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«Facilitating Higher-Order Thinking: Synthesizing Pedagogical Frameworks for the Development of Complex and Coherent Conceptual Systems Michael A. ...»

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Inferences Regarding Cognitive Development According to Paris and Paris (2001), "teachers can provide information and opportunities to students of all ages that will help them become strategic, motivated and independent learners" (p. 89). Zimmerman (2008) claims that SRL "enablefs] learners to transform their mental abilities... into academic performance skill" (p. 166). It appears that learners can develop metacognitive and meta-affective processes, which can be targeted and assessed by instructors. SRL requires foresight, monitoring, control and reflection; and deep motivation is required to integrate skills and attitudes to develop deep comprehension of any subject matter.

Dynamic Complexity Complex Dynamic Systems Ni and Branch (2008) describe complexity as "a common phenomenon existing in biological organisms, geological formations and social constructions... however, complexity as a factor in educational technology tends to be maligned, oversimplified, or otherwise insufficiently addressed..." (p. 29). Erdi (2008) describes the evolution of the idea of "complex systems" as distinct from simple systems; the latter are described in terms of one cause and one effect, with small changes to the cause resulting in small changes to the effect in a predictable manner. On the other hand, complex systems contain circular causality, logical paradoxes and strange loops, where small changes to causes may produce dramatic effects, and results are unpredictable (emergent). Dynamic (or dynamical) complexity refers to temporal processes; where "irreversibility and periodicity are recurring themes" (Erdi, 2008, p. 3). While complexity theory has been applied in many subject areas, human cognition is one fruitful area of inquiry. "The notion of cognitive complexity... has been used as a basis of discussion on the complexity of personal constructions of the real world... The complexity of the world view of a subject can be measured... [for example] a subject with the ability to see people as a mixture of 'good' and 'bad' characteristics has a higher 'cognitive complexity' [than one who sees friends as good people and enemies as bad ones]." (p. 4).

To Sterman (2001), "Systems dynamics is fundamentally interdisciplinary... We take actions that make sense from our short-term and parochial perspectives, but due to our imperfect appreciation of complexity, these decisions often return to hurt us in the long run" (p. 10). An understanding of "systems thinking" is especially important when inquiring into cause and effect relationships in complex situations.

The heuristics we use to judge causal relationships systematically lead to cognitive maps that ignore feedbacks, nonlinearities, time delays, and other elements of dynamic complexity. To judge causality, we use cues such as temporal and spatial proximity of cause and effect, temporal precedence of causes, covariation, and similarity of cause and effect. In complex systems, however, cause and effect are often distant in time and space, and the delayed and distant consequences of our actions are different from and less salient than their proximate effects—or are simply unknown. The interconnectedness of complex systems causes many variables to be correlated with one another, confounding the task of judging cause. Research shows that few mental models incorporate any feedback loops. For example., studies have found virtually no feedback loops in the cognitive maps of political leaders; rather, the leaders focused on particular decisions they might make and their likely consequences— an event-level representation. Experiments in causal attribution show people tend to assume each event has a single cause and often cease their search for explanations when the first sufficient cause is found. (Sterman,

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Dynamic systems theories make use of mathematical functions, which describe the relationships of successive system-states of mathematical spaces, which comprise any number of points in any number of mathematical dimensions. Each point in a system space, at each point in time, is characterized by a binary value (0 or 1), and the values of all points at one moment in time define the state of the system (the system-state). The mathematics that define the relations of one system-state to the next (and the next, and the next) increase in complexity with the number of dimensions in the system and with the length of time under consideration. This abstract general model has proven itself to be extremely useful in many fields of study (the math is derived from the equations of thermodynamics, which cover a three-dimensional spatial system and are very useful in physics); new forms of computer architecture {neural net technology and connectionist machines) have been derived from this idea, and educational psychologists have applied such notions as feedback loops and reciprocal causation to the description of learning processes. Biologists have applied the notion of self-organizing systems to maturation and development Since cognitive functions (and the neurophysiological systems upon which cognition is generally believed to depend) are highly complex, and since teaching/learning systems are even more complex (involving the interactions of human beings with each other and with educational materials), it is useful to understand how dynamic processes (such as reciprocal causation) may be applied in pedagogical terms.

The ideas of ecological psychology (Young, 2004) have been developed in accordance with the principles of dynamic systems, and provide cogent insights into the interdependent functions of thinking/acting systems.

Lewis (2005) also pointed to the potential utility of the dynamic systems (DS) perspective in psychology.

Nonlinear dynamic systems operate through reciprocal, recursive, and multiple causal processes, offering a language of causality consistent with the flow of activation among neural components. Consequently, psychological accounts informed by DS ideas may be more biologically plausible and better able to integrate neural findings... DS ideas may provide a foundation for building models that incorporate the rich psychological categories of emotion theory with the biological realism of neuroscience, by addressing causal relations and part-whole relations in a manner relevant for both. (Lewis, 2005, p. 169) Nonlinearity is the property of mathematical functions that entails discontinuous (rather than incremental) changes in system-states; because information in dynamic systems is carried through variations in complex multidimensional patterns of activity (as opposed to stepwise linear increments), it is possible that the stable patterns (equlibrium states) of a system at one point in time may change drastically in relation to the stable patterns that had characterized the system previously. For example., the initiation of a nuclear chain reaction, or the introduction of a catalyst in a chemical reaction, produce irreversible changes in the functions of sub-atomic systems.

