrated to me that it is possible to prioritize individual-environment interrelations (or couplings) theoretically and empirically. Now, I think it impossible (and meaningless) to adequately capture the individual independently of their relationship with the environment.
3. Newell, K.M., Liu, Y-T, & Mayer-Kress, G. (2001). Time scales in motor learning and development. Psychological Review 108, (1), 57-82.
This article introduces powerful complex systems concepts that can be applied to learning, including the attractor space as a conceptual-probabilistic space that an individual intentionally navigates through during learning, and variations in time-scales that are often overlooked as possibilities when we are examining learning. This work also calls attention to the ever-present issue of sameness or stability versus variation or instability in human behavior. Newell and Mayer-Kress also point out that, in part due to variability and its masking under the circumstances of aggregation, aggregated time-series data can fail to represent individual behavior when it is measured over time. Finally, this article embraces seeking non-linear functions to describe changes in behavior that result from learning. As a complexity informed researcher, these latter points prompt me to be ever mindful of the unit-of-analysis (i.e. the individual or the collective group) and to not assume that change over time will manifest in linear ways.
4. Overton, W.F. (2013). A new paradigm for developmental science: Relationism and Relational-Developmental Systems. Applied Developmental Science 17 (2), 94-107.
Overton begins his article by explaining the flaws in the current linear, mechanistic paradigm that much developmental (and, I would charge, educational) research is couched in. Once the reader understands that phenomena are poorly understood if viewed like clockwork and examined through methodologies that prize splitting, atomism, reductionism, and componential thinking, Overton introduces an alternative—the relational paradigm. The relational paradigm embraces nonlinearity, emergence, context, process-substance, and holism. He calls us to reconsider the theoretical, the empirical and the practical aspects of our work when he writes that the “analysis of parts must occur in the context of the parts’ functioning in the whole. The context-free specifications of any object, event, or process—whether it be a DNA, cell, neuron, evolution, the architecture of mind, or culture—is illegitimate within a holistic system.” The meta-theory of relational developmental systems that follows views individuals as active, adaptive, self-organizing and self-regulating organisms whose development and change results from the reciprocal interplay among elements at multiple levels of various nested systems. One of the most interesting facets of this approach is its focus on embodied, situated action as both an emergent property of and as an input to the system. This has influenced my own theoretical and design work on identity.
5. Opfer, V.D. and Pedder, D. (2011). Conceptualizing teacher learning. Review of Educational Research 81 (3), 376-407.
In this influential article, Opfer and Pedder use a complexity framework to re-imagine teacher learning and professional development (PD). They call attention to the importance of describing the contexts in which learning happens, identify that simple decisions might have complex, unpredictable, but non-random causes, and propose that teachers’ learning should be conceptualized as manifesting from within nested systems that incorporate feedback mechanisms to adapt and change over time. Opfer and Pedder move away from the process-product assumptions behind much of the teacher PD literature and instead evoke interacting learning orientation systems within and among individuals. They critique linear, unidirectional and single entry-point conceptualizations of learning, and call for mixed methods studies that can describe small- and large-scale change and attend to context. These ideas spurred me to consider teacher PD as a complex dynamic system and therein reconsider my role as a facilitator, designer, and evaluator.
6. Marchand, G.C & Hilpert, J. (2023). Contributions of complex systems approaches, perspectives, models, and methods in educational psychology. In P. Schutz & K. Muis (Eds.), Handbook of Educational Psychology. (Ch.7. pp139-161). DOI:10.4324/9780429433726-9
This very recent review of complexity in educational psychology offers an orientation to complex systems, and a review of the influence of complex dynamic systems perspectives in various educational psychology research areas such as motivation, student engagement, emotion, self-regulated learning, collaborative learning, and teacher-student relationships. In the second part of the chapter, Marchand and Hilpert consider how mixed methods, quantitative methods, and qualitative methods can contribute insights into complex systems at various units-of-analysis in educational psychology research. They propose that “embracing a CS ontology requires an examination of the epistemological assumptions about research, including research design, the desire for replication, and integration of timescales and multiple levels of analysis.” Significantly, they also elevate issues of diversity, equity and inclusion as they are “multiply influenced and deeply rooted in context and culture.”
7. Hamaker, E.L. (2012). Why researchers should think “within-person”: A paradigmatic rationale. In M.R. Mehl & T.S. Conner (Eds.), Handbook of Researcher Methods for Studying Everyday Life. (Ch.3, pp.43-61). New York: Guilford.
Can large sample research reveal general laws that apply to each individual within the sample? Is what is revealed in the aggregate true in general for each person? Hamaker argues not necessarily, and presents various scenarios in which within-person relationships among variables may differ in strength and direction from what may be found at the population level between persons. This chapter explains the ergodicity principle (see also Molenaar’s work), which holds when population statistics, between-variable relationships, and time-lag effects match individual ones—conditions that almost never hold in psychological and educational research. Further, she urges us to consider that in order to understand how variables behave within persons, they must be studied over time. She goes on to describe concepts in autoregression and, crucially, link these to regulatory mechanisms that may vary in their influence on system variability. Finally, she presents multilevel modeling in relation to time series data. Overall, this chapter calls us to very seriously consider the validity of the inferences we make when we collect aggregate, cross-sectional data and frame it in terms of theoretical frameworks that are often specified at the individual level. From a complex systems perspective, it reminds us to remain extremely clear about the unit(s)-of-analysis that we are examining and the assumptions we are making about their variability or stability under particular conditions.
