**3. Complex adaptive system (CAS) thinking**

A less reductionist, less mechanistic, more accurate depiction of classroom teaching and learning will necessarily acknowledge their complexity. The framework of complexity theory (an umbrella term applied to the analysis of a range of dynamic, non-linear systems) is a transdisciplinary theoretical framework presenting a nonlinear, non-mechanistic scheme through which to view change within systems. Emerging originally from disciplines such as computer science, cybernetics, chaos

theory, and the natural sciences [30–32], complexity theory has been applied to the natural sciences since the 1950s, and to the social sciences for approximately the last 30 years, as a tool for understanding systems containing multiple agents (in the case of classrooms: pupils, teachers, ideas, environment) whose adaptation, development or change (classroom system learning) is resistant to explanation using the traditional scientific method, or as Newell puts it, "phenomena resistant to reductionist analysis [33]." Complexity theory breaks with linear, causal, or deterministic explanatory frameworks [34], rejecting a version of reality in which "a knowledge of inputs is adequate to predict outputs [1]". Complexity theory distinguishes between systems that are merely complicated and systems that are complex. Complicated systems, such as clocks or engines, have many moving, interacting parts that behave in centralized, repetitive, predictable ways. They remain consistent over time. In contrast, complex systems display less predictable, bottom-up, emergent, and non-linear behaviors, because the elements constantly and mutually affect one another [35]. Central to the behavior of complex systems (and therefore to this discussion) are the concepts of self-organization and emergence. Complex systems are said to have self-organizing properties, meaning that they are not centrally governed or controlled, instead of individual agents in the system act with degrees of autonomy, through local decisionmaking. From these autonomous actions patterns of coherent, aggregate behaviors form across the system from the bottom-up; this is referred to as emergence. My contention in this chapter is that to some extent learning can be said to have emergent qualities and that complexity may provide a framework for depicting and explaining elements of classroom learning which are routinely omitted by mechanistic portrayals of classroom teaching and learning.

Complexity theory has been employed as a lens through which to analyze systems in and of education for a little under three decades now exploring a range of aspects including curriculum [36–39], educational research [1, 40–42], purposes of schooling [43], educational change [44, 45] and the philosophy of education [46]. A limited range of empirical studies have been undertaken into areas including school interventions [47], non-linear modeling for education systems [48, 49], and agent-based studies at system, school and classroom levels [50–52]. Since complexity theory is still a novel framework in education, support for the application of a complexity lens to classroom learning is currently limited but growing. A number of studies have examined classrooms, focusing on links between classroom systems and complexity characteristics, analoging pupil interactivity with the non-linear, ensemble agent behavior characteristic of complex systems. My justification for framing the primary classroom as complex draws on these accounts which suggest that complexity has useful applications in the analysis of classrooms and classroom learning.

Systems that adapt themselves through complex emergence are described as complex adaptive systems (CAS). Typical examples from the natural sciences include ant colonies, insect swarms, or clouds, and city traffic is an example often cited from the human social sciences. In each case, patterns of complex aggregate behaviors emerge through the mutually self-interested actions of individual agents following simple rules. The system "learns" and adapts itself through the network of agent interactions without top-down control from any central authority. CAS is said to function more bottom-up than top-down. Whilst descriptions of CAS properties in the literature across multiple domains overlap considerably, the lack of any unified CAS field of study, a single body of literature, or agreed nomenclature has proved an impediment to achieving a universally applicable framing in the social sciences. As Sullivan points out, "it seems every theorist has his or her own list of characteristics, qualifying

properties, or optimal conditions for complex adaptive systems, each slightly different from the next [53]". Some have attempted to consolidate divergent definitions into more generalizable interpretations for CAS [53–58], however, even in synthesized forms, there is a considerable divergence from one framing to the next. Some theorists [1, 29, 33, 40, 44, 46, 53, 59, 60] have drawn on framings from complexity sciences to describe and discuss features of CAS in the field of education, though here too, no consensus exists about how to frame CAS.

