Abstract
The growing differentiation of specialties in education creates the need for a common framework. This chapter discusses the basic premises of complex dynamical systems theory (CDST), its intellectual foundations, and its applicability to the field of education, with a particular focus on the areas of learning and development, school reform, and the persistence of inequity in society. The vocabulary of CDST is reviewed and applied to these problem areas to help deepen our understanding of the challenges facing policymakers and practitioners and provide growing points for the integration of these areas of knowledge into a coherent basis for further research and exploration. The differences between CDST and traditional research paradigms are also duly considered.
From antiquity up to the present, the history of science may be characterized by a growing differentiation of knowledge into ever smaller compartments of expertise (Russell, 1967), resulting in the high level of specialization that characterizes present-day scholarship. In education as well, knowledge is particularized to the point where specialties are barely able to talk to each other. As a result, there is a growing need to integrate what we know from different sources to enhance our understanding of the most difficult challenges facing the field, such as the persistence of the achievement gap, the replication of socioeconomic differences across generations in spite of the best efforts of our schools, the inertia of our educational system in the face of the growing clamor for reform, the diversity of student backgrounds and needs (academic and nonacademic), and the inequities in funding for education across states and neighborhood demographics. In spite of the ever-expanding volume and complexity of our knowledge base in education, the problems we try to address now are not very different from the ones we faced several decades ago. Yet our perspectives on how to conceptualize and investigate these issues have shifted during that period with a growing awareness of how deep-seated socioeconomic inequities based on race, gender, sexual orientation, and other factors create a need to analyze how the residual sociogenic markers from slavery, colonialism, the discovery doctrine, and other systems of dominance and subjugation may still influence our thinking and explicate in that context the historical origins of our research, that is, the choice of topic, research questions, design, instrumentation, methodology, interpretation of the findings, and ensuing subject–object relationships (Dixon-Román, 2017; Lather, 2013; Mazzei, 2013; Rosiek, 2013).
Complexity dynamical system theory (CDST) is uniquely capable of integrating knowledge from disparate disciplines and orientations, provided its subject matter can be defined in terms of systems and their subcomponents, as is the case, for example, for many biological, social, economic, or cellular systems. It has been widely documented that education is well suited for the systemic treatment (Koopmans, 2020a), and we have good systemic descriptions of, for example, cognitive development and learning (Bidell & Fischer, 1994; Fischer & Bidell, 2006; Lerner, 2006; Lerner & Overton, 2008; Piaget, 1967, 1971b; Steenbeek & van Geert, 2013; van der Maas & Molenaar, 1992; van Geert, 1998; van Vondel et al., 2016; Vygotsky, 1978), identity and motivation (Garner & Kaplan, 2019; Kaplan et al., 2019), classroom interactions (Geveke et al., 2020; Pennings et al., 2014; Pennings & Mainhard, 2016), educational leadership (McQuillan, 2008, 2020), and the socio-historical determinants of educational systems and how they are investigated (Dixon-Román, 2017). In addition, several methodological reviews have been conducted to evaluate the implications of CDST for education research (Hilpert & Marchand, 2018; Jacobsen, 2019; Koopmans, 2014, 2020a). Given accomplishments such as these, the question is pertinent whether CSDT is capable of using the shared systemic qualities in these areas of knowledge to generate an integrated narrative that may, in turn, help address some of the more intractable challenges facing the field. And if so, what are these shared systemic qualities, and what makes them complex?
The plan for this chapter is as follows. A brief synopsis is provided of some of the theoretical frameworks that represent CDST, and its main constructs will be highlighted with relevant educational examples. This discussion lays the groundwork for the application of CDST to three areas of expertise within the education field, where the perspective has been shown to be particularly useful: (a) facilitating learning and development, (b) educational reform, and (c) the sociocultural and socioeconomic underpinnings of inequality and the role of the schools therein. Subsequently, I examine how a dynamical systems view may provide opportunities to develop an integrated perspective across these three areas and how such an integration might inspire improvements.
Theoretical Foundations
There are many ways to distinguish the various theoretical perspectives encompassed by CDST (e.g., Goldstein, 1999; Guastello & Liebovitch, 2009). Few scholars would disagree, however, that the following five are fundamental traditions in the field:
Cybernetics (Ashby, 1947, 1957, 2004; von Bertalanffy, 1967; Wiener, 1961) is a multidisciplinary orientation that describes systems in terms of feedback loops, that is, behavioral outcomes that are fed back into the system as input conditions, the hierarchical relationships between systems and their subcomponents, and the processes of self-perpetuation that maintain those systems (Maturana, 1970/1980; Maturana & Varela, 1973/1980).
General systems theory (von Bertalanffy, 1969) postulates a wide applicability of the systems metaphor across scientific disciplines such as physics, biology, medicine, behavioral science, or any others with few general principles about their structure and functioning (von Bertalanffy, 1969).
Chaos theory (Poincaré, 1914/2007; Prigogine & Stengers, 1984) is a mathematical formulation of how small shifts in input values can produce systemic turbulence later on, and it describes the nonrandomness of the dynamics underlying those turbulent patterns.
Catastrophe theory (Gilmore, 1981; Thom, 1975) is a mathematical formulation of the conditions under which systemic change may be gradual or qualitative.
Complexity theory (Bak, 1996; Waldrop, 1992) comprises an array of models that have in common that they are concerned with a process that lies between order and chaos, where the interdependence between systems creates a propensity toward transformation.
These five perspectives share a focus on the behavior of complex dynamical systems, and they claim applicability in a wide range of scientific disciplines. In conjunction, these models yield a more or less unified conceptual framework to address questions of systemic stability and transformation that is potentially of great use describing processes of education, schooling, and development. In this review, I use the term “complex dynamical systems theory” (CDST) to refer to this unified conceptual framework, and some of the critical constructs from this theory are highlighted below (i.e., complexity, autopoiesis, and qualitative transformation). The latter of these also includes a consideration of its counterpart (i.e., systemic stability or homeostasis).
Complexity
“Complexity” is traditionally viewed as the state of being multifaceted, and much of the literature in social science, education, business, and elsewhere defines it that way. So, we talk about “a complex world,” “a complex organization,” a “complex situation,” or a “complex personality.” Complexity theory further qualifies this definition in several ways. First and foremost, complexity theory views complexity not as a state, but as a dynamical process. Examples of complexity, seen this way, could be the adaptation of a biological organism to its surroundings or the intellectual maturation of a child in the course of its interaction with the environment. In spite of this agreement among complexity scholars generally, there is a great deal of variety in how the term is used. Three previously published review articles (Alhadeff-Jones, 2008; Koopmans, 2017b, 2020a) provide comprehensive overviews of the different varieties of complexity, and they describe how our understanding of the concept evolved over time.
Once interactions take place between individuals, they form a system, as their behavior becomes interdependent. Cybernetic literature refers to this dependency as conditionality (Ashby, 1947, 1957, 2004), and it maintains that it is a defining characteristic of complex systems in general. One of the implications of the definition of complexity provided above is that the creation of systems through the interaction between individual involves a process called “self-organization” or “self-assembly.” Although originating from physics (Glansdorff & Prigogine, 1971), the idea has found wide application, including in the social and life sciences, where it has been argued that through interaction, individual components create and maintain systemic structures that may reorganize in response to environmental pressure (Feltz et al., 2006).
