*4.1.2 Link 2: Complexity in the qualitative difference in knowledge structures*

There is no obvious complexity construct that capture the distinctions between different types of knowledge. At the same time, the complexity angle constrains the


*Note: The columns correspond to the six knowledge truisms described in Table 1. The rows correspond to the complexity constructs described in Table 2. The X marks the proposed relevance of a complexity construct for a given knowledge truism.*

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*Exploring Links between Complexity Constructs and Children's Knowledge Formation…*

ways in which organizations can differ. For example, given that complex systems consist of elements that interact with each other, differences need to be limited to the elements (e.g., number, type) or the way elements interact (e.g., coupling strength). *Graph theory* can specify the number of connections, thus distinguishing between qualitatively different networks (e.g., small-world networks, scale-free networks). And *ascendency* can capture the coupling strength among elements, thus

Applied to cognition, several complexity measures have been developed to capture coupling strength [103, 104]. These include a child's reasoning during a gear-turning task [105], a child's predictions of the faster sinking object [106], and a child's attempts to balance beams on a fulcrum [107]. Thus, it is reasonable to assume that knowledge structures can differ in the number of mental elements and/or in how the mental elements combine. The organization of preconceptions, for example, might be more restricted than the organization of misconceptions.

There are several complexity constructs that capture the idea of knowledge construal. *Self-organization* is one of these constructs: It states that the system's organized behavior emerges without a direct linear cause–effect relation. Thus, it rejects the idea that an outside force can specify the exact details of the system's organization. Work on children's stepping behavior has provided early evidence for this conceptualization [108]. More generally, knowledge construal is likely to be

*Affordance* is another complexity construct that emphasizes the separation between outside forces and internal organization. This construct rejects the idea altogether that there is objective outside information. Affordances are instead intricately linked to the agent's actions and action capabilities, and thus exist as part of the agent's knowledge structure. In the field of cognition, the concept of affordance can be seen in research of networks that explain decision making, working memory, and mental representations [109–111]. Thus, it is possible that knowledge construal

The construct of *synchrony* hints at a possible mechanism by which a system's organization could be construed. It captures the idea that elements affect each other in a mutually constraining way. This resulting interdependence of elements can amplify the initial coordination to the point that it no longer reflects the outside that gave rise to it (see also *interaction-dominant cognition*; [112, 113]). Synchrony has been used to map out neural connections (see also *connectome*; [114]) and the neural networks that give rise to cognitive performance [115–117]. More generally, there is evidence of synchronization between brain activity and the body/physiology that

*4.1.4 Link 4: Complexity in the context dependence of knowledge acquisition*

There are several complexity constructs that anticipate context effects (i.e., that seemingly irrelevant changes in context can affect children's learning). Consider, for example, the construct of *self-organized criticality*. This construct describes a system that has several different possible organizations available, which are decided upon by only miniscule changes in the context. Thus, context effects are at the essence of this complexity construct. Indeed, there is evidence that self-organized criticality plays a role in knowledge formation ([113, 120, 121]; see also *metastability*; *multistability*; [122, 123]). Therefore, the context effects seen during learning might be the

*DOI: http://dx.doi.org/10.5772/intechopen.97642*

differentiating systems of various stabilities [80].

*4.1.3 Link 3: Complexity in the construal of knowledge*

is analogous to the emergence of an affordance.

has been used to capture cognition (e.g., [118, 119]).

result of such self-organized criticality.

self-organized, too.

#### **Table 3.**

*Relevance of complexity constructs to knowledge formation.*

#### *Exploring Links between Complexity Constructs and Children's Knowledge Formation… DOI: http://dx.doi.org/10.5772/intechopen.97642*

ways in which organizations can differ. For example, given that complex systems consist of elements that interact with each other, differences need to be limited to the elements (e.g., number, type) or the way elements interact (e.g., coupling strength). *Graph theory* can specify the number of connections, thus distinguishing between qualitatively different networks (e.g., small-world networks, scale-free networks). And *ascendency* can capture the coupling strength among elements, thus differentiating systems of various stabilities [80].

Applied to cognition, several complexity measures have been developed to capture coupling strength [103, 104]. These include a child's reasoning during a gear-turning task [105], a child's predictions of the faster sinking object [106], and a child's attempts to balance beams on a fulcrum [107]. Thus, it is reasonable to assume that knowledge structures can differ in the number of mental elements and/or in how the mental elements combine. The organization of preconceptions, for example, might be more restricted than the organization of misconceptions.

### *4.1.3 Link 3: Complexity in the construal of knowledge*

There are several complexity constructs that capture the idea of knowledge construal. *Self-organization* is one of these constructs: It states that the system's organized behavior emerges without a direct linear cause–effect relation. Thus, it rejects the idea that an outside force can specify the exact details of the system's organization. Work on children's stepping behavior has provided early evidence for this conceptualization [108]. More generally, knowledge construal is likely to be self-organized, too.