The question of whether a school classroom is a CAS has been studied and discussed by some [29, 53, 59] including me [61] with mixed, but indefinite, conclusions, which depend largely on the CAS definition used and the organizing principles at work in the classroom. I have previously acknowledged [61, 62] that a primary classroom is not a CAS as originally conceived in the natural or computational sciences. However, along with others, I maintain that classrooms have sufficient CAS-like characteristics to warrant using a CAS framing to seek otherwise tacit insights about the nature of classroom learning. The most significant voices concerned with CAS thinking and education (Davis [1, 63, 64], Sumara [1], Mason [44, 45], Morrison [46], Sullivan [53] to name some) agree that caution should be exercised when attempting to conceive of the school classroom as a CAS, or equating emergence with learning. Analogies were taken from complexity science on radically emergent systems, for example, insect swarms, suggests that a classroom organized along similar principles would maximize knowledge sharing between pupils, have little by way of top-down leadership, prioritize individual self-interest and investigate questions to which neither pupils nor teachers know the answer. This is contrary to how most classrooms operate, whereby teachers exercise central executive control, pupil to pupil knowledge sharing may be considered cheating and the teacher tends to know "the answer". Whilst complexity offers "intriguing and generative metaphor(s)" for the classroom system [33], there are obvious limitations to such analogies. Despite some reservations, however, there is agreement among those who have examined learning through a complexity lens (Davis [1, 63, 64], Newell [33], Sullivan [53], Hardman [29] in particular) that instruction alone does not cause learning and that there are, as yet unearthed insights about learning which a CAS framing may elicit.

Whilst no two definitions of CAS in the literature align exactly, there are certain characteristics I deem to be most relevant to school classrooms that appear repeatedly in CAS definitions, shown in **Table 1**. These form the core framework for this discussion of emergent learning. Based on these criteria, a complex adaptive classroom system is one containing multiple autonomous, interacting pupils, whose inter-relationships create networked, self-organized, non-linear behaviors from which change (learning) emerges at different levels (individual, small groups, whole class).

#### **3.1 The idea of a complex adaptive classroom**

Complexivist educational researchers have explored ways in which characteristics of school classrooms overlap with descriptions of CAS, pointing out strengths and weaknesses in the comparison. Burns and Knox [65] compared De Bot et al.'s [66] descriptions of the development of complex systems over time, with their own analysis of classrooms. They found a number of correlations, including that both consists of sets of interacting variables (pupils, teachers, resources, environment), both had unpredictable outcomes (learning outcomes, critical incidents), both are part of and connected to other systems (family, institutional, community), both are sensitive to initial conditions, meaning that small changes or incidents can result in


#### **Table 1.**

*CAS characteristics salient to classrooms and classroom learning.*

large differences over time and both develop through interaction and through internal self-organization. These qualities produce the inherent instability which predisposes classroom systems to emergent change over time. Davis and Sumara [1] posit that to really understand the dynamics of the classroom it is necessary to stop thinking linearly, a point which is supported and explained, with reference to how the social world behaves, by Byrne [67] who asserts that outcomes are determined by multiple causes moving in non-linear ways. Typical classroom examples of this are the multiple factors that might determine whether a pupil contributes verbally or not to a class discussion. These might include (though are not limited to) peer pressure, personal ambition, knowledge of an answer, fear of failure, confidence level, social status, degree of interest, or desire to go to lunch. If the classroom is a CAS, one would also expect these factors to interact with one another and exert influence over other pupils indirectly ("if my neighbor keeps quiet I will speak up/keep quiet; if my neighbor speaks up I will compete to speak first/keep quiet") making causality non-linear, an argument which most teachers would not find it difficult to make. The point here is that classrooms consist of more than simply 30 separate linear interactions between teachers and pupils. Pupils influence one another in multiple visible and invisible ways making it difficult to trace the antecedent(s) of any given event or outcome.

Arguing that classrooms display CAS behaviors, Guanglu [68] points to the non-linear, recursive nature of teaching and learning, in which pupils' and teachers' interconnections produce continuous recursions of understanding, interpretation, re-understanding, and reinterpretation. Teaching and learning do not always follow

#### *Classroom as Complex Adaptive System and the Emergence of Learning DOI: http://dx.doi.org/10.5772/intechopen.101699*