In this scenario, there is a hierarchical relationship between systems and their subsystems such that the behavior of higher-level systems cannot be readily reduced to that of the interaction of its component parts, although those components are instrumental in shaping the system at large (Ashby, 1947, 2004). The behavior of the system in its entirety cannot be reduced to that of the individual components because the system as a whole is distinct as an entity from the sum of the behaviors of these components. This characteristic is often referred to as “irreducibility,” better known as “the whole is not equal to the sum of its parts.” Under this assumption, the behavior of the individual components in the system shapes the larger system while at the same time, this larger system is distinct and delineates the behavior of the individuals residing within it: “Part and whole contain each other in a continuing, current, and ongoing process of communication and interrelationship” (Minuchin & Fishman, 1981, p. 13). In educational settings, pedagogical interactions exemplify the irreducibility of the learning outcomes at the classroom level, which describe overall outcomes that cannot be reduced to the specific behaviors of the participants. Instead, those outcomes occur over and above the behavior of the individual components as a result of their interactions and should therefore instead be seen as a distinct analytical entity. Teachers will relate to the idea that the classroom is a behavioral space that includes the interactive behavior of its individual inhabitants while also being a behavioral entity in its own right.
Autopoiesis
CDST insists that systems are not structures but processes. They come into being through self-organization, and they maintain themselves through a process of ongoing self-creation and regeneration. One basic insight from cybernetics is that systems preserve themselves through interaction. This latter process is sometimes referred to as “autopoiesis.” Autopoiesis refers to the notion that systems regenerate themselves (Maturana, 1970/1980). The idea of regeneration implies a feedback loop between the higher-level system and its lower-level components as stipulated by cybernetics. Autopoietic theory argues that the perpetuation of the system through such interactions is a driving force to its longevity. Autopoietic systems prioritize their perpetuation through the interaction between its elements. This process is self-referential in the sense that systems components interact to assert the structure and the identity of the system they form through those interactions (Varela, 1979).
The original formulation of autopoiesis as a feature of the chemistry of living cells concerns a closed system that regenerates itself in an ongoing feedback loop with no exchanges with other systems nor the environment (Luisi, 2003; Maturana, 1970 /1980). Thus, systems reproduce their essential features irrespective of what goes on around them. Using the construct of autopoiesis to understand human cognition and human organizations requires us to assume that the term also applies to open systems, that is, systems that exchange energy, matter, and information with the environment and with other systems and components, and that the tendency toward conservation and self-recreation can be understood in the context of the system’s adaptive process. That assumption is not without its detractors (Luisi, 2003). Yet the idea that systems are driven toward self-perpetuation in an open fashion is pertinent to obtaining a deeper understanding of educational change and the facilitators and inhibitors thereto. In this way, the concept of autopoiesis as a systemic inclination is highly relevant to educators, who deal with facilitation and inhibition on an ongoing basis. Razeto-Barry (2012) provided a definition of the construct that supersedes the open versus closed dichotomy by allowing self-generation to include interaction of the organism with its surroundings (allopoiesis). Likewise, Hayles (1999) allowed for the autopoietic process as an assertion of systemic autonomy in relation to other systems and for the autopoietic inclinations in the system to be supplemented by allopoietic ones (i.e., exchanges with the environment or other systems). Such understandings make it possible to examine the application of this idea to education.
Systems such as schooling and societal inequity are both known to be resistant to change, thus creating the need to identify the processes that inhibit transformation. The theory of autopoiesis argues that the drive toward self-preservation and thus toward stability is an inherent aspect of the interaction between components and how it repeats unless the underlying dynamics of the systems and its response to and from its surroundings pushes it toward transformation through allopoiesis. The role of cognition in living systems such as individuals who internalize an understanding of the structures of which they are part when they interact illustrates how allopoiesis complements autopoiesis (Maturana & Varela, 1973/1980). These cognitive representations are guided by the same principles as those described above for intellectual development and learning under guidance, except that they do not presume closed systems.
Understood this way, autopoiesis does not only apply to the intellectual development of individuals but also to systems of ideas, interactions, and explanations that support extant socioeconomic structures and frameworks of inequity (e.g., eugenics, poverty, and opportunity gaps), thus preserving a societal status quo. These self-perpetuating processes can be found in the interactions between people and organizations and subjected to research, interrogation, and critique (Dixon-Román, 2017; Lather & St. Pierre, 2013). This self-perpetuation is sometimes referred to as “cybernetic inheritance,” the idea that through interactions within the system, societal exclusivities based on race and wealth perpetuate the belief system from which they emanate, thus creating an autopoietic self-reference across the time spectrum, to which these systems owe their persistence.
The use of systems approaches to supersede distinctions between types of systems (humans, cells, information), between the subject and object of study, between physical and information systems, and between living and nonliving systems (e.g., Lather, 2013; Maturana & Varela, 1973/1980) mirrors developments taking place in social network analysis, which now has greatly enhanced flexibilities in the determination of the unit of analysis (e.g., Barabási & Albert, 1999) to include networks of genes, socioeconomic disparities, the Internet, and more. This expanded view of systems is sometimes associated with the term “posthumanism,” which provides a broader definition of the systems of bodies, tools, ideas, and information transmission that redefines the place of humans in the larger constellations of culture, technology, artificial intelligence, and society, making them less central than they were once presumed to be (Hayles, 1999).
Qualitative Transformation
CDST has a rich vocabulary of transformative scenarios (Koopmans, 2009). As are many other disciplines, education is very concerned with change, reforming our schools, enhancing opportunities for minority students, reducing the opportunity gap, and producing greater equity. Are the underlying principles of change articulated by CDST applicable to those situations? To address this question, some of the concepts of transformation proposed by the theory are further explained below, and their applicability to the educational system is evaluated. This discussion focuses on the following concepts: first- versus second-order change, emergence or radical novelty, self-organized criticality, catastrophic transformation, attractors and repellers, sensitive dependence on initial conditions, and entropy reduction through increased complexity. The list is by no means exhaustive. Below is a summary of these main ideas.
First- Versus Second-Order Change
Change can be gradual in the sense of being continuous or qualitative (discontinuous). The former scenario is referred to in the literature as “first-order change” (“the more it changes, the more it stays the same”) and the latter as “second-order change,” typically thought of as “real” change (Watzlawick et al., 1974) in the sense that it modifies the basic settings of the system. First-order change is also described as “problem formation” and second-order change as “problem resolution.” This idea is of particular relevance to the educational system, where change has many complications (Cuban, 1990; Fullan, 2016; Hess, 1999; Koopmans, 2016a). The educational reform literature, for example, discusses how ongoing attempts to develop and implement new initiatives in the system with the intention of raising test scores or otherwise improve educational outcomes in fact creates a situation in which the ongoing activity and turbulence do not result in any real transformation of the system. Typically, new initiatives are not given the time they need to be accommodated in the local culture of the school building, and consequently, they get replaced by new initiatives that in the end, face the same outcome. The underlying dynamic, known as the “policy churn” (Hess, 1999; Koopmans, 2016a) is that policymakers and others outside of the school building system earn credit for development the initiatives, creating an incentive to do so, while the implementers are left with the challenge of demonstrating their effectiveness in a short range and being perceived as ineffective if no results are produced over the short run. Thus, the distinction between first- and second-order change is a useful analytical tool to plan for, analyze, and evaluate the forces that facilitate and inhibit transformation, and the policy churn is a prime example of first-order change.