*Affordance* is another complexity construct that emphasizes the separation between outside forces and internal organization. This construct rejects the idea altogether that there is objective outside information. Affordances are instead intricately linked to the agent's actions and action capabilities, and thus exist as part of the agent's knowledge structure. In the field of cognition, the concept of affordance can be seen in research of networks that explain decision making, working memory, and mental representations [109–111]. Thus, it is possible that knowledge construal is analogous to the emergence of an affordance.

The construct of *synchrony* hints at a possible mechanism by which a system's organization could be construed. It captures the idea that elements affect each other in a mutually constraining way. This resulting interdependence of elements can amplify the initial coordination to the point that it no longer reflects the outside that gave rise to it (see also *interaction-dominant cognition*; [112, 113]). Synchrony has been used to map out neural connections (see also *connectome*; [114]) and the neural networks that give rise to cognitive performance [115–117]. More generally, there is evidence of synchronization between brain activity and the body/physiology that has been used to capture cognition (e.g., [118, 119]).

#### *4.1.4 Link 4: Complexity in the context dependence of knowledge acquisition*

There are several complexity constructs that anticipate context effects (i.e., that seemingly irrelevant changes in context can affect children's learning). Consider, for example, the construct of *self-organized criticality*. This construct describes a system that has several different possible organizations available, which are decided upon by only miniscule changes in the context. Thus, context effects are at the essence of this complexity construct. Indeed, there is evidence that self-organized criticality plays a role in knowledge formation ([113, 120, 121]; see also *metastability*; *multistability*; [122, 123]). Therefore, the context effects seen during learning might be the result of such self-organized criticality.

*Theory of Complexity - Definitions, Models, and Applications*

that knowledge is self-organized.

organized in scale-free patterns.

**Constructs from Non-Living Systems**

**X X**

Hysteresis **X X** Attractors **X**

Self-preservation **X**

**X X**

*Note: The columns correspond to the six knowledge truisms described in Table 1. The rows correspond to the complexity constructs described in Table 2. The X marks the proposed relevance of a complexity construct for a given* 

Chaos **X**

Selforganization

Self-organized criticality

Balance/ Equilibrium

Dissipation pressure

Autocata kinetics/ Teleodynamics

*knowledge truism.*

Self-similarity **X**

**Constructs from Living Systems**

Affordance **X** Synchrony **X**

*Relevance of complexity constructs to knowledge formation.*

**Constructs from Thermodynamic Systems**

complex system organize themselves. There is indeed evidence of self-organization in cognitive activity. For example, the idea of self-organization has been invoked to address the origins of language (e.g., [70]), to observe the emergence of knowledge (e.g., [95]), to explain the systematic problem-solving behaviors of infants (e.g., [96, 97]), and to apply effective pedagogy [98]. Hence, it is reasonable to assume

Another complexity construct that anticipates knowledge organization is *self-similarity*—the idea that an organized pattern repeats itself at various nested levels. Here too there is evidence that self-similarity applies to cognition. It was studied primarily by looking for *scale-free patterns* in cognitive behavior [99]. The signature of scale-free pattern is a *1/f scaling*, also known as *pink noise* (e.g., [100, 101]). Analyses of the variability in reaction time have revealed pink-noise patterns, indicating that the variability in a short time series is similar to that in a longer time series (e.g., [102]). Hence, it is reasonable to assume that knowledge is

*4.1.2 Link 2: Complexity in the qualitative difference in knowledge structures*

There is no obvious complexity construct that capture the distinctions between different types of knowledge. At the same time, the complexity angle constrains the

> **Nature of Knowledge Acquisition of Knowledge Change of Knowledge Structure Diversity Construal Context Persistence Conflict**

> > **X X**

**X**

**X**

**52**

**Table 3.**

More generally, the power of seemingly irrelevant aspects of the outside are highlighted by the constructs of *chaos* (i.e., sensitivity to initial conditions) and *hysteresis* (i.e., sensitivity to the history of the system). Here again there is evidence that these concepts are applicable to cognitive processes [124]. Stamovlasis [125], for example, has demonstrated hysteresis in students' science learning, modulated by parameters such as logical thinking ability. Thus, it is possible that context effects seen during learning might be the result of the inherent complexity of knowledge formation.

#### *4.1.5 Link 5: Complexity in the persistence of knowledge structures*

There are several complexity constructs that anticipate persistence in the organization of a system's elements. *Hysteresis* is an example of such a construct, namely, because it captures the lingering of a specific organization past outside changes. The construct of *attractors* captures the idea of persistence more generally—that a system's organization can resist perturbation and return to its preferred behavior once the perturbation ends. Applied to children's cognition, the idea of an attractor was used to explain perseverative search behavior [126]. It has also been examined in the study of recurrent neural networks [127, 128]. Thus, it is reasonable to assume that knowledge persistence is the result of an attractor.