this pattern, in fact, the linear transmission of information remains common in many classrooms and arguments for more direct instruction are currently strengthening [69–71]. However, some degree of openness and randomness are characteristic of even in the most tightly controlled classrooms and at times learning can take on forms more akin to "mutual fertilization, pollination [and] active catalytic(s) [38]". Guanglu suggests that this mutuality is seen in the experience, commonly reported by teachers, of gaining a new or better understanding of the subject matter they are teaching, through the act of teaching it [68]. Support for conceptualizing school classrooms as CAS also comes from Hardman [29] who asserts that sudden or unanticipated emergence of novel outputs in classroom activity is inevitable, partly due to the internal diversity of classrooms, including the uniqueness of individual pupils' (and teachers') brains. Novelties might include sudden realizations, moments of inspiration, original ideas or solutions derived from collaborative experimentation. Diversity is a theme which Davis and Sumara [1] pick up. They suggest that differences, counterpoints, and asymmetries between agents within a system cause the very perturbations from which self-organization and emergence originate. Diversity in this sense does not refer to demographic identity differences (race, gender, etc), but to the myriad tangible, intangible, perceptible, and imperceptible differences which exist between human beings which in the classroom may cause differences in perspective, motivation, intent, action or utterance. These might include, personality traits, personal histories, family environment, inherited traits, self-esteem, self-confidence, or mood. In a CAS, internal diversity is one factor that helps maintain a system's vibrancy and promote adaptation, keeping it far from equilibrium. In the context of a primary classroom this is seen in the way that given sufficient autonomy, pupil interactions rarely follow prescribed pathways or result in predictable outcomes. Collisions between individual diversities create collisions between ideas and perspectives which in turn creates the pluriform, entangled messiness so evident to teachers. From the mess, however, novelty and innovation often emerge.

A few suggestions are evident in these descriptions which lend support to the framing of classrooms as CAS. Firstly, that classrooms, like other CAS, have many moving parts which, given sufficient opportunity to interact, will produce productive instability. Secondly, that instability is causally connected to learning insomuch as randomness changes interactive behaviors and injects novelty, which can qualitatively change learning states. Thirdly, there is an implication that even in classrooms characterized by linear transmission and high degrees of centralized teacher control, openness is inevitable to some degree. Described in these accounts of classrooms and adding some legitimacy to comparisons with descriptions of CAS, are factors beyond, or resistant to, control. Despite the structure of organized schooling, the structure of the curriculum, and the necessary order imposed by teachers, diversities reveal themselves when pupils enjoy sufficient autonomy and openness in the classroom system and this creates opportunities for unpredictability and non-linear change. An example of non-linear emergent learning is evident in the common understanding that alongside the top-down influence of the teacher, pupils also influence and change one another through mutual self-influence [63]. The flow of content, explanation, and questioning does not only travel unidirectionally from teacher to pupils and result in the development of neat predictable knowledge, understanding, and skills. Alexander et al. point out that "change that happens in the learner, be it dramatic or imperceptible, or immediate, or gradual exerts a reciprocal effect on the learner's surroundings [9]". This depiction offers a strong positive comparison between classrooms and CAS, implying that there is also a flow of information and influence

between pupils, towards the classroom environment and climate and, presumably, back towards the teacher as well. This suggests that as pupils change, they also change one another, the teacher and their surroundings, including the environment, through their mutual interconnectedness, much like the behavior of a CAS. Davis and Sumara refer to this phenomenon when stating that complex systems, such as classrooms, are systems that learn. Within such systems, they suggest

*"one cannot reliably predict how a student or a classroom collective will act based on responses in an earlier lesson, or sometimes a few minutes previous. In other words, strict predictability and reliability of results are unreasonable criteria when dealing with systems that learn." [1]*

This means that in a classroom, change (learning) is unlikely to only unfold entirely as intended or directed by the structures of organized schooling, the curriculum, or the teacher. The system and its constituent agents will also adapt and change in ways not predicted or intended by those governing structures. This is evident in the common occurrence of classroom ethos, culture, and atmosphere changing over the course of a week, month, term, semester, or academic year. Such changes are behavioral, relational, environmental, and knowledge-based and can be felt by pupils and teachers in the dynamics of the classroom system. The system adapts because the collective adapts. Groups adapt because individuals adapt. Haggis suggests that emergence is always unpredictable to some extent, stating that "what emerges will depend on what interacts, which is at least partly determined by chance encounters and changes in environments [41]." This supports Biesta's point [72] that learning cannot be reliably predicted but is a retrospective judgment. A principal learning characteristic of classrooms according to complexivists is their tendency towards selforganization and self-maintenance, what Sullivan [53] refers to as "adapt[ing] of their own accord." Some degree of self-organization is inevitable in any system which is not entirely mechanistic and deterministic and since wholly determining the opinions, predilections, desires, impulses, thoughts, and behaviors of groups of pupils is impossible (not to mention undesirable), the tendency for self-organization to exert an influence on classrooms is understandable.