8. Fromm, J. Types and Forms of Emergence. Retrieved from https://arxiv.org/ftp/nlin/papers/0506/0506028.pdf
Framed in scientific and engineering systems, Jochen Fromm’s paper on emergence nonetheless calls us to consider multi-agent systems such as those studied in education. He defines terms such as emergence and emergent properties, and cross-references them with terms that we strive to operationalize in educational research such as prediction and causation. Fromm presents various taxonomic levels for conceptualizing emergence in relation to causality and as he does so, prompts us to consider how we might think about feedback loops and relations between system components (whether these be individuals or structural aspects of educational systems). For those researchers who are attempting to describe educational systems using complex systems concepts, this paper might provide ideas about how to frame and even assign nomenclature to the nature of the relations among system components and the anticipated consequences of components’ behavior over time.
9. Koopmans, M. & Stamovlasis, D. (2016). Complex Dynamical Systems in Education https://www.amazon.com/Complex-Dynamical-Systems-Education-Applications/dp/3319 801759
In this edited volume, Dr. Matt Koopmans and Dr. Dimitrios Stamovlasis provide an in-depth but accessible presentation of complex dynamical systems applied to a variety of problems, issues, and units-of-analysis in educational research. The first half of the book presents major concepts and the second half of the book includes chapters that demonstrate a variety of empirical approaches. If you are interested in learning more about quantitative approaches to research that applies complexity to education, this book will expose you to a variety of techniques.
10. Jacobson, M. (2006). Complex systems in education: Scientific and educational importance and implications for the learning sciences. Journal of the Learning Sciences 15, 11-34.
As a final reading, I recommend this article because it helps to frame an answer to the question of how we familiarize students with complex systems concepts and complexity informed thinking, so that no matter their career trajectory they are equipped to think critically about the world using systems ideas and methods. Jacobson provides a sympathetic treatment to the idea of cognitive challenges associated with learning about complex systems. Human beings tend to prefer simple, mechanistic explanations over complex, uncertain ones. Novices struggle to appreciate pattern and complexity. Students have difficulty appreciating agent-based models and simulations. Fortunately, Jacobson also outlines some pedagogical design principles that may help teach students about complex systems. These include experiential learning, collaborative learning and discussion, and the social construction of theories and models. While we grapple with how to characterize educational phenomena using the ontology and epistemology of complex systems, we should not forget to promote the capacity for complex and contextual thinking by teachers, students, administrators, and policymakers.
Essential Readings in Complexity
Dr. Joanna K. Garner, Old Dominion University
It is an honor to be asked to share my top ten essential readings in complexity, but it was not easy to choose only ten sources! I managed to curate the following list using three criteria. The first is that the resource has been influential in my own intellectual journey of becoming dissatisfied with the linear, component-driven paradigm that was in favor when I was first a psychology student in the early 1990’s (yes, I am that old), and subsequently embracing the complexity paradigm through the mid-way point of learning about the ecological approach to perception, action, and human development. A second criterion was that each source explores one or more big, cross-cutting ideas in complexity. The third criterion is that, although the Complexity Theories in Education SIG audience is broad, I present resources that speak to my “home” discipline of educational psychology. The result of applying these criteria is that most (but not all) of the resources I chose are articles rather than books or edited volumes; that the selections offer ideas about complexity as a core feature of phenomena and as an appropriate methodological approach for studying phenomena; that the resources include reference lists to entice you into further reading; and, finally, that the theory or system being characterized originates from one of several social science disciplines.
While this last feature might make some of my choices a little controversial, my decision to include them reflects a fundamental value that I hold dear—to keep moving forward on an intellectual journey, there is much to be gained from not staying in a single lane. Like Matt Koopmans’ reflections last month, I feel it is important to acknowledge work that is highly relevant but just tangential enough to not be included in the list. I encourage you to think about Ellen Skinner and colleagues’ expansion of Bronfenbrenner’s ecological systems approach through a complexity lens (1). Consider how Waddock and colleagues use complexity to explore large scale, wicked problems (2). Revisit E.J. Gibson & Walk’s classic visual cliff experiment from an ecological perspective on learning that embraces notions of feedback loops and discontinuity (3). And, seriously consider the theoretical and empirical implications of choosing a particular unit-of-analysis by reading Aaron Fisher and colleagues’ argument that aggregate data should not be evoked to describe an individual (4).
1. Ellen A. Skinner, Nicolette P. Rickert, Justin W. Vollet & Thomas A. Kindermann (2022) The complex social ecology of academic development: A bioecological framework and illustration examining the collective effects of parents, teachers, and peers on student engagement. Educational Psychologist, 57:2, 87-113, DOI:10.1080/00461520.2022.2038603
2. Waddock, S., Meszoely, G., Waddell, S., & Dentoni, D. (2015). The complexity of wicked problems in large scale change. Journal of Organizational Change Management, 28 (6), 993-1012. DOI:10.1108/JOCM-08-2014-0146
3. Gibson, E. J., & Walk, R. D. (1960). The” visual cliff”. Scientific American, 202 (4), 64-71.
4. Fisher, A.K., Medaglia, J.D. & Jeronimus, B.F. (2015). Lack of group-to-individual generalizability is a threat to human subjects research. PNAS 115 (27) E6106-E6115 https://doi.org/10.1073/pnas.1711978115
Top Ten Essential Readings List
1. Thelen, E., & Smith, L. B. (1998). Dynamic Systems Theories. In R. M. Lerner & W.
Damon (Eds.), Handbook of child psychology: Theoretical models of human development (pp. 258–312). John Wiley & Sons, Inc.