Emergence or Radical Novelty
In accordance with the idea of complexity as discussed above, change in higher-level systems is often said to be the result of interactions between its lower-level components, a process called “emergence” (Goldstein, 1999). An example of emergence is when egalitarian interactions between team members in an organization lead to higher-level structural changes. The notion of emergence is often used to describe the difference between the type of top-down leadership in organizations that reinforces the status quo in those organizations (first-order change, problem formation) and bottom-up structures in which the formation of teams, selection of leaders, and so on result in the accommodation of new initiatives at higher levels of the organization, thus leading to reorganization and reform (second-order change, problem resolution), or, as the emergence literature has it, “radical novelty” (Goldstein, 1999). The notion of emergence has been developed in the organizational literature in the quest of effective management practices and the enhancement of efficiency and profitability (McKelvey, 2004) but can be usefully extended to transformation in educational systems toward more effective organizations with greater responsiveness to the needs of its stakeholders. “Self-transcending constructions” refers to the proclivities residing within the system toward such transformation (Goldstein, 1999, 2014), also referred to as a “springboard to emergence” (Hayles, 1999, p. 11) or “new becomings” (Mazzei, 2013, p. 739). Hayles (1999) and Koopmans (2016a) provided more detail about the underlying mechanisms of this potential. Suffice it to say here that the openness toward transformation in the system is an essential aspect of qualitative transformation in educational and other organizations. Addressing inertia in the education system would involve scrutinizing the self-transcending constructions inside the system, the arrangements that are put in place and meant to be conducive to future transformation. Examples of such constructions in the educational system are site-based management, instructional rounds, and distributed leadership (Elmore, 2004, 2016), approaches that restructure the system at one level in a way to generate potential for transformation at the next level.
Self-Organized Criticality
One process through which discontinuous changes are made possible is called “self-organized criticality.” Self-organized criticality is said to occur in a system if the repeated occurrence of first-order change generates friction such that a qualitative transformation becomes imminent. Per Bak’s (1996) proverbial sandpile is an example. If one pours grains of sand on a pile that resides on a stable flat surface, there will be critical moments where the pile shifts to relieve the mounting friction between grains due to the continued pouring, thus causing avalanches (qualitative transformation). The process then replicates as long as the pouring continues, which is to say that self-organized criticality, the friction between the grains, is ongoing with any relief being indispensable but only temporary as long as the pouring continues.
An example of self-organized criticality is accommodation in the Piagetian sense. Repeated failure by the developing child to assimilate input from the environment because contradictions are detected between the child’s frame of reference and the nature of the new input generates tension in the system, which ultimately produces a transformation, as the child confronts the inadequacy of the explanations, and transforms its frame of reference to accommodate the new input. The repeated failure to assimilate is essential to this process and well captured by the sandpile metaphor. Successful accommodation, on the other hand, creates equilibrium only on a temporary basis because contradictions between environmental input and the frame of reference representing this environment will continue to occur, as do the avalanches in Per Bak’s sandpile. It attests to the clairvoyance of Piaget’s theory that new concepts such as this one can be readily accommodated into the theory.
Catastrophic Transformation
One of the key insights of CDST is that changes in systemic outcomes are not necessarily proportionate to changes in the input conditions, and therefore, we need to know the conditions under which change is incremental versus transformational (Nicolis & Prigogine, 1989). As a general formulation, this idea is not new. It is well known that many relationships between predictors and outcomes are nonlinear. CDST has two additions to make. One is that it seeks to model the conditions under which change is continuous versus discontinuous, one of the primary concerns of catastrophe theory. This theory comprises a family of models that articulate mathematically the conditions under which qualitative transformation takes place in a system from an original state to a novel state and under which conditions change is gradual without changing the underlying state of the system. In gradual changes, behavioral shifts reassert the status quo in the system, whereas qualitative changes constitute an innovation in how the system operates. The predictors characterizing these relationships are called “control parameters.” These determine the conditions under which qualitative change will occur and the conditions under which it does not. Catastrophe theory identifies seven transformative scenarios of progressive mathematical complexity. Gilmore (1981) and Thom (1975) summarize the mathematical features of seven types of catastrophic transformations. The aspect they have in common is “singularity,” a mathematically unacceptable region in the coordinate space that coerces qualitative transformation in the relationships between the variables describing the system.
The most well known of these scenarios is the cusp model, which contains a folded outcome plane. Cusp describes how variations in the values of two control parameters can decide whether continuous or discontinuous change will appear on the outcome surface. Catastrophe theory also postulates that in the response to shifts in the control parameters, there is a delay in the point at which change evolves from being gradual to being discontinuous. This hesitation in making the transformation from one state to another is part of the mathematical formulation of the model, called “hysteresis,” and it results from the need to circumvent unacceptable regions.
In a classic article, van der Maas and Molenaar (1992) discussed how cusp models can be used to mathematically characterize the underlying mechanisms of stage-wise transformations in the child’s problem-solving behavior as proposed by Piaget (e.g., 1967, 1971a, 1971b). One of their proposed models includes preoperational and concrete operational mental structures as predictors for the child’s cognitive level of functioning; another, associated with neo-Piagetian insights, proposes perceptual salience and cognitive capacity for that purpose. In either of these two instances, assimilation is manifest as a gradual change and accommodation as a qualitative one, where the incompatibility between the frame of reference and environmental input produces an unacceptable region coercing systems change, as the mathematical theory would predict. In a comprehensive review of the application of cusp models on learning and development, Stamovlasis (2016a) identified a range of contingencies under which learning is continuous versus discontinuous, such as students’ working memory capacity and content knowledge. The value of this work lies in the fact that it provides models and examples of how more complex transformative scenarios apply to the field and yield a deeper understanding of the underlying dynamics of transformation in educational systems. It also provides ideas of direct use for practitioners. For instance, discontinuous learning and second-order change characterize a different kind of learning than what you could call incremental learning, and it is important for instructors and others to be able to distinguish these two processes. Although one may not need CDST to recognize this distinction, CDST differs from other theories in that it brings these aspects into focus and models the conditions under which learning can be expected to be incremental versus discontinuous. And teachers can, of course, influence those conditions to some extent (e.g., short-term memory, content knowledge).
Sensitive Dependence on Initial Conditions
One of the central ideas of chaos theory is sensitive dependence on initial conditions, the notion that infinitesimal shifts in the behavior of a system may result in systemic turbulence later. The idea was originally formulated by Poincaré (1914/2007) at the beginning of the 20th century but did not gain momentum in the field until the 1960s, when Edward Lorenz, the MIT meteorologist, in the search for nonlinear models for the prediction of weather patterns, discovered that small changes in how measurements in a time series were rounded resulted in qualitative differences in the trajectory of data points later on, thus giving rise to the idea that small initial variabilities may lead to unpredictable and disproportionate outcomes (e.g., Gleick, 1987).