#### **3.2 CAS classroom framing: Some cautions and discussions**

It is necessary to ask, however, to what extent this phenomenon can be said to positively influence learning. In a CAS such as an ant colony, immune system, or decentralized finance block-chain, the self-organization and its concomitant adaptation is the learning. The fluctuation and interaction of many agents (be they ants or genes) all influencing one another, all influencing the system and being influenced by it, produces change that exceeds the individual possibilities of the agents. However, this analogy does not translate perfectly into school classrooms because, as Biesta [72] points out, education is not a morally neutral activity, but a purposeful, values-orientated one, and because of this, what is learned matters. He argues that describing learning as whatever emerges as a result of classroom interactions ignores the fact that education exists so that people learn something, not just anything. This argument fits with assertions from others [42, 73] that a CAS framework has considerable limitations when analyzing classroom learning because classroom learning is goal-orientated and has prescribed directions in which teachers must steer all pupils. As Kuhn puts it

*Classroom as Complex Adaptive System and the Emergence of Learning DOI: http://dx.doi.org/10.5772/intechopen.101699*

> *"It may be argued that there is a fundamental mismatch between complexity and educational enterprise as in essence complexity is descriptive whereas education is normative, or goal-orientated. {…} complexity offers organizational principles for describing how the world and humans function. Education, however, is orientated towards achieving certain goals [42]."*

These descriptions of the purposes of education are demonstrably incompatible with depictions of CAS, in which higher complexities may emerge as a consequence of agents operating individually out of mutual self-interest. Kuhn goes on to state "complexity merely describes, whereas education aims to make a difference [42]". A consequence of this purposefulness that characterizes education (and which distinguishes it from learning in the general sense) is the centralized control of the teacher. Teachers impose expectations and structures on classroom activity and do so in the interest of curricular aims and purposes. Biesta [72] describes how this introduces "an asymmetrical element into the educational process" which is "one of the main reasons why educational learning is radically different from collective, interactive, explorative learning". Without the imposition of purposive structures, the likelihood of emergent learning aligning with curriculum aims is low and the risk that nothing of curricular value will be learned, potentially high. Individuals in a classroom system are not all equal and teachers do not permit pupils to behave out of self-interest, for good reason. Ramussen agrees that educational learning has "special intentions in mind" [74], describing teaching as a "social arrangement and organization aimed at intensifying possibilities for learning and the results of learning". The absence of any overarching "special intentions" in a CAS found in nature or in human systems at a great scale, such as cities or economies, weakens the case for classrooms being viewed as CAS. Sullivan's study [53] illustrates this. Examining three different lessons (a music class, a mathematics class, and an English class) through a CAS lens, he noted that not all the classrooms displayed complex adaptive behaviors. He suggests that a key factor in whether a classroom can usefully be classified as a CAS is whether adaptations within the system are triggered by the teacher or by the collective. If the teacher orchestrates all or most responses to daily events (snow days, timetable changes, pupil absence) with little involvement from the pupils, then adaptations cannot be described as bottom-up. In concluding he states

*"One may say that classrooms are inevitably complicated, and I would certainly agree. One may even say that all classrooms exhibit some measure of complexity, and I might agree. To assume, however, that a class will network itself in such a way that it adapts in any meaningful way is too much to assume [53]."*

Radford [40] bridges arguments for and against comparisons between classrooms and CAS using a metaphoric continuum between what he refers to as "clockishness" and "cloudishness". He draws on Popper's assertion [75] that all systems can be viewed on a continuum between deterministic, reducible, and predictable (clockish) on one hand, and indeterminate, unpredictable, and open (cloudish) on the other. Radford's contention is that even the most deterministic systems, such as clocks, have degrees of unpredictability, and that likewise, the most open and unpredictable systems, such as clouds, have some degree of predictability. Viewed at sufficient resolution, a clock will reveal its lack of mechanistic causality and a cloud will reveal its causalities. All phenomena, according to Radford, can be thought of as having degrees of both "clockishness" and "cloudishness". The question is, which is the most useful or accurate explanatory framework for depicting a given system. Some researchers have attempted to describe

the "cloudish" features of classrooms and how exploring them might lead to new insights about classrooms and classroom teaching and learning. Semetsky for example presents a radical vision of a self-organized classroom, characterized by decentralized control, pupil autonomy, and an absence of direct instruction. She posits that this would "naturalize the concept of learning [76]" through the introduction of greater choice for pupils. She envisages a classroom in which there are no right or wrong responses or answers, just an array of choices for pupils, creating an environment with an "inherent incapacity for students to experience failure at any point within the process" because there is no "special educative aim". This vision of classroom learning is considerably more cloud-like than clock-like and would require a radical overhaul of curriculum structures, not to mention the very purposes of education. Semetsky acknowledges that this radical vision has the potential to be counter-productive, however. She draws on Cillier's warning about chaotic system behaviors or "catatonic shutdown [77]" and suggests that a multiplicity of pupil options may contribute to complete disorganization rather than self-organization. This is similar to Waldrup's assertion that whilst frozen (clockish) systems can benefit from "loosening up a bit", turbulent (cloudish) systems "can always do better by getting themselves a little more organized [78]".