Although this chapter focuses on complex dynamic systems (CDS) as a metatheory that can be applied to human development rather than to education, I very much appreciate the way the authors lay out key CDS principles and ideas such as self-organization, attractor landscapes, and how they call attention to mechanisms of stability and change that underpin learning and development and that are revealed when we attend to dynamics and relationships in our data. The authors summarize the perspectives of other influential scholars in human development who draw on CDS principles including Waddington, Lewin, and Lerner. The mid-section of the chapter presents a useful set of steps that can be followed to promote CDS thinking about a
phenomenon and gives empirical examples of how time-series data can reveal insights into children’s attempts to master cognitive and physical tasks. Ultimately, this chapter reminds me not to forget that developmental processes and nested time-scales are inherent in educational contexts that are often only described on the basis of short-term interventions and cross-sectional data.
2. Gibson, J. J. (1979). The ecological approach to visual perception. Boston: Houghton Mifflin.
I first came across this book as an undergraduate student in whom the reductive, modular, and computational ontological and epistemological assumptions of cognitive psychology were rapidly becoming ingrained. However, in this book, Gibson introduces ideas that represent a different approach to understanding perception—one that is holistic, situated, functional, and embodied. If we extrapolate these ideas to other human abilities and tasks, we are called to consider the agent-in-context and to characterize behavior as an emergent property of the individual and the environment. This book demonstrated to me that it is possible to prioritize individual-environment interrelations (or couplings) theoretically and empirically. Now, I think it impossible (and meaningless) to adequately capture the individual independently of their relationship with the environment.
3. Newell, K.M., Liu, Y-T, & Mayer-Kress, G. (2001). Time scales in motor learning and development. Psychological Review 108, (1), 57-82.
This article introduces powerful complex systems concepts that can be applied to learning, including the attractor space as a conceptual-probabilistic space that an individual intentionally navigates through during learning, and variations in time-scales that are often overlooked as possibilities when we are examining learning. This work also calls attention to the ever-present issue of sameness or stability versus variation or instability in human behavior. Newell and Mayer-Kress also point out that, in part due to variability and its masking under the circumstances of aggregation, aggregated time-series data can fail to represent individual behavior when it is measured over time. Finally, this article embraces seeking non-linear functions to describe changes in behavior that result from learning. As a complexity informed researcher, these latter points prompt me to be ever mindful of the unit-of-analysis (i.e. the individual or the collective group) and to not assume that change over time will manifest in linear ways.
4. Overton, W.F. (2013). A new paradigm for developmental science: Relationism and Relational-Developmental Systems. Applied Developmental Science 17 (2), 94-107.
Overton begins his article by explaining the flaws in the current linear, mechanistic paradigm that much developmental (and, I would charge, educational) research is couched in. Once the reader understands that phenomena are poorly understood if viewed like clockwork and examined through methodologies that prize splitting, atomism, reductionism, and componential thinking, Overton introduces an alternative—the relational paradigm. The relational paradigm embraces nonlinearity, emergence, context, process-substance, and holism. He calls us to reconsider the theoretical, the empirical and the practical aspects of our work when he writes that the “analysis of parts must occur in the context of the parts’ functioning in the whole. The context-free specifications of any object, event, or process—whether it be a DNA, cell, neuron, evolution, the architecture of mind, or culture—is illegitimate within a holistic system.” The meta-theory of relational developmental systems that follows views individuals as active, adaptive, self-organizing and self-regulating organisms whose development and change results from the reciprocal interplay among elements at multiple levels of various nested systems. One of the most interesting facets of this approach is its focus on embodied, situated action as both an emergent property of and as an input to the system. This has influenced my own theoretical and design work on identity.
5. Opfer, V.D. and Pedder, D. (2011). Conceptualizing teacher learning. Review of Educational Research 81 (3), 376-407.
In this influential article, Opfer and Pedder use a complexity framework to re-imagine teacher learning and professional development (PD). They call attention to the importance of describing the contexts in which learning happens, identify that simple decisions might have complex, unpredictable, but non-random causes, and propose that teachers’ learning should be conceptualized as manifesting from within nested systems that incorporate feedback mechanisms to adapt and change over time. Opfer and Pedder move away from the process-product assumptions behind much of the teacher PD literature and instead evoke interacting learning orientation systems within and among individuals. They critique linear, unidirectional and single entry-point conceptualizations of learning, and call for mixed methods studies that can describe small- and large-scale change and attend to context. These ideas spurred me to consider teacher PD as a complex dynamic system and therein reconsider my role as a facilitator, designer, and evaluator.
6. Marchand, G.C & Hilpert, J. (2023). Contributions of complex systems approaches, perspectives, models, and methods in educational psychology. In P. Schutz & K. Muis (Eds.), Handbook of Educational Psychology. (Ch.7. pp139-161). DOI:10.4324/9780429433726-9
This very recent review of complexity in educational psychology offers an orientation to complex systems, and a review of the influence of complex dynamic systems perspectives in various educational psychology research areas such as motivation, student engagement, emotion, self-regulated learning, collaborative learning, and teacher-student relationships. In the second part of the chapter, Marchand and Hilpert consider how mixed methods, quantitative methods, and qualitative methods can contribute insights into complex systems at various units-of-analysis in educational psychology research. They propose that “embracing a CS ontology requires an examination of the epistemological assumptions about research, including research design, the desire for replication, and integration of timescales and multiple levels of analysis.” Significantly, they also elevate issues of diversity, equity and inclusion as they are “multiply influenced and deeply rooted in context and culture.”
7. Hamaker, E.L. (2012). Why researchers should think “within-person”: A paradigmatic rationale. In M.R. Mehl & T.S. Conner (Eds.), Handbook of Researcher Methods for Studying Everyday Life. (Ch.3, pp.43-61). New York: Guilford.
