The three themes that address this connection are:
- research as complex learning: In educational research, the goals are to understand and influence significant social practices that are inherently complicated, dynamic, and changeable (…) The generalizability of educational research is obviously challenged by differences among people and contexts, but time and space also matter.
- research valid for applied outcomes: To meet the considerable challenges of practical applications, educational research must meet high standards of scientific inquiry (…) Our first point under this theme is the importance of establishing a conceptual framework as a foundation (…) A second point about quality centers on methodological adequacy (…) A third point that has emerged from our experiences centers around generalizability methods to extend the concept of test reliability
- research on the application of research to practice: The third theme centers around the possibilities and problems of applying “what we know,” realizing that knowledge is always imperfect. Given the research base of the highest quality, engineering is required to fit the results to new and different settings. Primary among the challenges to this task in education is the disconnect between the worlds of research and practice.
Calfee, R. C., Miller, R.G., Norman, K., Wilson K., Trainin, G., 2006. Learning to Do Educational Research. In Translating Theory and Research Into Educational Practice: Developments in Content Domains, Large-Scale Reform, and Intellectual Capacity, edited by Mark A. Constas and Robert J. Sternberg, Mahwah, N.J.: Lawrence Erlbaum Associates, pp. 77-104
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It is generally recognized that complex systems are comprised of multiple, inter-related processes. In terms of restricted complexity, the goal of scientific practices is to study these processes, in order to uncover the rules or laws of complexity (…) complexity becomes the umbrella term for the ideas of chaos, fractals, disorder, and uncertainty. Despite the difficulty of the subject matter, it is believed that, with enough time and effort, we will be able to construct a unified theory of complexity – also referred to as the ‘Theory of Complexity’ (TOC) or the ‘Theory of Everything’ (TOE) (…) Seth Lloyd, a professor in mechanical engineering at MIT, has compiled a list of 31 different ways in which one can define complexity!
If we accept the fact that things are inherently complex, then it means that we cannot know phenomena in their full complexity. In other words, complex phenomena are irreducible. Acknowledging complexity therefore has a profound impact not only on the status of scientific practices, but also on the status of our knowledge claims as such. More specifically, because our knowledge of complex phenomena is limited, our practices should be informed by, and subject to, a self-critical rationality (…) Acknowledging the irreducible nature of complexity also influences our understanding of the general features of complexity
Features of Complex Systems:
- Complex Systems are constituted by richly interconnected components
- The component parts of complex systems have a double identity premised on both a diversity and a unity principle
- Upward and Downward causation give rise to complex structures: the competitive and cooperative interactions between component parts on a local level give rise to self-organisation which is defined as ‘a process whereby a system can develop a complex structure from fairly unstructured beginnings’
- Complex Systems exhibit self-organizing and emergent behavior: Self-organisation is a necessary condition for emergence, which is defined as ‘the idea that there are properties at a certain level of organization which cannot be predicted from the properties found at lower levels but not sufficient!
- Complex Systems are Open Systems: the intelligibility of open systems can only be understood in terms of their relation with the environment (…) there is an energy, material, or information transfer into or out of a given system’s boundary (…) the environment cannot be appropriated by the system, so the boundary between a system and its environment should be treated both as a real, physical category, and a mental category or ideal model
Woermann, M., 2011. What is complexity theory? Features and Implications. Systems Engineering Newsletter, 30, 1-8, available here
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All the properties that follow:
- A system is complex when it is composed of many parts that interconnect in intricate ways
- A system presents dynamic complexity when cause and effect are subtle, over time.
- A system is complex when it is composed of a group of related units (subsystems), for which the degree and nature of the relationships is imperfectly known. The overall emergent behavior is difficult to predict, even when subsystem behavior is readily predictable. Small changes in inputs or parameters may produce large changes in behavior
- A complex system has a set of different elements so connected or related as to perform a unique function not performable by the elements alone
- Scientific complexity relates to the behavior of macroscopic collections of units endowed with the potential to evolve in time
- Complexity theory and chaos theory both attempt to reconcile the unpredictability of non-linear dynamic systems with a sense of underlying order and structure
make up for this definition I like sooo much:
Complexity is the property of a real world system that is manifest in the inability of any one formalism being adequate to capture all its properties.