Morrison presents a similar critique and asks

*"whether self-organization is such a good thing, or whether it will lead to diversity, inefficiency, time-wasting, mob rule, and a risk of people going off in so many different directions that the necessary connectivity between parts of an organization, its values and direction will be lost or suffocated [46]."*

This is a valid question. Judging when sources of novelty and disruption risk undermining sources of coherence within a system is crucial to maintaining a productive edge of chaos states and is a crucial aspect of teacher professional judgment. In a CAS such equilibrium is maintained through self-organization. In a classroom, it is largely due to the influence of the teacher. A key illustration of why the conception of classrooms as CAS both is, and is not, accurate and useful.

Others present visions of classrooms as self-organizing adaptive systems, which are less adversarial to the purposes of education than Semetsky's. Fong for example, suggests that the concept of self-emergent order is well suited to early learning environments because of their natural tendency to balance the "dual worlds of emergent order and imposed control [79]" and the challenges teachers face in managing the latter in busy nursery or kindergarten classrooms. Sullivan [53] also takes a positive view of the classroom as a CAS and posits that in classrooms where the features of CAS such as self-organization, distributed control, and agent-interaction (the more cloudish characteristics) are maximized, novel learning emerges. Defining emergent learning as the "acquisition of new knowledge by an entire group when no individual member possessed it before [53]" Sullivan suggests that some curriculum subjects lend themselves more than others to the conditions in which such learning might emerge (literacy more so than mathematics in his example). One such feature of CAS which might be emphasized and capitalized upon in the interest of classroom learning is neighbor interactions. In their study of Canadian mathematics teachers Davis and Simmt noted that with sufficient density of short-range pupil interactions and networking, the emergence of novelty was likely. Their concept of neighbor interactions includes, but also stretches beyond, pupils sitting on the same table. They emphasize that "neighbors in a knowledge-producing community are not physical bodies or social groupings. Rather, the neighbors that must "bump" against one another are ideas [63]". They recommend

### *Classroom as Complex Adaptive System and the Emergence of Learning DOI: http://dx.doi.org/10.5772/intechopen.101699*

maximizing conditions in which pupils' ideas can collide, not just between neighbors on tables, but across the topography of the classroom system, because "agents within a complex system must be able to affect one another's activities [1]".

It is clear that school classrooms share several characteristics with CAS, however, the extent to which any classroom can usefully be described as complex depends on how it is organized. Classrooms that operate under strictly centralized control ("clockish") will share fewer features of CAS, whereas classrooms which function in more decentralized or distributed ways ("cloudish") are likely to create space for the sort of autonomy which invites more CAS-like behaviors. Under such organizational principles, pupils may interact in networked and non-linear ways, becoming selforganizing, and inviting learning to emerge bottom-up, rather than always traveling top-down from the teacher. **Figure 1** depicts three broad typical organizing principles

**Figure 1.**

*Centralised [A], decentralized [B], and distributed [C] classroom organizing principles. Adapted from Davis and Sumara [1].*

common to many classrooms: centralized, decentralized, and distributed. When centrally organized [A], communication flows linearly from the teacher to the pupils but there is little or no interaction between pupils. When organized in a distributed manner [B], groups of pupils interact, including with the teacher, however, there is little or no mutual interaction between pupil groups. In a more distributed organization [C], interactions occur between any individuals with no central organization from the teacher. Newell [33] points out that all three organizational principles may be enacted at different times in any given classroom (even within a single lesson). In classrooms where decentralized or distributed forms are common, ideas are more likely to collide, pupils are more likely to become mutually influential, novelty and innovation may be more apparent, and learning may emerge which exceeds what any individual pupil previously knew or understood.

However, as Semetsky [76] has noted and my own research [62] attests, events, occurrences, and interactions that challenge or obstruct learning are also more likely in decentralized and distributed classrooms structures. With greater pupil autonomy comes greater unpredictability, greater likelihood of social conflict, and greater unevenness in pupil participation. Many theorists [80–87] have also noted that pupil interaction alone rarely results in elaborated learning and that the organizing and structuring influence of the teacher is essential in transforming pupils' hunches and intuitions into knowledge and understanding. With this in mind, and notwithstanding the evident CAS-like qualities of classroom learning, it is relevant to ask what the potential pedagogical benefits of a CAS classroom framing might be.