Can large sample research reveal general laws that apply to each individual within the sample? Is what is revealed in the aggregate true in general for each person? Hamaker argues not necessarily, and presents various scenarios in which within-person relationships among variables may differ in strength and direction from what may be found at the population level between persons. This chapter explains the ergodicity principle (see also Molenaar’s work), which holds when population statistics, between-variable relationships, and time-lag effects match individual ones—conditions that almost never hold in psychological and educational research. Further, she urges us to consider that in order to understand how variables behave within persons, they must be studied over time. She goes on to describe concepts in autoregression and, crucially, link these to regulatory mechanisms that may vary in their influence on system variability. Finally, she presents multilevel modeling in relation to time series data. Overall, this chapter calls us to very seriously consider the validity of the inferences we make when we collect aggregate, cross-sectional data and frame it in terms of theoretical frameworks that are often specified at the individual level. From a complex systems perspective, it reminds us to remain extremely clear about the unit(s)-of-analysis that we are examining and the assumptions we are making about their variability or stability under particular conditions.
8. Fromm, J. Types and Forms of Emergence. Retrieved from https://arxiv.org/ftp/nlin/papers/0506/0506028.pdf
Framed in scientific and engineering systems, Jochen Fromm’s paper on emergence nonetheless calls us to consider multi-agent systems such as those studied in education. He defines terms such as emergence and emergent properties, and cross-references them with terms that we strive to operationalize in educational research such as prediction and causation. Fromm presents various taxonomic levels for conceptualizing emergence in relation to causality and as he does so, prompts us to consider how we might think about feedback loops and relations between system components (whether these be individuals or structural aspects of educational systems). For those researchers who are attempting to describe educational systems using complex systems concepts, this paper might provide ideas about how to frame and even assign nomenclature to the nature of the relations among system components and the anticipated consequences of components’ behavior over time.
9. Koopmans, M. & Stamovlasis, D. (2016). Complex Dynamical Systems in Education https://www.amazon.com/Complex-Dynamical-Systems-Education-Applications/dp/3319 801759
In this edited volume, Dr. Matt Koopmans and Dr. Dimitrios Stamovlasis provide an in-depth but accessible presentation of complex dynamical systems applied to a variety of problems, issues, and units-of-analysis in educational research. The first half of the book presents major concepts and the second half of the book includes chapters that demonstrate a variety of empirical approaches. If you are interested in learning more about quantitative approaches to research that applies complexity to education, this book will expose you to a variety of techniques.
10. Jacobson, M. (2006). Complex systems in education: Scientific and educational importance and implications for the learning sciences. Journal of the Learning Sciences 15, 11-34.
As a final reading, I recommend this article because it helps to frame an answer to the question of how we familiarize students with complex systems concepts and complexity informed thinking, so that no matter their career trajectory they are equipped to think critically about the world using systems ideas and methods. Jacobson provides a sympathetic treatment to the idea of cognitive challenges associated with learning about complex systems. Human beings tend to prefer simple, mechanistic explanations over complex, uncertain ones. Novices struggle to appreciate pattern and complexity. Students have difficulty appreciating agent-based models and simulations. Fortunately, Jacobson also outlines some pedagogical design principles that may help teach students about complex systems. These include experiential learning, collaborative learning and discussion, and the social construction of theories and models. While we grapple with how to characterize educational phenomena using the ontology and epistemology of complex systems, we should not forget to promote the capacity for complex and contextual thinking by teachers, students, administrators, and policymakers.
Our first contributor in our essential readings series is Dr. Matthijs Koopmans.
Matthijs Koopmans, professor of educational leadership, joined the faculty at Mercy College in 2011. His research interests include school reform, complexity theory, and time series analysis. His latest publications include a book and two articles, on the application of time series analysis to fractal estimation. He is one of the founding editors of the International Journal of Education, and is on the editorial board of Nonlinear Dynamics, Psychology, and Life Sciences. He earned his doctorate from the Harvard Graduate School of Education.
Ten Essential Titles in Complexity Theory and Nonlinear Dynamics: A Subjective Overview
Matthijs Koopmans – Mercy University (USA)
What are the most essential readings in nonlinear dynamics and complexity theory, and why are they so important? In response to a charge from this website to address this question, I compiled a list of ten essential titles in complexity theory, which is shown below with a justification for each title. I used the following three selection criteria: 1. Personal relevance, 2. Foundational value to the field of complexity, and 3. Only books, no articles. With respect to the first point, I focused on those texts that had a shaping influence on my own scholarship, and on which I continue to rely to this day. Thus, this overview is subjective in that it situates these writings in a personal context. Regarding the second criterion, I decided to limit my discussion to texts that are generally considered as having been influential to complexity scholars and have found a wide range of application – the classics if you will. The third point is related. The books listed here mostly have a broad appeal, as they are not constrained by the specialties represented by refereed professional journals. A consequence of applying these selection criteria is that all texts in this list were published quite some time ago; the most recent one came out more than 25 years ago. Yet these are also the contributions that have lost none of their value over the years, and to which we keep returning when in need of a clear perspective, a good rationale for the use of complexity theory in applied settings or a source of inspiration to unclog our thinking.
All inclusions have omissions, and so it is here. I must confess to a feeling of restlessness about the absence of Mandelbrot’s text on fractals as well as a few other fundamental items, such as Holland’s Hidden order, Kaufman’s At home in the universe, Sprott’s Chaos theory and time series analysis, and Waldrop’s Complexity, all of which would have deserved a place here. There is also no coverage of social network analysis, a perspective that is rapidly gaining ground in complexity circles, including some very good textbooks, but whose influence on my scholarly activities has been very limited up to this point. And then, many influential writings on the application of complexity theory appeared as articles instead of books. Examples are van der Maas and Molenaar’s seminal paper on the application of catastrophe theory to Piaget’s theory of intellectual development (Psychological Review, 1992), van Geert’s successful synthesis of Piaget and Vygotsky based on complexity theory (Psychological Review, 1998), Molenaar’s revolutionary manifesto on psychology as a science of individuals rather than populations (Measurement, 2004), and Goldstein’s groundbreaking work on emergence (Emergence: Complexity and Organization, 1999, 2014). Articles such as these deserve their own listing. Despite these exclusions, lots of good reading remains. My Ten Essential Titles are the following:
Abraham, F. D., Abraham, R. H., & Shaw, C. D. (1990). A visual introduction to dynamical systems theory for psychology. Aerial Press.
