Academic Skill Learning and the Problem of Complexity I: Creational Purposeful Integrated Capability at Skill (CPICS)

Physical and mental skills are intended to achieve success at acting purposefully. As capability at any skill increases, the need to adjust details of application to complexity of context and goals will increase as well. It will become more and more important to prepare mentally for what I now term Creational Purposeful Integrated Capability at Skill (CPICS). This paper develops what I mean by CPICS. Theory concerning Complex Dynamical Systems (CDS) such as the brain and other evidence points to the likelihood that the mental operations by which our brain produces any kind of skillful behavior cannot remain constant, but rather must develop through stages for skill to progress most profitably. Using early stages of math learning as an example, I propose that what can hold back some students at development of a skill is that even if presented with all the information need for progress, some students have not yet discovered how to make the most useful mental restructuring that is also needed. This paper proposes and discusses as an example details of what may be especially useful restructuring for early stages of math skill learning. This example is then taken as helping to identify the more general type of restructuring that is especially useful for addressing complexity of application that produces CPICS at every stage of skill improvement. 1. The Role of Mental Restructuring in Skill Improvement The discussion that follows builds upon earlier work (Gardiner et al, 1996; Gardiner, 2000, 2003, 2008, 2019). By skillful “engagement” (Gardiner, 2008) I refer to the specific brain actions that produce skillful physical behavior (such as at walking) or skillful mental behavior (such as at solving a math problem). William James pointed out more than a century ago (James, 1890, 1896) that to live in a complex world we must simplify our interactions with it. But, to paraphrase Einstein’s famous saying, we must think as simply as possible, but not more simply than possible. 2. Insight from Bicycle Riding, Theory of Complex Dynamical Systems (CDS) and Related Evidence 1 Gardiner: Academic Skill Learning and the Problem of Complexity: I Published by The Open Repository @ Binghamton (The ORB), 2019 Physical skills such as at learning to ride a bicycle illustrate what this paper now discusses in relation to academic learning as well. Once learners understand the bicycle and what they must accomplish, further progress must depend on their somehow developing better ways to use their brains to produce bike riding skillfully. Suggestions and help at training by parents, and training wheels can help, but ultimately qualitative improvement in engagement must take place out of direct control by the learners and outside of their conscious awareness. Capability at riding suddenly jumps from not possible to possible. Once possible the capability may continue to develop. But not until this first step. Development of academic skills such as at math, I now argue, also depends on improvement in brain engagement particular to that skill, though not as visibly initially. Bicycle riders cannot ride at all until they make the qualitative engagement change. The math learner who has not made such change at math thinking can still at first manage to some degree with less adequate engagement, but must work harder mentally to compensate and increasingly all but the strongest can be expected to fall behind. And as with bicycle riding, further engagement changes that further improve capability cannot take place until the first step has been made. Why must the brain apparently change its operations as it builds skill at bicycle riding, or more generally as I now argue? Our brain’s enormous complexity appears to be at the heart of our most advanced capabilities (Chomsky, 1972), and its highly complex operations develop in time and in mental spaces created by the brain, and thus are dynamic. General properties of Complex Dynamical Systems (CDS) such as the brain have been under study since the middle of the 20 century. Current work is exploring implications of this theory to Education (Koopmans, 2014; Koopmans & Stamovlasis, 2016). Here we now examine how this theory and related evidence can help us understand why all skill development, including academic skill development, is likely to involve changes in how the brain engages at a kind of skill: 1) The portion of brain activity devoted to any kind of capability is likely to be isolated to a sufficient degree functionally so that special capability can develop. A complex system must often develop specialized functions (such as at bike riding or math) distinguished from the operations of the system as a whole, through use of subsystems (von Berthalanffy, 1969). The subsystem for a particular skill can be expected to depend on activity not only in one but rather in many parts of the brain. The ways in which different subsystems pull together and manage strategically the resources for different kinds of skill cannot be entirely identical, for the operational goals the subsystems address are not identical, but as discussed in a companion paper and Gardiner (2019), subsystem operations can 2 Northeast Journal of Complex Systems (NEJCS), Vol. 1, No. 1 [2019], Art. 7 https://orb.binghamton.edu/nejcs/vol1/iss1/7 DOI: 10.22191/nejcs/vol1/iss1/7 become strategically similar in ways that can have important implications for skill development. 2) A subsystem may itself involve further division into functionally interacting subsystems. Here we are especially interested in how a subsystem producing a kind of skillful behavior develops engagement capability for execution of skillful actions. 3) It is likely that for skillful behavior to continue to improve, a subsystem producing any kind of skill must change its operations in stages. In living creatures (Maturana, 1970; Maturana & Varela, 1973) operations of brain and other systems must be sufficiently stable at any time for the creature to be able to live (see also Wiener, 1948). On the other hand, the human brain continues to grow and develop its capacities significantly after birth. The need to retain stability but also to improve operations over development supports the value of evidence for staging found in overall mental development (e.g. Piaget, 1985; Dawson and Fischer, 1994). Watzlawick, Weakland and Fish (1974) have distinguished two ways for system performance to improve. By first order change they refer to improvements that take place without basic changes in system configuration. But greater improvement can require second order change, where a subsystem reconfigures itself in some way to achieve a new functional capability. Nicolis and Prigogine (1989) in fact propose that a measure of complexity of a system is its capacity to make reorganizing transformations. The importance of staged development in brain systems as a whole supports the likelihood of such staging also in subsystems devoted to kinds of skill. Chase and Simon (1973) provide evidence of such subsystem changes as skill at chess develops. Developmental changes specific to a kind skill can explain movement of capability for a particular kind from more general features of capability (Ackerman, 2011, Ericsson, 2013; Ericsson et al, 2006). 4) Jumps in Skillful Performance: Evidence that skillful performance can sometimes jump upwards as skill advances (Zeeman, 1976, Stamovlasis, 2016, Sideridis and Stamovlasis, 2016) implies that some change in functional operation has taken place. 5) Integration within Subsystem Development: Systems and subsystems profit from integrated operation, as the actions of a thermostat meant to help control house temperature illustrates. The thermostat affects the house temperature most efficiently through connections that integrate thermostat actions with production of other actions by machines that cool or heat the house. Integration of operation 3 Gardiner: Academic Skill Learning and the Problem of Complexity: I Published by The Open Repository @ Binghamton (The ORB), 2019 with application within a brain subsystem producing skillful behavior can be expected to profit from such integration as well. 6) Capacity for Bifurcation in System or Subsystem Development: As a complex system develops, it can reach positions where its further development can proceed in different ways. “Bifurcation” refers to a position in development where two different paths for further development become possible (Nicolis & Prigogine, 1989). 3. Mental Strategy Addressing Complexity in Purposeful Application of Skillful