The scope and nature of the changes taking place in the system are not necessarily deducible from changes in the initial conditions of the system, a notion originally forwarded by chaos theory (Poincaré, 1914/2007). This irreducibility must be separately accounted for in our change models (Nicolis & Prigogine, 1989). Recent developments in CDST have yielded a wide array of representations of relationships between outcomes and the systems conditions to which they respond, including many conditions that generate nonlinear or unpredictable behavior. Nicolis and Prigogine (1989), Sprott (2001), and Gilmore (1981) provided excellent overviews of some of these scenarios. The insight that the scope of change cannot always be overseen in advance adds a word of caution to the implementation of major educational policy initiatives.
Attractors and Repellers
Chaos and catastrophe theories have in common the notion that “attractors” and “repellers” characterize the underlying dynamics of systemic behavior. Attractors describe the tendency of a system to gravitate toward certain coordinates in the behavioral outcome space, and repellers describe the opposite, that is, the tendency to stay away from certain other coordinates. Attractors are a source of stability (equilibrium) within the system. They describe the nonrandomness of the behavior of systems, and although there is great variability in the behavior of the system of interest, this variability is said to evolve around these orientation points. For instance, mean functions can serve as an attractor to a system. In an orderly system, there may be a single attractor to demarcate the central tendency in the systems behavior; variability can then be determined in terms of its deviation from this central measure. In a system in transformation, there could be two attractors, one for the system’s past state and one for the system’s future state, with a turbulent present in between. In such cases, the attractor regime underlies a qualitative and, therefore, complex transformation. Catastrophe theory describes many of these transformations in a way that can be relevant to teaching and learning as it moves the system from one state to another (Stamovlasis, 2016a).
Repellers are the opposite of attractors. They are the orientation points in the outcome space from which the system tends to stay away due to singularity or being in the tail end of an outcome distribution. The interplay between the forces of attraction and repulsion generates the behavior that is seen when systems are turbulent. The underlying dynamics of attraction and repulsion generate the type of nonlinear transformation described above. Key to the evolution of systems is that the attractor structure can change. A typical process for such change is called “bifurcation,” the splitting of the attractors from one into two attractors (also referred to as “period doubling”). A progression of multiple bifurcations creates the multiattractor regime typically associated with turbulence. Such systems are sometimes defined as being “far from equilibrium,” that is, systems that are in an ongoing state of turbulence because their behavior revolves around a larger number of attractors (Goldstein, 1988, 1990). In far from equilibrium systems, behavior gravitates many of those orientation points in a manner that may seem highly unpredictable, thus introducing complexity into the system.
In such situations, systemic behavior appears to be chaotic, although in fact, the attractor structure is a manifestation of its underlying order. Although these more complicated attractor regimes do not often readily translate to occurrences in education, the bimodality in learning outcomes (a fast group and a slow group) exemplifies a two-attractor scenario as a classroom of students is in the process of mastering certain learning content, with some picking it up faster than others, leading to greater variability in the course of the transition (Stamovlasis, 2006). During such a transition, the tendency to move away from the middle ground between the two modes characterizes the repeller in this scenario.
Entropy Reduction Through Increased Complexity
Another aspect of change that is of interest in this context is notion that a reduction of unpredictability, or “entropy,” in cognitive and information structures can be attained through increased complexity (e.g., conditional probability, learning, accommodation in the Piagetian sense). More differentiated frames of reference or models result in greater predictability of events and behavior (Koopmans, 2017b; Shannon, 1948). Entropy was originally defined in thermodynamics as disorder or randomness in systems and in terms of the ensuing unpredictability of their behavior. Here, we rely on the term as it is used in information theory (Shannon, 1948), where entropy is defined as the differences in probability with which each of an a priori defined set of outcomes will occur. If the probability is equal for each outcome, the probability distributions offer little or no guidance predicting the behavior of a system, whereas different probability values identify outcomes favored by the system. Compare, for example, the following two strings of probability values: {0.4, 0.2, 0.2, 0.1., 0.1} and {0.2, 0.2, 0.2, 0.2, 0.2}. In the first instance, predicting a future outcome is facilitated by the probability values attached to each of the five outcomes in the string, whereas in the second instance, there is no such preference, and therefore, knowing the probability values is unhelpful for the prediction of future occurrences. This example shows in a nutshell why incorporating previous knowledge about a system into a prediction of its behavior in the future is advantageous. Uncertainty can be further reduced by applying conditional probabilities, which use previous knowledge to enhance the accuracy of predictions. Thus, the uncertainty of outcomes is reduced by increasing the complexity of the framework used to make predictions about those outcomes.
The qualitative transformations of the frames of reference in the development of children that lead to Piagetian stage transitions (e.g., Piaget, 1967) is an example of reducing uncertainty by increasing complexity. As frames of reference get more differentiated, the child’s ability to accurately predict environmental occurrences is enhanced, and thus, his or her responses will be more predictable (i.e., less entropy). Generally, more complex and detailed frames of representation enhance the predictability of systems’ behaviors. For example, the Linnean catalogue of species in biology facilitates the identification and classification of their typical behaviors, and likewise, group-level information can be used to predict behavior in human systems.
The methodological implications of the notions discussed here for empirical research are considerable but beyond the scope of this chapter. A comprehensive overview of the use of CDST research methodology in education was provided by Koopmans and Stamovlasis (2016). More general discussions about research design and statistical methods were provided by Brown and Liebovitch (2010), Guastello and Gregson (2011), Koopmans (2021), Sprott (2001), and many others.
Areas of Application
The relevance of CDST to the field of education is further discussed in the section that follows in three selected areas of application. These are (a) facilitating learning and development, (b) educational reform, and (c) the socioeconomic and sociocultural underpinnings of inequity. There is fairly extensive CDST literature on the first two of these topics, and we therefore have a body of knowledge and empirical research supporting the application of CSDT. All three have clear dynamical implications when it comes to the problem formulation and lend themselves well to the CDST treatment. In addition, considering these three areas creates opportunities to examine important crossovers between them. In what ways are intellectual development and student learning connected to inequities in the system that inhibit learning for some but not for others? Do efforts to reform the educational system have the potential to be conducive to learning and development generally and specifically the inequities therein? Seen as a complex dynamical system, we can explore the relationships between these aspects of the educational endeavor and the possibilities and limitations of the CSDT framework. There are other areas of knowledge within the field where progress in CSDT has been considerable, such as curriculum development (Deogratias, 2018; Doll, 1993), motor development (Thelen & Smith, 1995), the central nervous system (Kelso, 1995), or physical education (Corrêa et al., 2016). The present analysis could be fruitfully extended to include a discussion of these areas as well.