There is no better way to get fired up about all things dynamic than by consulting this book, often referred to in complexity circles as the yellow book, in reference to the color of its sleeve. At the time of its publication, the application of chaos and complexity theory in psychology and the social sciences was a new idea, creating the need for a rapid understanding of the basic concepts minus the elaborate mathematical justification typically found in the dynamical literature at the time. This book outlines the use of dynamical systems theory in psychology through the visual depiction of dynamical processes in charts and figures, which, taken together, reframe our understanding of basic psychological processes in dynamical terms. The sections of the book are patched together in a rather crude fashion and the explanations accompanying the figures are not always of sufficient clarity and depth, but true to its purpose, the visuals are doing the talking in this book, and they help the reader gain an intuitive grasp of the basic principles underlying chaos theory, complexity, and other dynamical phenomena. In a way, the book I edited with Steve Guastello and David Pincus, Chaos and complexity in psychology: The theory of nonlinear dynamical systems (Cambridge University Press, 2009), builds on this text by supplementing its sketchy intuitions with a detailed explication of the linkages between theory and evidence in a wide range of psychological applications, including perception, cognition, neurology, mental health and child development.
Bak, P. (1996). How nature works: The science of self-organized criticality. Springer.
Power laws, fractal shapes and self-organized criticality are essential pieces of the complexity puzzle, and this book provides lucid explanations as well as proverbial examples of each. So, there is the sandpile experiment in which the gradual pouring of grains leads to avalanches on the pile, the fractal organization of fjords within fjords that constitute the Norwegian coast, the power law distribution that correlates the frequency of earthquakes with their intensity on the Richter scale, and more. I expect that the theory of self-organized criticality will have staying power in education. It helps us understand how transformation works, and how to detect a propensity toward change in organizations, both of which are key to the field. In addition, the power law distributions discussed here offer an alternative to the oft cherished assumption of normally distributed outcomes, in which extreme measurements are marginalized. This book provides a foundation to a wide range of applications of complexity theory, in other words, whose relevance to education and other disciplines can be readily appreciated. For this reason, it is one of the most frequently cited titles in my published work.
Bateson, G. (1972). Steps to an ecology of mind: A revolutionary approach to man’s understanding of himself. Ballantine.
This book brings together Gregory Bateson’s most essential writings. It is a truly multi-disciplinary festschrift that covers a wide territory, including his early writings in anthropology from the mid-nineteen thirties, as well as those on metacognition, animal intelligence, systemic transformation and the highly controversial double bind theory concerning the mental health implications of dysfunctional patterns of family interaction. Much of this work is connected to the Macy conferences that took place throughout the nineteen forties and fifties, and which largely defined the cybernetic movement at the time. This group of scholars searched for general principles underlying biological, cultural, and social phenomena as well as having early ventures into the areas of artificial intelligence and robotics. Bateson’s writings made an important contribution to this endeavor. They are interesting and thought-provoking, and for me, they continue to be a source of intellectual stimulation.
Beran, J. (1994). Statistics for long-memory processes. Chapman-Hall.
When making inferences about a population based on data from a sample, it is usually assumed that the datapoints represent independent observations. For the analysis of recurrent measures in a single unit, this assumption cannot be taken for granted as it could produce biased estimates. Time series analysis is a technique that has been expressly developed to address this issue by modelling the dependencies between neighboring observations on the time scale. However, as originally conceived, this method is not very good at estimating the dependencies between observations that are far removed from each other, a situation referred to as long-memory processes. Yet, it is those long-memory processes that typically characterize chaos or fractality in time series data. Beran provides a foundational statistical text on how to handle such situations, and it is essential reading for those who have an interest in the extension of conventional statistical methods to tackle complex processes.
Gilmore, R. (1981). Catastrophe theory for scientists and engineers. Wiley.
Catastrophe theory consists of seven transformative scenarios of progressively greater mathematical complexity. The common aspect in these scenarios is singularity, a mathematically unacceptable region in the coordinate space that forces qualitative transformation in the relationships between the variables defining the system. The most well-known example of such models is the cusp, in which variability in two predictors, or control parameters, determines whether changes on the outcome surface are linear or nonlinear. I have my reservations about the way some scholars use of catastrophe theory as a basis for the statistical regression analyses of empirical data, but as a mathematical formulation of the conditions under which qualitative transformation takes place, the theory is indisputably powerful, and this text provides an excellent overview.
Kaplan, D., & Glass, L. (1995). Understanding nonlinear dynamics. Springer.
This text is aimed at undergraduate students in the biological sciences, and it covers the basics of nonlinear dynamical theory and complex systems from that vantage point. The book strikes exactly the right balance between theory, models, and applications, and is full of relevant and interesting examples. The mathematical formulation of the dynamical processes is not avoided, but it is presented at a level that anyone with high school mathematics should be able to understand. Thus, the book takes us to unfamiliar terrain using familiar conventions. Under the header Dynamics in Action, inserts are provided throughout the book to illustrate nonlinear dynamics in published research and to show simulations of the differential equations that capture most of the dynamical processes discussed here. Challenging but doable exercises are scattered throughout. The book also offers one of the best and most concise definitions of chaos that I have encountered. It can be found on pp. 27-33, with an elaboration (also concise) on pp. 314 – 338. A revised and updated edition of this text is long overdue.