Ferreira, P., 2001. Tracing Complexity Theory. Full presentation available here
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- Sensorimotor. Birth through ages 18-24 months.
- Preoperational. Toddlerhood (18-24 months) through early childhood (age 7)
- Concrete operational. Ages 7 to 12.
- Formal operational. Adolescence through adulthood.
Piaget Stages of Development, available here and here
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Gagne identifies five major categories of learning:
- verbal information: facts of knowledge
- intellectual skills: problem solving, discriminations, concepts, principles
- cognitive strategies: meta-cognition strategies for problem solving and thinking
- motor skills: behavioral physical skills
- attitudes: actions that a person chooses to complete
Learning tasks for intellectual skills can be organized in a hierarchy according to complexity:
- stimulus recognition,
- response generation,
- procedure following,
- use of terminology,
- concept formation,
- rule application, and
- problem solving
Each different type requires different types of instruction. The theory outlines nine instructional events and corresponding cognitive processes:
- Gaining attention (reception)/show variety of computer generated triangles
- Informing learners of the objective (expectancy)/pose question: “What is an equilateral triangle?”
- Stimulating recall of prior learning (retrieval)/ review definitions of triangles
- Presenting the stimulus (selective perception)/ give definition of equilateral triangle
- Providing learning guidance (semantic encoding)/ show example of how to create equilateral
- Eliciting performance (responding)/ ask students to create 5 different examples
- Providing feedback (reinforcement)/ check all examples as correct/incorrect
- Assessing performance (retrieval)/ provide scores and remediation
- Enhancing retention and transfer (generalization)/ show pictures of objects and ask students to identify equilaterals
Conditions of learning, Robert Gagne. In InstructionalDesign.org. Full text available here/ For more click here or here or search: Gagne, R. (1985). The Conditions of Learning (4th.). New York: Holt, Rinehart & Winston.
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The term originally appeared in Kuhn’s “The Structure of Scientific Revolutions” book in 1962. He had been struggling with the word since the ’40s:
According to Kuhn, he discovered incommensurability as a graduate student in the mid to late 1940s while struggling with what appeared to be nonsensical passages in Aristotelian physics(…) He could not believe that someone as extraordinary as Aristotle could have written them. Eventually patterns in the disconcerting passages began to emerge, and then all at once, the text made sense to him: a Gestalt switch that resulted when he changed the meanings of some of the central terms. He saw this process of meaning changing as a method of historical recovery. He realized that in his earlier encounters, he had been projecting contemporary meanings back into his historical sources (Whiggish history), and that he would need to peel them away in order to remove the distortion and understand the Aristotelian system in its own right (hermeneutic history) (…) Kuhn realized that these sorts of conceptual differences indicated breaks between different modes of thought, and he suspected that such breaks must be significant both for the nature of knowledge, and for the sense in which the development of knowledge can be said to make progress.
Kuhn was influenced by the bacteriologist Ludwik Fleck who used the term to describe the differences between ‘medical thinking’ and ‘scientific thinking’ and Gestalt psychology, especially as developed by Wolfgang Köhler.
Kuhn’s original holistic characterization of incommensurability has been distinguished into two separate theses:
- taxonomic involves conceptual change (…) no over-lap principle that precludes cross-classification of objects into different kinds within a theory’s taxonomy/ no two kind terms may overlap in their referents unless they are related as species to genus, in contrast to
- methodological, which involves the epistemic values used to evaluate theories (…) it is the idea that there are no shared, objective standards of scientific theory appraisal, so that there are no external or neutral standards that univocally determine the comparative evaluation of competing theories
The Incommensurability of Scientific Theories, In Stanford Encyclopedia of Philosophy, first published Wed Feb 25, 2009; substantive revision Tue Mar 5, 2013, available here
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