Facilitating Learning and Development
There is a rich developmental tradition of theory and research that is explicitly grounded in nonlinear dynamical theories, including Piaget and Vygotsky’s theories of learning and development and many contemporary extensions thereof (e.g., Chapman, 1992; Fischer, 1980a, 1980b; Garcia, 1992; Lerner, 2006; Lerner & Overton, 2008; van Geert & Fischer, 2009). It is impossible to do justice to the depth and significance of this work in a short frame, and this section limits itself to some of the essentials of the connections between these developmental theories and CDST. The conversation focuses on Piaget and Vygotsky but could be extended to more contemporary dynamical models of development as well. Vygotsky’s (1978) zone of proximal development (ZPD) and Piaget’s (e.g., 1967, 1971b) theory of intellectual development, including the stages, are early examples of the application of complexity to learning and development. Although much of the current vocabulary in complexity had not yet been developed at the time, this work remains fundamental to the field, and it can be readily extended using recently developed concepts of CDST. The ZPD illustrates the nonlinear relationship between learning by oneself and learning under guidance of a more knowledgeable peer or adult and the dynamical tension between those two states that creates opportunities for learning, as in self-organized criticality. ZPD describes how the interaction between the learner and teacher creates a pedagogical system with several characteristic complexity features: the interaction between the organism and its environment, a temporal dimension of this process, qualitative transformation of the developmental level due to guidance, and an underlying attractor regime where the levels of learning with and without guidance are the orientation points for the description of these learning dynamics.
Piaget’s theory of intellectual development includes descriptions of the dynamics through which the organism attains equilibrium in the face of disequilibrating influences from the environment. Learning, development, and intelligence are seen as an adaptive process (Piaget, 1971a), including terms such as “object concept” and “reflective abstraction,” that are seen as dynamical interactions between the organism and its environment instead of static internal mind/brain representations (van Geert & Fischer, 2009). Modern insights in complexity have made it possible to create a synthesis between Piaget’s theory of intellectual development and Vygotsky’s developmental theory (van Geert, 1998). Both described adaptive learning behavior to resolve tensions and contradictions (entropy reduction) between the learner’s frame of reference and the input or expectations from the environment. As such, both are examples of a dynamical process of “order creation” (van Geert & Fischer, 2009). Van Geert (1998) described in detail the simulation studies on the basis of which the integration of these two theories can be justified and what empirical evidence is needed to support these models. See Koopmans (2020a) for a more extensive overview of this work.
This work argues that Piaget’s theory (1967, 1971b) and its modern extensions, such as skill theory (Fischer, 1980a, 1980b; Fischer & Bidell, 2006) and developmental systems science (Lerner, 2006), go back to the same essentials as Vygotsky’s: time, adaptation, and qualitative transformation. These theories are often cited as prime examples of dynamical theory because they view the discontinuity of learning and development in terms of a search for equilibrium between environmental input and the developing child’s frame of reference (accommodation). Particularly Piaget’s terminology is remarkably well aligned with later developments.
One of the best formulations of the equilibrium-seeking behavior, postulated in Piaget’s theory, can be found in Chapman (1992) and is quoted below:
Every organization tends to conserve itself as such.
Each organization is open to environmental influences that modify its various parts, bringing them into conflict with the whole. A dominance of the parts over the whole at this point leads to disintegration, and a dominance of the whole over the parts leads to stagnation.
The whole modifies itself in order to reduce the conflict with the parts.
This compromise tends to evolve into a more stable form of equilibrium characterized by mutual preservation of parts and whole. However, this higher equilibrium is never actually reached because of the novelties constantly introduced by the environment. It is therefore described as an ideal equilibrium toward which all real equilibria tend. (p. 41)
This definition clarifies the autopoietic and the adaptive nature of this behavior such that the cognitive system and its interface with the environment constitutes an “open system” that is in constant flux as it deals with the novelties coming from the environment, and hence, it is dynamic.
The commonalities between Piaget and Vygotsky’s developmental theories have been discussed previously (Glassman, 1994; Tudge & Winterhoff, 1993). Van Geert (1998) was the first one to use CDST to propose a formal integration of the two models in terms of the probability distribution of the activation of particular content (skills, rules, principles) in the face of environmental contingencies, thus specifying both as “adaptive systems.” This work provides empirical support for the basic CDST premise that qualitative transformation in a system is typically accompanied by turbulence, as is postulated by many CDST models (e.g., Lewin, 1947; Thom, 1975), whereas gradual transformation is not. Turbulence is manifest in the elevated levels of variability in task performance over time within individuals and horizontal decalage or variability between them in the proximity of the outcomes to the expected points of stage transformation. Turbulence can be ignored, or it can result in qualitative transformations, which, in turn, increase the potential for transformations available to the system in the future (Chapman, 1992). Thus, the accommodation in the Piagetian sense counts as a self-transcending construction in the system by enhancing its potential for change in the future.
Both Piaget’s stage transitions and Vygotsky’s ZPD can be seen as examples of an attractor regime: in Vygotsky’s case, the knowledge, skills, and performance with and without guidance and in Piaget’s case, assimilation within the existing frame of reference versus accommodation of environmental input into a new frame. Furthermore, the processes leading up to stage transitions of the type described in Piaget’s and Fischer’s theories constitute an example of self-organized criticality, where the accumulation of input incompatible with the frame of reference results in the tension that ultimately leads to accommodation, whereas performance levels with adult or peer guidance stipulated under ZPD constitute a self-transcending construction in the sense that it creates a learning environment that is conducive to transformation, that is, the acquisition of new knowledge and skills. The mathematical underpinnings of these developmental and learning processes according to CDST were explained by van der Maas and Molenaar (1992; see also above).
Based on insights from CDST, we have also been able to better differentiate aspects of the environment in which the development of the individual is embedded, including the acknowledgment that the interplay with environment can be described at different levels, such as the relations between the developing individual and its immediate environmental microsystem and its relations with higher-level systems such as the mesosystem of the school, the exosystems of the neighborhood, and the macrosystem of society at large (Bronfenbrenner, 1977). The relational philosophy of human development was further extended by Lerner (2006) and Lerner and Overton (2008), who described the organism-environment interactions and the individual-context relations as instances of integrated systems, calling for an analysis of the interactive processes through which these systems are formed and maintained (i.e., self-organization). The inclusive and hierarchical nature of these interactions illustrate complexity. Thus, a science of developmental systems postulates a process ontology instead of a state ontology, which is to say that it concerns the study of ongoing transformation in the organism-context interactions and the identification of the determinants of gradual and qualitative change in those interactions. In that vein, developmental systems science also questions the artificial distinction between nature and nurture, the genetic and environmental determinants of behavior, which are sometimes modeled as distinct sources of influence (e.g., Rowe, 1994). This artificial separation can then in turn be used to provide genetic explanations for social phenomena related to the opportunity gaps in society, such as disparate health and achievement outcomes. Developmental systems science instead argues for nature and nurture as an integrated system with a dynamic interplay between its components. See Lerner (2006) for further detail.