Nicolis, G., & Prigogine, I. (1989). Exploring complexity: An introduction. Freeman.
Given that change is such a central concern in the applied sciences – we talk all the time about interventions and their outcomes, educational reform, narrowing the achievement gap, etc., it is remarkable that our underlying theories of how change works continue to be largely one-dimensional (e.g., logic models, performance goals, linear regression, structural equation models). One way of making the case for complexity theory is by pointing to the manifold of transformative scenarios it embodies (e.g., catastrophes, emergence, the sandpile, bifurcation, perturbation, dissipation). This book unifies these various theories of change into a comprehensive and coherent account. It requires a willingness on the part of the reader to get engaged in the mathematics of complex transformation, but doing so yields a deeper understanding of how the various transformative scenarios hang together as a single structure and how aspects of this structure can be applied as needed to any problem of interest.
Prigogine, I., & Stengers, I. (1984). Order out of chaos: Man’s new dialogue with nature. New York: Bantam.
Rarely is the sense of being part of a scientific revolution as undeniable as when reading this book. While it focuses on the application of chaos theory in biology, physics and chemistry, the vast potential of the ideas expressed here lies in their applicability to virtually any empirical science, including education, psychology, and other social sciences. The book argues that we need to be able to contemplate far from equilibrium scenarios and other forms of instability in the systems, and how they can lead to order creation. Those concerns are not very well served by normal science (nor by some of the current work in complexity theory, for that matter). Part of what makes this book groundbreaking is that it integrates quantitative and qualitative science into a single paradigm, creating a ‘third force’ in our discussion of research methods in the empirical sciences. This third force views qualitative processes as being within the purview of mathematics and views the linear model that the guides much of our quantitative research as a special case of a much larger paradigm that also includes such things as period doubling, bifurcations, irreversibility, entropy, instability, and strange attractor regimes underlying seemingly random fluctuations in systems’ behaviors. The features, in other words, that make systems dynamic, interesting, and sometimes unpredictable.
Varela, F. J. (1979). Principles of biological autonomy. North Holland.
One of the key insights of complexity theory is that systems do not merely exist but form and maintain themselves through the interaction between components and the higher-level systems defined by those components. These interactions can be seen, then, as a production process, sometimes called autopoiesis. This book deals with the far-reaching implications of this idea, by considering such things are autonomy, identity, separateness, and individuality as instances of systemic self-preservation, and then formulates a theory about how this separateness gets asserted in the ongoing flow of the biological process. Varela’s approach is highly idiosyncratic, but the issues are profound. To me, this book is one of the most fascinating highlights of the scholarship coming out of the cybernetic movement. Tucked inside this volume as Appendix B is a general formulation of Gregory Bateson’s double bind theory called n-bind. I happened to be working in that area at the time and had an exchange with Varela about this theory. I also sent him a copy of a paper I had written on this subject (which came out in 2001 in Nonlinear Dynamics, Psychology, and Life Sciences). He seemed amused that someone had picked up on n-bind and confessed that he had forgotten about it. This book has been long out of print and deserves to be re-issued. In the meantime, it can be accessed at Principles Of Biological Autonomy [PDF] [4k6aoohpudf0] (vdoc.pub).
Watzlawick, P., Weakland, J., Fisch, R. (1974). Change: Principles of problem formation and problem resolution. Norton.
This text is applied in its orientation, albeit not in the field of education. This volume was written by three family therapists, who were part of a movement that was known at the time as the Palo Alto Group. This collective concerned itself with the applicability of general systems concepts to family interaction. The text is concerned with the persistence of undesirable situations and the challenge of changing them in the face of resistance. While the authors focus on the treatment of families, much of what they say is highly relevant to educators and educational policy makers as well. The book makes a distinction between first-order change and second-order change. The former of these refers to the appearance of transformation through processes that in effect reinforce existing constellations. First-order change is therefore referred to here as problem formation. Second-order change refers to processes that reconfigure the entire system. Family therapists strive for this kind of change in the face of dysfunctional family interactions, and therefore, the authors coined the term problem resolution for it. Whether the relationship between types of change and the types of problem resolution is as straightforward as it is made out to be here is a question up for discussion: we know that real change can make matters the worse. Yet the usefulness of the vocabulary introduced here for the applied sciences is beyond dispute, and educators should make better use of it.
Matthijs Koopmans, professor of educational leadership, joined the faculty at Mercy College in 2011. His research interests include school reform, complexity theory, and time series analysis. His latest publications include a book and two articles, on the application of time series analysis to fractal estimation. He is one of the founding editors of the International Journal of Education, and is on the editorial board of Nonlinear Dynamics, Psychology, and Life Sciences. He earned his doctorate from the Harvard Graduate School of Education.
Ten Essential Titles in Complexity Theory and Nonlinear Dynamics: A Subjective Overview
Matthijs Koopmans – Mercy University (USA)
What are the most essential readings in nonlinear dynamics and complexity theory, and why are they so important? In response to a charge from this website to address this question, I compiled a list of ten essential titles in complexity theory, which is shown below with a justification for each title. I used the following three selection criteria: 1. Personal relevance, 2. Foundational value to the field of complexity, and 3. Only books, no articles. With respect to the first point, I focused on those texts that had a shaping influence on my own scholarship, and on which I continue to rely to this day. Thus, this overview is subjective in that it situates these writings in a personal context. Regarding the second criterion, I decided to limit my discussion to texts that are generally considered as having been influential to complexity scholars and have found a wide range of application – the classics if you will. The third point is related. The books listed here mostly have a broad appeal, as they are not constrained by the specialties represented by refereed professional journals. A consequence of applying these selection criteria is that all texts in this list were published quite some time ago; the most recent one came out more than 25 years ago. Yet these are also the contributions that have lost none of their value over the years, and to which we keep returning when in need of a clear perspective, a good rationale for the use of complexity theory in applied settings or a source of inspiration to unclog our thinking.