The constructs of agency, *autopoiesis, autocatakinetics*, and *teleodynamics* have also been linked to human behavior [129, 130] and mental activity (e.g., [83, 85, 130–134]). In fact, Barab et al. [131] have applied the idea of autocatakinetics specifically to children's science learning.

#### *4.1.6 Link 6: Complexity in the role of conflict in conceptual change*

There are two complexity constructs that anticipate the power of conflict to change a system's organization: that of *balance* and *dissipation pressure*. Both of these constructs stem from the study of thermodynamic systems. Under this framework, the perceived conflict can be conceptualized as something that changes the balance of forces and, thus, changes the dissipation pressure. These changes, in turn, affect the likelihood that an existing organization can no longer dissipate the pressure, ushering the change in organization.

The concept of balance is not foreign to work on children's cognition [135]. For instance, Piaget's constructivist account of cognitive disequilibrium highlighted the interplay of the counteracting processes of transformation and conservation [136, 137]. Also, Piaget's notion of adaptation is seen as a process of equilibration between processes of assimilation and accommodation [138]. The role of perceived conflict fits well within this line of work. Thus, the complexity angle offers a way of conceptualizing the role of conflict in ways that are consistent with systemic laws.

#### **4.2 Summary of how complexity is linked to knowledge formation**

In this section, we sought to explore the extent to which selected knowledge truisms align with complexity constructs. Our analysis showed that this link is indeed present, though to various degrees: Most prevalently, complexity anticipates the organization of elements and the persistence of knowledge. It also anticipates the influence of the outside context and the impact of conflict on conceptual change. Note, however, that complexity constructs differed in how well they covered knowledge truisms. For example, the idea of knowledge construal was covered by several complexity constructs, while the idea of knowledge persistence was covered primarily by thermodynamic constructs. It remains to be seen if this disparity

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*Exploring Links between Complexity Constructs and Children's Knowledge Formation…*

identifies a shortcoming of the current theorization of complexity or our interpre-

Having provided an alignment between complexity constructs and knowledge formation, we now derive complexity answers to the ongoing questions related to children's science learning. We specifically focus on questions of (1) how to best define knowledge, (2) how to support children's learning, and (3) how to replace

While it is widely accepted that knowledge is more than a set of isolated factoids, there is uncertainty about how to best conceptualize such interconnected whole. Complexity provides important constraints for the depiction of knowledge. By this conceptualization, knowledge is defined as the coordination among elements, analogous to a set of synchronizing metronomes, a flock of birds, or an ecosystem. That is to say, knowledge is stable only in the continuous interaction among mental elements. Accordingly, **Figure 1** might need to be revised: Whether understanding is naïve or competent, mutually constraining interactions among elements are required in both.

There is also uncertainty about how to capture different types of knowledge unequivocally—for example, between novices and experts. In the balance-beam task, for example, it is still debated whether the difference between implicit and explicit knowledge spans four levels [139], seven levels [140], or none at all [141]. Complexity sheds light on the matter by specifying the ways in which structures can differ. Correspondingly, implicit knowledge might consist of few elements that are constrained to a local action. Explicit knowledge, in contrast, might involve elements that span various circumstances and thus couple with each other on the basis

There is no agreed-upon understanding of the processes that turn information into knowledge. Complexity science specifies that this process involves the synchronization of experiences into a self-sustaining whole. Furthermore, thermodynamic constructs show that such synchronized aggregations emerge when there is a balance between clustered energy and pressure. Thus, to decide on the ideal pedagogy, one must first identify the 'clustered energy' in the learning context, as well as the nature of 'pressure'. One must then ensure that these two aspects are in some sort of

Applied to the balance-beam task, clustered energy could be conceptualized as information about the beams (visual, haptic). There is also information across trials, for example, that some of the beams balance at their geometric center. The pressure, on the other hand, could be conceptualized as the task that children are asked to complete: to balance individual beams on a fulcrum. The narrower the fulcrum, the more pressure there is on the system to organize its elements. For pedagogy to be effective, therefore, the salience of the beam's weight distribution must be calibrated with the narrowness of the fulcrum upon which the beam should be balanced. This calibration between information and task pressure has to fit the competence of the individual child and adjust flexibly to changing competences.

*DOI: http://dx.doi.org/10.5772/intechopen.97642*

**5. Implications for science learning**

children's mistaken beliefs with scientifically valid insights.

Even elements might be synchronized patterns of interacting parts.

**5.1 How to best define knowledge and its elements**

of symbolic correspondences that can be verbalized.

**5.2 How to support children's learning**

equilibrium to allow for learning.

tation of knowledge findings.

identifies a shortcoming of the current theorization of complexity or our interpretation of knowledge findings.