Educational Reform
Traditionally, educational systems have often been described as “loosely coupled systems” (Weick, 1976), systems that function relatively independently. Thus, classrooms have autonomy and are unaffected by what transpires in other classrooms or at higher levels of the system, such as school buildings. The same can be said of schools within districts. Weick (1976) argued that the advantage of having systems loosely coupled is that crises in a given component of the system, say, a given classroom, do not reverberate to other parts of the system, such as neighboring classrooms. The drawback of this arrangement is that there are limited opportunities for teachers and others to share effective practices, and some have argued that loose couplings are in part instrumental in creating the slow pace of change that we currently have in the system (Elmore, 2004, 2016). In response, approaches such as distributed leadership, instructional rounds, and professional learning communities have been developed to create opportunities for professional interaction between teachers and other school personnel and to allow self-organization around professional goals and objectives (Elmore, 2004; Roberts, 2012). Such processes create a bottom-up alternative to the inherently top-down processes of educational administration and leadership and to the top-down view that has inspired much of the reform work that has taken place over the past 2 decades. Complexity theory argues that systemic parts and wholes sustain each in an ongoing interactive relationship, and so it is with change and school reform, such that the spontaneous interaction at the lower levels of classroom and professional development settings result in emergent patterns of co-regulation that may reverberate through the larger systems. Such changes could be impactful provided that the higher-level systems of leadership and administration may in turn be responsive to those developments. As such, they exemplify the self-transcending constructions that create the potential for radical novelty in the system.
From a historical perspective, one of the major triggers for the educational reform movement in the United States was a report submitted to the Reagan administration in the early 1980s titled A Nation at Risk (National Commission of Excellence in Education, 1983). The report was written in response to a charge, among others, to evaluate the quality of teaching and learning in the United States and to compare the standing of American education to that in other industrialized nations. Although constructive in its intent, the tone of the report was predominantly negative, as illustrated by its memorable observation that
the educational foundations of our society are presently being eroded by a rising tide of mediocrity that threatens our very future as a Nation and a people. What was unimaginable a generation ago has begun to occur — others are matching and surpassing our educational attainments. (p. 9)
In its diagnosis of this situation, the report noted underqualified teachers in math and science, school years that consist of fewer school days than those in other nations, and teacher preparation programs that are unduly focused on pedagogical methods rather than learning content. To this day, this report has set the tone, in media reports and in much of the research literature, about the discussion of the educational system as one that needs repair. This deficit-oriented approach has provided an impetus for many large-scale educational reform efforts, particularly in urban districts where poverty tends to be concentrated, such as Baltimore (Cibulka, 2003), Milwaukee (Hess & Sattin-Bajaj, 2013), Newark (Russakoff, 2015), and San Diego (Hubbard et al., 2006). The reform efforts in districts such as those were typically justified in terms of the improvement of the public school system and the creation of national models to realize change on a larger scale.
Yet somehow, the issues that the educational system was expected to address under these reform efforts have shown themselves to be intransigent in spite of the concerted efforts at the administration and policy levels to produce transformation through new programs and initiatives in the schools, revisions to the organizational charts of schools and districts, and revised performance expectations (e.g., Hess, 1999; Hubbard et al., 2006). There is, of course, no shortage of ideas about how the system ought to be transformed. However, one of the dilemmas that the educational system faces is that schools and districts do incorporate innovations in their practices on an ongoing basis, to the credit of policymakers and others working outside of the system (Elmore, 2016; Hess, 1999; Koopmans, 2016b), while those who are implementing those initiatives are faced with the challenge of making the innovations work, often within a timeline that does not allow for them to be fully incorporated into the culture and daily practice of the school system. Thus, with premature evidence being unsupportive, these initiatives tend to be discarded to be replaced by yet newer ones, which, in due course, meet the same fate. Hess (1999) referred to this situation as the policy churn, a process where intensive ongoing reform activity creates ongoing turbulence, which renders the appearance that change is taking place while in fact, things remain the same, an instance of first-order change, in other words (Koopmans, 2020a; see also above).
Some of the greatest thinking in the educational reform movement (Cuban, 1990; Elmore, 2004) has a dynamic orientation, although its terminology is only casually aligned with CDST. Koopmans (2016a) systematized insights from the school reform literature according to CDST. We learn from this review that the incorporation of new initiatives into the local school building and district cultures is a systemic phenomenon and that it is key to their success because the implementers are able to learn from their mistakes and build local institutional knowledge about what works well as they continue to improve the program and distinguish first-order change from real transformation. New programs can be embedded into the local system through the professional interactions between teachers and other school personnel, professional development routines, teacher-student interactions, and so on, but even under those circumstances, the implementation story is an invaluable aspect of the determination of a program’s success because it concerns the self-organization of systems components around a specific set of goals and objectives. The receptiveness of the system to such changes would be a self-transcending construction, where the system sets itself up to accommodate changes resulting from the local interactions around these innovations, which, in turn, lead to higher-level transformation. Thus, such would constitute emergence, or radical novelty, and an alternative to the first-order change of the policy churn.
Lately, our thinking has been drifting away from ambitious large-scale reform efforts such as those mentioned above in favor of more modest local initiatives. Elmore (2016), one of the initial proponents of the idea of “getting to scale,” more recently argued that getting to scale may be naïve because it is premised on simplistic notions about learning and human development and is heavily context dependent at both the micro levels (e.g., teacher-student interaction) and macro levels (school- and district-level policy). There is a growing sense in the research literature that to reform educational systems, the starting point should be the practicing school teachers, creating changes in the system from the bottom up, rather than policymakers, curriculum developers, consultants, funding agencies, and others whose profession resides outside of the school building, who innovate from the top down and whose priorities might not be aligned with the local concerns at the classroom and school building levels (Elmore, 2016; Fullan, 2016). This way, small changes at the local level can evolve into major changes at the higher systemic levels (schools, districts), raising the possibility of the sensitive dependence of these higher-level systems on local fluctuations. The intransigence and loosely coupled nature of these systems make such change difficult to attain.
Fullan (2016) argued that the drivers we had for going to scale (accountability, test scores) were wrong to begin with because they justify innovation in terms of the traditional outcomes-focused model instead of focusing on the processes that generate these outcomes in a circular causal process playing out across systemic levels (classroom, school building). Drivers that are more likely to be successful would include capacity building, collaboration, pedagogy, and systemic policies: self-transcending constructions, in other words, that strengthen the system’s capacity for transformation. In the end, Fullan rejected going to scale as an approach as well because it requires replication across vastly different types of settings even though much of what goes on in educational systems is and has always been local. The major urban educational reform efforts such as those mentioned above were essentially top-down efforts, which is to say that mandates came from the top and teachers, parents, and students were expected to adjust to a new status quo. What we learned in Newark, San Diego, Milwaukee, and many other places is that reform from the top will not work unless there is buy-in from the teachers and the parents (Hess & Sattin-Bajaj, 2013; Hubbard et al., 2006; Russakoff, 2015). Successful reform, according to this view, includes a transformation of the entire educational system, including parents, community, and other stakeholders, such as consultants, professional organizations, and the policy arena.
