**5. Implications for science learning**

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

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

that knowledge persistence is the result of an attractor.

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

specifically to children's science learning.

ushering the change in organization.

conflict in ways that are consistent with systemic laws.

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

formation.

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

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

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

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,

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

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

**54**

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 children's mistaken beliefs with scientifically valid insights.

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

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. Even elements might be synchronized patterns of interacting parts.

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 of symbolic correspondences that can be verbalized.

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

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 equilibrium to allow for learning.

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.

## **5.3 How to replace mistaken beliefs with scientifically valid insights**

The challenge in science education has been largely attributed to the presence of mistaken beliefs. However, the results are mixed on the recommendation to assess existing beliefs first, prior to administering a science lesson [142–144]. Complexity science can again shed light on the issue. Specifically, lessons derived from thermodynamics provide a cautionary note to the logic of first providing children with an assessment. This is because, in the language of complexity, assessments are equivalent to the pressure on the system to organize itself. This pressure might force children to come up with ordered behavior that resembles a belief. The risk, therefore, is that the assessment pushes the learner to form an ad-hoc belief, rather than assessing the presence of an already existing belief.

The solution lies in combining pressure (the assessment) with support (the information relevant to the solution), rather than offering the assessment on its own. This recommendation is in line with the resubsumption theory [144, 145]. It is also in line with the finding that a child's explicit goal to change mistaken beliefs has a positive effect on learning [146–148]. This is because such explicit buy-in from the learner shifts the nature of the pressure in ways that allows children to actively search for scientifically valid patterns (vs. latch onto the most obvious patterns to coordinate experiences).

Ultimately, the complexity viewpoint implies that the challenge of science learning lies in the nature of science itself, rather than in the presence of mistaken beliefs. This is because the patterns of order relevant to science concepts are often hidden behind more salient but irrelevant science concepts. For example, in the case of balance beams, visual features are likely to have priority over haptic features, making the irrelevant aspect of the beam's shape more readily available than the relevant weight distribution. Therefore, to improve science learning, one would need to invest in ways of making relevant patterns of order more salient than irrelevant ones, paired with gearing children's action toward detecting these relevant patterns.

#### **5.4 Summary of complexity-based answers to open questions**

In this section, we sought to address practical implications of a complexity view of learning. On the question of the nature of knowledge, for example, complexity science provides details on how to conceptualize the interaction of mental elements that gives rise to knowledge. And on the question of learning, complexity science can pin down the pedagogy that could help children ignore irrelevant aspects of the context. The complexity angle can even address questions about conceptual change: It undermines the common suggestion of assessing children's naïve beliefs in the absence of instruction; and it highlights strategies that can help children learn about abstract science concepts. While these suggestions are merely hinted at, they can offer an important impetus to science-education research.

### **6. Conclusion**

In line with the volume's goal of deepening the meaning of complexity, we traced the connection between complexity constructs and children's learning. Our specific focus was on children's science education, a topic with remaining open questions despite previous attempts to apply complexity ideas. Our rationale was that neither the field of complexity nor the field of children's learning are streamlined: Both areas feature inconsistencies and gaps [149]. The synthesis we offered was designed to substantiate this link, potentially fostering progress in both fields.

**57**

**Author details**

misconceptions.

learning.

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

Our approach started with a preliminary step—namely, to consider issues of cognition separately from issues of complexity. To this end, we defined central characteristics of knowledge formation without considerations of complexity; and we defined central characteristics of complex systems without considerations of cognition. This two-pronged preliminary step made it possible to explore the link between complexity and learning in a principled way, rather than trying to prove a-priori assumptions about it. Thus, by cross-tabulating the list of knowledge truisms with the list of complexity constructs, we were able to substantiate the

The cross-tabulation shows that our chosen knowledge truisms were anticipated

A limitation of this work pertains to taking some shortcuts when generating the two initial lists. For example, we settled on six knowledge truisms, potentially at the expense of important nuances. And we prioritized prominent complexity constructs, potentially at the expense of lesser-known constructs. We also overlooked ongoing controversies, for example on the topic of constructivism, on self-organized criticality, or on how to apply thermodynamics to cognitive processes. For these reasons, our lists are undoubtedly incomplete. Nevertheless, this work offers a starting point from which to develop a complexity-based framework for children's

robustly by complexity constructs. Building on this alignment, we were able to derive answers relevant to science education. For example, the knowledge-complexity alignment specifies that knowledge is a mental synchronization of experiences. Such synchronization can emerge when there is a balance between direct instruction and active learning that is calibrated to highlight relevant patterns of order (vs. irrelevant patterns of order). This calibration can be difficult to establish when relevant patterns are inherently hidden, as is the case in abstract science concepts. In turn, this difficulty can explain the challenge of science education, going against the prevailing assumption that science-education challenges stem from children's

Michael J. Droboniku\*, Heidi Kloos, Dieter Vanderelst and Blair Eberhart

\*Address all correspondence to: drobonmj@mail.uc.edu

provided the original work is properly cited.

Department of Psychology, University of Cincinnati, Cincinnati, OH, United States

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

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

knowledge–complexity link in a relatively objective way.

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

Our approach started with a preliminary step—namely, to consider issues of cognition separately from issues of complexity. To this end, we defined central characteristics of knowledge formation without considerations of complexity; and we defined central characteristics of complex systems without considerations of cognition. This two-pronged preliminary step made it possible to explore the link between complexity and learning in a principled way, rather than trying to prove a-priori assumptions about it. Thus, by cross-tabulating the list of knowledge truisms with the list of complexity constructs, we were able to substantiate the knowledge–complexity link in a relatively objective way.

The cross-tabulation shows that our chosen knowledge truisms were anticipated robustly by complexity constructs. Building on this alignment, we were able to derive answers relevant to science education. For example, the knowledge-complexity alignment specifies that knowledge is a mental synchronization of experiences. Such synchronization can emerge when there is a balance between direct instruction and active learning that is calibrated to highlight relevant patterns of order (vs. irrelevant patterns of order). This calibration can be difficult to establish when relevant patterns are inherently hidden, as is the case in abstract science concepts. In turn, this difficulty can explain the challenge of science education, going against the prevailing assumption that science-education challenges stem from children's misconceptions.

A limitation of this work pertains to taking some shortcuts when generating the two initial lists. For example, we settled on six knowledge truisms, potentially at the expense of important nuances. And we prioritized prominent complexity constructs, potentially at the expense of lesser-known constructs. We also overlooked ongoing controversies, for example on the topic of constructivism, on self-organized criticality, or on how to apply thermodynamics to cognitive processes. For these reasons, our lists are undoubtedly incomplete. Nevertheless, this work offers a starting point from which to develop a complexity-based framework for children's learning.