The development of connectionism as a theory of cognitive processing may well have invalidated the assertion that the "container theory" of mind as a repository of mental objects, with its attendant representational baggage, is "the only game in town" (Fodor, 1985, p. 90). Rather than using symbolic representations of objects as mental units, connectionism uses binary nodes, arranged in hierarchical networks, to transform information (from 'inputs' to 'outputs'). This process, modelled on a simplified view of biological nervous systems (and sometimes called "neural net" machine architecture), is accomplished through the assignment of (excitatory or inhibitory) "weights" which are associated with the connections between the nodes. Such machines have been trained (through the adjustment of these weights) to perform pattern recognition tasks, an accomplishment which is relatively impracticable through the processing of symbolic representations. The operation of connectionist machines has demonstrated that information processing can proceed without semantically transparent symbols.

Connectionism provides insight into understanding how cognitive appraisals can emerge without any necessity for direct correspondences between material objects and mental ideas; physical processes and mental functions are related only indirectly. Connectionist machines also illustrates the notion of functional dynamics, which incorporates the understanding that relations between conceptual objects (which determine the outcomes of cognitive functions) are continually subject to change with time; as connection weights are adjusted, the relations between inputs and outs vary commensurately.

Connectionism provides a new operational theory of cognitive (mental) structures, one which is susceptible to analysis in mathematical terms (since the connection weights are quantified). Furthermore, connectionist machines (aside from their genesis as simplified models of nervous system structures and functions) display features which demonstrate a resemblance to human functionality; since the relations between inputs and outputs involve the operation of all elements in the network ("parallel distributed processing"), damage to parts of the system result in performance deficits rather than in complete failure of the system to perform its task. This phenomenon ("graceful degradation") may be seen as evidence for the superiority of connectionism as a theory of mind, as (in contrast) the sequential processing of symbolic representations is halted (or severely compromised) if any step in the process is prevented.

The connectionist theory of mind serves to illustrate the applicability of general systems theory to mental function. The binary nodes in a connectionist network are analogous to arrays of points in theoretical system-space (each of which, in theory, is assigned a binary value). The transformation of such a system from moment to moment in time may be described mathematically in terms of functional dynamics;

thermodynamics exemplifies the application of dynamic functions to the behaviour of physical materials, and it is possible that mental functionality, and linguistic discourses, may be amenable to description in terms of complex dynamic functions (Franklin, 1995;

Globus, 1995; Clark, 2001). The new theory of mind would require no direct correspondence between mental and concrete objects, a situation that is quite consistent with neo-pragmatic philosophy (which obviates the necessity for beliefs to correspond with a purely objective reality; Rorty, 1991). Another way to grasp this idea is to understand that a single pattern of variation in data conveys different information to different interpreters, each of whom provides the context for her own interpretation.

In a nonrepresentational cognitive system, clear (that is, rational and perspicuous) thinking is characterized by coherency (logical consistency) amongst syntactic and semantic functions (language usage); this in contrast to foundational systems of knowledge, which require a basis of epistemic truth. The value of this new way of thinking about understanding lies in its deliverance from a dependency on the foundational ideas of ancient and modern philosophy. Our understanding of wisdom (in the contemporary scheme) is transformed; rather than comprising knowledge of how things really are, the construct of wisdom relates to a consistency in the (dynamic) maintenance of relationships between objects (both abstract and concrete). Coherent conceptual schemata are those which are justified by the most reliable of available evidence, and which are assembled in accordance with consensual rules of logic and mathematics (formal languages) as well as those of natural language semantics.

Bereiter and Scardamalia (1996) point out that learning objectives vary in their levels of abstractness (on a continuum from fully situated in a context to fully abstract), and that deep (intentional) learning requires high levels of abstract thought. Bereiter (1997) explains that models of artificial intelligence that are based on rule-based information processing (the manipulation of symbolic representations of things and events) provides a poor way of describing learning, failing to explain basic cognitive processes such as pattern recognition or transfer of learning; however DS approaches to cognition can manage pattern recognition, and allow us to abstract relations between variables. Bereiter and Scardamalia (1998) note that "folk psychology" (the "container" metaphor of mind) does not support the best teaching practices; appreciation of literature, number sense, mental maps, and creativity cannot be appreciated through ideas of linear, step-by-step cognitive processing.

According to Bereiter and Scardamalia, teachers must distinguish ways of conceptualizing knowledge and its uses; no single approach will handle all situations.

Understanding the nature of deep, coherent knowledge requires a connectionist (nonrepresentational) understanding of mind and recognition of knowledge objects as abstract artefacts. Deep understanding means understanding deep (domain-related) things about a subject; rather than recollecting ideas and relationships, deep understanding implies abilities to interact intelligently with people and objects, to explain and solve problems, and to be aware of the limits of one's understandings. Of course, language rules are subject to change (especially those of natural languages, where new words and meanings are continually being invented), and new evidence (confirming or disconfirming existing schemata) arises all the time.

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