The learning experiences described here with regards to educational reform reinforce a complexity-based organizational theory (e.g., McKelvey, 2004), which argues that organizational change tends to come from below, involving such processes as the spontaneous formation of teams, identification of leaders, and bottom-up creativity: processes, in other words, where change occurs at higher levels of the organization due to the interaction between lower-level components (emergence), a process of bottom-up transformation such that the interaction between systemic components (e.g., teachers) produces transformation in the higher-level systems of which these components are part (Goldstein, 2009, 2014). One of the failures of the traditional reform model is that it assumes the generalizability of practices from one school building to others, a notion that is codified in the idea of bringing effective practices to scale. Instead, there now is a growing realization that local solutions tend to work at the local level. Teachers and learners are unique, as is their interactive process. Thus, any reform model needs to be able to respect those differences.
Socioeconomic and Sociocultural Underpinnings of Inequality
In what ways do schools affect the upward social mobility of their students? We presume that education enhances such mobility yet also find that socioeconomic differences in society are remarkably persistent in spite of the efforts of our educational system to ameliorate them (Downey, 2020). The notorious intransigence of the educational system is at least in part attributable to the fact that many of the factors that affect its success lie outside of its control (Berliner & Biddle, 1996). For example, one major predictor of student achievement is family socioeconomic status, a variable on which the educational system can have at most an indirect effect, although the impact of family socioeconomic status on student learning is considerable. The argument is that due to these remaining inequalities, one might presume a dynamical process where the educational system reinforces existing inequalities in society while those same inequalities (e.g., inequal funding) allow the education system to operate as a reinforcer. A general formulation of this putative feedback process can be found in Bourdieu (1977), who postulated socioeconomic and sociocultural reproduction systems. In such systems, all components (students, teachers, school leadership, and educational policy) would play their part keeping things in place, including these extant inequities (first-order change or problem formation). Although improved educational funding may not necessarily lead to improved educational outcomes, the inequity in the funding structure tends to reflect the inequalities in society that the educational system is expected to address (Baker, 2018), and as such, it is counterproductive to real reform and may lead to more of the same.
The tendency of systems to reassert and reproduce themselves in the ongoing interactive process in order to endure is an example of autopoiesis (Maturana & Varela, 1973/1980; and see above). In theory, this feature is typically associated with biological systems. However, according to some, it can be expanded to other systems, such as economical ones. In either case, the interaction between components can be seen as a process of reproducing the system through communication. Bourdieu’s theory is primarily concerned with exchange of cultural capital (i.e., social assets such as the production of knowledge, skills, and status symbols) that strengthens existing societal structures or enables upward social mobility in society and the perpetuation of inequality through the exchange of cultural capital. The idea applies equally to other aspects of self-perpetuation, such as the persistence of sociogenic codes associated with societal oppression, the assemblage of sociopolitical relations in society, and their reflection in how the educational system functions (Dixon-Román, 2017).
To what extent does our schooling process inhibit or exacerbate the systemic inequity in society? The achievement gap is an empirical manifestation of the reproduction of inequality (Downey, 2020), whereas the college persistence of students from working-class families to obtain access to the production of knowledge is an example of cultural capital utilized toward the emancipation of minority populations and thus, a challenge to the replication of social class differences. Maturana and Varela (1973/1980) focused on autopoiesis and cognition, referring to the individuals’ internalization of systemic structures (here, inequity). They argued that the individual’s appraisal of these structures tends to be instrumental in their perpetuation as well. Whatever environmental input the developing individual learns or internalizes, it includes an internalization of the values and priorities associated with cultural capital and how it reinforces social class differences. This requires addressing those dynamics as well in the instructional process through which those dynamics may be countermanded. The applicability of autopoiesis for systems such as education has been questioned. Urry (2003) argued against the notion of autopoiesis in educational systems because it implies that elements such as poverty and inequality might be functional components in the maintenance of educational systems, which would be antithetical to their aspiration and primary function. However, educational systems are components of larger systems (e.g., the sociopolitical relations among stakeholders, the policy arena), and the resistance to change may be part of the autopoietic behavior at those higher systemic levels. The influence of poverty on educational outcomes and our limited desire to address this issue is a frequently cited example of such stagnation and the tendency of systems of inequality to perpetuate themselves in an autopoietic manner because political interests are served by maintaining the status quo. The inertia in the educational system may be better understood if these conservative aspects of systemic assertion and perpetuation are considered.
Complexity Across Systems
CDST identifies a set of relatively simple principles that potentially apply across a wide range of situations and scientific disciplines. Such a framework is especially appealing when it is applied to phenomena where the conceptualization in terms of systems, interactions, equilibrium, nonlinear transformations, and so on makes intuitive sense. Although the idea of education as a dynamical system has been around for a long time (e.g., Dewey, 1933/1974) and continues to be seen as relevant (e.g., Cuban, 1999; Elmore, 2004), a systematic accounting of the applicability of complex, dynamical, and system features to the educational process and institutions is a more recent development (e.g., Koopmans & Stamovlasis, 2016, 2020; Marchand & Hilpert, 2020).
The implication of the discussion conducted in this chapter is that there is an interface between these systems of learning and development, educational reform, and the persistence of inequality such that a larger system of teaching and learning in society stands in a complex relationship with its components, which might include these three areas and others. The three areas discussed here may be seen as different examples of complex systems and how they function and provide the basis for a meaningful operationalization of the hypothesized systemic processes, such as attractors in Piagetian accommodation, self-transcending constructions as a basis for educational reform, and inequity in society as an autopoietic phenomenon. Arguably, the CDST terminology is fundamental to a deeper understanding of the phenomena described in the relevant literature and the interrelationships between them. How does inequity in society constrain learning and development? How do educational reform efforts affect teacher-student interactions? How does the rewarding interaction between teachers and students affect the purported effectiveness of schools and districts facilitating student learning and development? These concerns are broader than what can be answered within the boundaries of a specific expertise. Thus, to view, for example, educational reform in terms of the quality of teacher-student interactions helps appreciate the relationship between these levels of description in the system. Likewise, data about (in)equity at the school and district levels and beyond will help address the question how schools help redress this situation in society at large through the interactions that take place within the classroom. In each of these instances, it is helpful to distinguish the educational system in the global sense from the component interactions through which it carries out its mission locally.
The complexity perspective allows for the study of complex processes through the investigation of the interactive processes that constitute complexity in the system. Thus, CDST analyzes individuals in terms of their relationships with other individuals in the same system and the system as a whole instead of isolating individuals from their systems through sampling and then examining how their behavior covaries with that of other individuals in the sample who are similarly separated from their context. In a purely statistical sense, complexity research analyzes the dependency between observational units, whereas traditional quantitative research assumes their independence when estimating sampling variability (see e.g., Guastello et al., 1998; Stamovlasis, 2016b). This difference has important implications for how data are collected and analyzed and to what questions researchers orient their work. Analyzing the relationships between systemic components requires a holistic perspective on the phenomenon of interest. This orientation marks an important difference between CDST and linear cause and effect models, such as those investigated through randomized control trial studies, which surmount the local dependencies of the system under study to enable generalization across settings (Koopmans, 2014, 2016b, 2020a).