All inclusions have omissions, and so it is here. I must confess to a feeling of restlessness about the absence of Mandelbrot’s text on fractals as well as a few other fundamental items, such as Holland’s Hidden order, Kaufman’s At home in the universe, Sprott’s Chaos theory and time series analysis, and Waldrop’s Complexity, all of which would have deserved a place here. There is also no coverage of social network analysis, a perspective that is rapidly gaining ground in complexity circles, including some very good textbooks, but whose influence on my scholarly activities has been very limited up to this point. And then, many influential writings on the application of complexity theory appeared as articles instead of books. Examples are van der Maas and Molenaar’s seminal paper on the application of catastrophe theory to Piaget’s theory of intellectual development (Psychological Review, 1992), van Geert’s successful synthesis of Piaget and Vygotsky based on complexity theory (Psychological Review, 1998), Molenaar’s revolutionary manifesto on psychology as a science of individuals rather than populations (Measurement, 2004), and Goldstein’s groundbreaking work on emergence (Emergence: Complexity and Organization, 1999, 2014). Articles such as these deserve their own listing. Despite these exclusions, lots of good reading remains. My Ten Essential Titles are the following:
Abraham, F. D., Abraham, R. H., & Shaw, C. D. (1990). A visual introduction to dynamical systems theory for psychology. Aerial Press.
There is no better way to get fired up about all things dynamic than by consulting this book, often referred to in complexity circles as the yellow book, in reference to the color of its sleeve. At the time of its publication, the application of chaos and complexity theory in psychology and the social sciences was a new idea, creating the need for a rapid understanding of the basic concepts minus the elaborate mathematical justification typically found in the dynamical literature at the time. This book outlines the use of dynamical systems theory in psychology through the visual depiction of dynamical processes in charts and figures, which, taken together, reframe our understanding of basic psychological processes in dynamical terms. The sections of the book are patched together in a rather crude fashion and the explanations accompanying the figures are not always of sufficient clarity and depth, but true to its purpose, the visuals are doing the talking in this book, and they help the reader gain an intuitive grasp of the basic principles underlying chaos theory, complexity, and other dynamical phenomena. In a way, the book I edited with Steve Guastello and David Pincus, Chaos and complexity in psychology: The theory of nonlinear dynamical systems (Cambridge University Press, 2009), builds on this text by supplementing its sketchy intuitions with a detailed explication of the linkages between theory and evidence in a wide range of psychological applications, including perception, cognition, neurology, mental health and child development.
Bak, P. (1996). How nature works: The science of self-organized criticality. Springer.
Power laws, fractal shapes and self-organized criticality are essential pieces of the complexity puzzle, and this book provides lucid explanations as well as proverbial examples of each. So, there is the sandpile experiment in which the gradual pouring of grains leads to avalanches on the pile, the fractal organization of fjords within fjords that constitute the Norwegian coast, the power law distribution that correlates the frequency of earthquakes with their intensity on the Richter scale, and more. I expect that the theory of self-organized criticality will have staying power in education. It helps us understand how transformation works, and how to detect a propensity toward change in organizations, both of which are key to the field. In addition, the power law distributions discussed here offer an alternative to the oft cherished assumption of normally distributed outcomes, in which extreme measurements are marginalized. This book provides a foundation to a wide range of applications of complexity theory, in other words, whose relevance to education and other disciplines can be readily appreciated. For this reason, it is one of the most frequently cited titles in my published work.
Bateson, G. (1972). Steps to an ecology of mind: A revolutionary approach to man’s understanding of himself. Ballantine.
This book brings together Gregory Bateson’s most essential writings. It is a truly multi-disciplinary festschrift that covers a wide territory, including his early writings in anthropology from the mid-nineteen thirties, as well as those on metacognition, animal intelligence, systemic transformation and the highly controversial double bind theory concerning the mental health implications of dysfunctional patterns of family interaction. Much of this work is connected to the Macy conferences that took place throughout the nineteen forties and fifties, and which largely defined the cybernetic movement at the time. This group of scholars searched for general principles underlying biological, cultural, and social phenomena as well as having early ventures into the areas of artificial intelligence and robotics. Bateson’s writings made an important contribution to this endeavor. They are interesting and thought-provoking, and for me, they continue to be a source of intellectual stimulation.
Beran, J. (1994). Statistics for long-memory processes. Chapman-Hall.
When making inferences about a population based on data from a sample, it is usually assumed that the datapoints represent independent observations. For the analysis of recurrent measures in a single unit, this assumption cannot be taken for granted as it could produce biased estimates. Time series analysis is a technique that has been expressly developed to address this issue by modelling the dependencies between neighboring observations on the time scale. However, as originally conceived, this method is not very good at estimating the dependencies between observations that are far removed from each other, a situation referred to as long-memory processes. Yet, it is those long-memory processes that typically characterize chaos or fractality in time series data. Beran provides a foundational statistical text on how to handle such situations, and it is essential reading for those who have an interest in the extension of conventional statistical methods to tackle complex processes.
Gilmore, R. (1981). Catastrophe theory for scientists and engineers. Wiley.