Historically, there is an affinity between complexity and ethnographic research that goes back to Gregory Bateson’s (1972) and others’ anthropological work, which takes an idiographic approach to the collection of data in non-Western communities. Bateson combined his interest in the dynamics in non-Western communities with the recent insights in cybernetics, which compelled him to conceptualize his data in terms of the abstract principles of the underlying dynamics of systemic behavior (e.g., schismogenesis, or cultural systems drifting apart). Complexity and ethnographic research both focus on qualitative instead of gradual quantitative processes, and they both focus on the exchanges between elements of a system, contrary to quantitative research, which is interested in the relationships between variables rather than systemic entities (Bloom, 2016). Where CDST and ethnography differ is that CDST has a commitment in the study of stability and change in systems, whereas ethnographic research traditionally did not entertain an apriorist research agenda.
Recent developments in the field of ethnography include a postqualitative research approach that investigates the natural and cultural markers of colonialism and human occupation of the land and other inequity systems to lay bare the entanglements of our representations of the world into those past events and how they feed back into the present (Murris et al., 2020). This work shifts the focus from the traditional anthropological study of “non-Western” cultures and its extension into “Western” environments such as the classroom to a query of the value systems and their behavioral expressions under which the distinction between “Western” and “non-Western” cultures became possible in the first place. Hayles’s (1999) second wave of cybernetics acknowledges the subject and object as being part of a single system that requires scrutiny its own right, an insight that is also acknowledged in the use of participant observation in traditional ethnography (Bogdan & Biklen, 1982). However, it is Hayles’s third wave of cybernetics that is most pertinent to the postqualitative variety of this research tradition: the idea that human self-organizing systems are not merely reproducing a cultural organization but instead can build a springboard toward emergence, that is, radical novelty, through which systems create the “capacity to evolve” (Hayles, 1999, p. 11). Thus, the analysis of assemblages that include human organizations, their physical surroundings, their historical past, and its justification as well as an investigation of how its sociogenic markers feed into the present necessitate a postqualitative approach that is strongly steeped into the substance of our query into the human condition, its embeddings into larger systems (living and nonliving), and its implications for educational systems in particular.
One important insight from complexity theory is that some phenomena are inherently qualitative and should therefore be investigated qualitatively (Bloom, 2016). Yet this acknowledgment does not necessarily rule out the quantification of qualitative phenomena in a statistical sense. Hence, the traditional reading of the term “qualitative research” is avoided in this discussion because, for example, the statistical research of catastrophe and chaos theories is qualitative as well (Freeman, 2000; Stamovlasis, 2016a). These approaches quantify the conditions under which changes in outcomes are qualitative to bring the system from one state to another. In this context, there is also clear potential to the use of mixed-methods research to investigate the layered structure of complex systems such that different types of methodology can be utilized within one research design to study the different layers of the system (Bullock & Poth, 2021; Koopmans, 2017a) and integrate results from different systems into a single framework of hypothesized input-output relationships.
Practitioners will relate to the insight that much of what matters in school buildings is local in nature because each building or system has its own particularities. Although the mathematical presentation of CDST theories may be off-putting to many, the basic premises of the paradigm is very much in line with the way practitioners tend to think about their working environment as one integrated entity in which all components and aspects interrelate in some kind of more or less coherent fashion. For example, this view situates individual students in their particular classrooms and particular classrooms inside particular school buildings and in relation to particular parents and communities. The generalization of evaluation findings across buildings and classrooms is of less immediate relevance to complexity research than the particularities of the interplay between these systemic components and their relationship to the local system at large.
The holistic view held by CDST also facilitates the study of the interface between components’ behaviors across systems, such as those discussed here. Does it make a difference, for example, for school administrators to coordinate distributed leadership processes involving the teaching faculty (Elmore, 2004), and does having that, in turn, generate more productive interactions in the classrooms? In what ways can teachers facilitate discontinuous learning? Clearly, in the interface between these areas, CDST could make a big difference to the field. Likewise, understanding how classroom- and building-level interactions can facilitate or inhibit the effectiveness of the role of the educational system vis-à-vis the enduring poverty and inequality in society might be a central concern in the research agenda to be formulated for the future of research, practice, and policy alike in the education field.
Conclusion
There is no definitive account of what complexity theory is, with different authors highlighting different aspects of it. Whether any of the aspects mentioned above are relevant depends in part on the analytical purpose of the application. Thus, in the examples above, autopoiesis is applied to Bourdieu’s notion of cultural reproduction because the idea of sociocultural reproduction helps understand the lethargy of our system of socioeconomic differences. Likewise, the ideas of emergence and self-transcending constructions are seen here as particularly suitable to address the issue of educational reform because generating such reform needs to be preceded by an understanding of the existing propensities within the system toward flexibility and change. The notion of attractors and their dynamics underlying qualitative transformation is particularly suitable to formulate the underlying dynamics of accommodation. In other words, what aspect of the complexity is invoked to tackle a research question depends on the problem and the researchers’ take on it. The terminology of complexity theory and the phenomena it depicts are not absolute but instead serve the analytical convenience of the researcher or practitioner, who therefore constructs their own complexity theory within the broader context of the complexity paradigm.
Systems are not absolute either. Their operational definition depends on the research question at hand. However, any systemic definition would insist that there is a dependency between its components and between those components and the larger constellations of which these components are part. In that sense, adaptive systems are complex by definition. A systemic formulation provides the analytical tools for an exploration of the commonalities between these areas in terms of the interactions between the systems and their components and across systems, where it concerns teachers, students, administrators, policymakers, and other stakeholders in the educational enterprise, whose behaviors vary and affect each other within this larger system or the ideas about those systems and the investigation thereof. Ultimately, CDST research has the overarching agenda of investigating the underlying dynamics of stability and change in systems, and education provides a wide array of possibilities to explicate those dynamics and inform the field about its most effective practices. In addition, a shared conceptual framework may facilitate the interaction between scholars and practitioners among a wide variety of areas of expertise and thereby reverse the increasing differentiation and compartmentalization of these specialties.
The possibility that principles developed in the hard sciences have a broader range of applicability that includes education, child development, and other social sciences continues to speak to the imagination of researchers and practitioners alike. The works of Piaget, Vygotsky, and Dewey attest to the fact that the field of education and its neighboring disciplines have a long-standing dynamical tradition, including an empirical component, that continues to be influential, informing both research and practice. Recent developments in CDST originating in mathematics, such as chaos theory and catastrophe theory and general systems, stimulate the investigation of principles of stability and change more rigorously, including the testing of dynamical statistical models and the postqualitative query of our frameworks of thought and action in its historical context to better understand the underlying processes. In education, examples of such research are found in Koopmans and Stamovlasis (2016) and Marchand and Hilpert (2020). In conjunction, these studies show how an understanding of the dynamics of learning, schooling, and educational policy can help address the long-standing challenges of the field, such as the emancipation of our students from constraints on learning and development, particularly in minority populations, and help find ways toward greater equity in society.
Footnotes
Acknowledgements
To Jeff Goldstein.
Author
MATTHIJS KOOPMANS is a professor of educational leadership at Mercy University. His research focuses on the application of complexity and nonlinear dynamical systems theories to education and on the use of time-series analysis for fractal estimation.