Catastrophe theory consists of seven transformative scenarios of progressively greater mathematical complexity. The common aspect in these scenarios is singularity, a mathematically unacceptable region in the coordinate space that forces qualitative transformation in the relationships between the variables defining the system. The most well-known example of such models is the cusp, in which variability in two predictors, or control parameters, determines whether changes on the outcome surface are linear or nonlinear. I have my reservations about the way some scholars use of catastrophe theory as a basis for the statistical regression analyses of empirical data, but as a mathematical formulation of the conditions under which qualitative transformation takes place, the theory is indisputably powerful, and this text provides an excellent overview.
Kaplan, D., & Glass, L. (1995). Understanding nonlinear dynamics. Springer.
This text is aimed at undergraduate students in the biological sciences, and it covers the basics of nonlinear dynamical theory and complex systems from that vantage point. The book strikes exactly the right balance between theory, models, and applications, and is full of relevant and interesting examples. The mathematical formulation of the dynamical processes is not avoided, but it is presented at a level that anyone with high school mathematics should be able to understand. Thus, the book takes us to unfamiliar terrain using familiar conventions. Under the header Dynamics in Action, inserts are provided throughout the book to illustrate nonlinear dynamics in published research and to show simulations of the differential equations that capture most of the dynamical processes discussed here. Challenging but doable exercises are scattered throughout. The book also offers one of the best and most concise definitions of chaos that I have encountered. It can be found on pp. 27-33, with an elaboration (also concise) on pp. 314 – 338. A revised and updated edition of this text is long overdue.
Nicolis, G., & Prigogine, I. (1989). Exploring complexity: An introduction. Freeman.
Given that change is such a central concern in the applied sciences – we talk all the time about interventions and their outcomes, educational reform, narrowing the achievement gap, etc., it is remarkable that our underlying theories of how change works continue to be largely one-dimensional (e.g., logic models, performance goals, linear regression, structural equation models). One way of making the case for complexity theory is by pointing to the manifold of transformative scenarios it embodies (e.g., catastrophes, emergence, the sandpile, bifurcation, perturbation, dissipation). This book unifies these various theories of change into a comprehensive and coherent account. It requires a willingness on the part of the reader to get engaged in the mathematics of complex transformation, but doing so yields a deeper understanding of how the various transformative scenarios hang together as a single structure and how aspects of this structure can be applied as needed to any problem of interest.
Prigogine, I., & Stengers, I. (1984). Order out of chaos: Man’s new dialogue with nature. New York: Bantam.
Rarely is the sense of being part of a scientific revolution as undeniable as when reading this book. While it focuses on the application of chaos theory in biology, physics and chemistry, the vast potential of the ideas expressed here lies in their applicability to virtually any empirical science, including education, psychology, and other social sciences. The book argues that we need to be able to contemplate far from equilibrium scenarios and other forms of instability in the systems, and how they can lead to order creation. Those concerns are not very well served by normal science (nor by some of the current work in complexity theory, for that matter). Part of what makes this book groundbreaking is that it integrates quantitative and qualitative science into a single paradigm, creating a ‘third force’ in our discussion of research methods in the empirical sciences. This third force views qualitative processes as being within the purview of mathematics and views the linear model that the guides much of our quantitative research as a special case of a much larger paradigm that also includes such things as period doubling, bifurcations, irreversibility, entropy, instability, and strange attractor regimes underlying seemingly random fluctuations in systems’ behaviors. The features, in other words, that make systems dynamic, interesting, and sometimes unpredictable.
Varela, F. J. (1979). Principles of biological autonomy. North Holland.
One of the key insights of complexity theory is that systems do not merely exist but form and maintain themselves through the interaction between components and the higher-level systems defined by those components. These interactions can be seen, then, as a production process, sometimes called autopoiesis. This book deals with the far-reaching implications of this idea, by considering such things are autonomy, identity, separateness, and individuality as instances of systemic self-preservation, and then formulates a theory about how this separateness gets asserted in the ongoing flow of the biological process. Varela’s approach is highly idiosyncratic, but the issues are profound. To me, this book is one of the most fascinating highlights of the scholarship coming out of the cybernetic movement. Tucked inside this volume as Appendix B is a general formulation of Gregory Bateson’s double bind theory called n-bind. I happened to be working in that area at the time and had an exchange with Varela about this theory. I also sent him a copy of a paper I had written on this subject (which came out in 2001 in Nonlinear Dynamics, Psychology, and Life Sciences). He seemed amused that someone had picked up on n-bind and confessed that he had forgotten about it. This book has been long out of print and deserves to be re-issued. In the meantime, it can be accessed at Principles Of Biological Autonomy [PDF] [4k6aoohpudf0] (vdoc.pub).
Watzlawick, P., Weakland, J., Fisch, R. (1974). Change: Principles of problem formation and problem resolution. Norton.
This text is applied in its orientation, albeit not in the field of education. This volume was written by three family therapists, who were part of a movement that was known at the time as the Palo Alto Group. This collective concerned itself with the applicability of general systems concepts to family interaction. The text is concerned with the persistence of undesirable situations and the challenge of changing them in the face of resistance. While the authors focus on the treatment of families, much of what they say is highly relevant to educators and educational policy makers as well. The book makes a distinction between first-order change and second-order change. The former of these refers to the appearance of transformation through processes that in effect reinforce existing constellations. First-order change is therefore referred to here as problem formation. Second-order change refers to processes that reconfigure the entire system. Family therapists strive for this kind of change in the face of dysfunctional family interactions, and therefore, the authors coined the term problem resolution for it. Whether the relationship between types of change and the types of problem resolution is as straightforward as it is made out to be here is a question up for discussion: we know that real change can make matters the worse. Yet the usefulness of the vocabulary introduced here for the applied sciences is beyond dispute, and educators should make better use of it.
