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Truth diagrams are introduced as a novel graphical representation for propositional logic. To demonstrate their epistemic efficacy a set of 28 concepts are proposed that any comprehensive representation for PL should encompass. TDs address all the criteria whereas seven other existing representations for PL only provide partial coverage. These existing representations are: the linear formula notation, truth tables, a PL specific interpretation of Venn Diagrams, Frege’s conceptual notation, diagrams from Wittgenstein’s Tractatus, Pierce’s alpha graphs and Gardner’s shuttle diagrams. The comparison (...) of the representations succeeds in distinguishing ideas that are fundamental to PL from features of common PL representations that are somewhat arbitrary. (shrink)

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Six characteristics of effective representational systems for conceptual learning in complex domains have been identified. Such representations should: (1) integrate levels of abstraction; (2) combine globally homogeneous with locally heterogeneous representation of concepts; (3) integrate alternative perspectives of the domain; (4) support malleable manipulation of expressions; (5) possess compact procedures; and (6) have uniform procedures. The characteristics were discovered by analysing and evaluating a novel diagrammatic representation that has been invented to support students' comprehension of electricity—AVOW diagrams (Amps, Volts, Ohms, (...) Watts). A task analysis is presented that demonstrates that problem solving using a conventional algebraic approach demands more effort than AVOW diagrams. In an experiment comparing two groups of learners using the alternative approaches, the group using AVOW diagrams learned more than the group using equations and were better able to solve complex transfer problems and questions involving multiple constraints. Analysis of verbal protocols and work scratchings showed that the AVOW diagram group, in contrast to the equations group, acquired a coherently organised network of concepts, learnt effective problem solving procedures, and experienced more positive learning events. The six principles of effective representations were proposed on the basis of these findings. AVOW diagrams are Law Encoding Diagrams, a general class of representations that have been shown to support learning in other scientific domains. (shrink)

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The representational epistemic approach to the design of visual displays and notation systems advocates encoding the fundamental conceptual structure of a knowledge domain directly in the structure of a representational system. It is claimed that representations so designed will benefit from greater semantic transparency, which enhances comprehension and ease of learning, and plastic generativity, which makes the meaningful manipulation of the representation easier and less error prone. Epistemic principles for encoding fundamental conceptual structures directly in representational schemes are described. The (...) diagrammatic recodification of probability theory is undertaken to demonstrate how the fundamental conceptual structure of a knowledge domain can be analyzed, how the identified conceptual structure may be encoded in a representational system, and the cognitive benefits that follow. An experiment shows the new probability space diagrams are superior to the conventional approach for learning this conceptually challenging topic. (shrink)

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Computational models of learning provide an alternative technique for identifying the number and type of chunks used by a subject in a specific task. Results from applying CHREST to chess expertise support the theoretical framework of Cowan and a limit in visual short-term memory capacity of 3–4 looms. An application to learning from diagrams illustrates different identifiable forms of chunk.

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Pioneering work in the 1940s and 1950s suggested that the concept of chunking might be important in many processes of perception, learning and cognition in humans and animals. We summarize here the major sources of evidence for chunking mechanisms, and consider how such mechanisms have been implemented in computational models of the learning process. We distinguish two forms of chunking: the first deliberate, under strategic control, and goal-oriented; the second automatic, continuous, and linked to perceptual processes. Recent work with discrimination-network (...) computational models of long- and short-term memory (EPAM/CHREST) has produced a diverse range of applications of perceptual chunking. We focus on recent successes in verbal learning, expert memory, language acquisition and learning multiple representations, to illustrate the implementation and use of chunking mechanisms within contemporary models of human learning. (shrink)

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The possibility of ideography is an empirical question. Prior examples of graphic codes do not provide compelling evidence for the infeasibility of ideography, because they fail to satisfy essential cognitive requirements that have only recently been revealed by studies of representational systems in cognitive science. Design criteria derived from cognitive principles suggest how effective graphic codes may be engineered.

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Individual differences in the strategies that control sequential behavior were investigated in an experiment in which participants memorized sentences and then wrote them by hand, in a non‐cursive style. Thirty‐two participants each wrote eight sentences, which had hierarchical structures with five levels. The dataset included over 31,000 letters. Despite the deliberately constrained nature of the task and stimuli, 23 patterns of behavior were identified from the durations of pauses that occurred before the inscription of letters at four chunk levels, spanning (...) letters, words, phrases, and sentences. A critical path task analytic model, Graphical Production of Memorized Sentences (GPoMS), shows that the control of writing relies on cues that continuously switch between motor actions and chunk retrievals in a just‐in‐time fashion at the level of letter information. GPoMS explains the individual differences in terms of variants of a motor production mechanism and variants of a chunk retrieval mechanism, which involve varying degrees of parallelism between cognitive actions and motor actions. A graphical technique for constructing GPoMS models was developed that enabled the estimation of ongoing working memory demands during production. (shrink)

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We discuss the relation of the Theory of Event Coding (TEC) to a computational model of expert perception, CHREST, based on the chunking theory. TEC's status as a verbal theory leaves several questions unanswerable, such as the precise nature of internal representations used, or the degree of learning required to obtain a particular level of competence: CHREST may help answer such questions.

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The Common Thread Of Induction JOHN H. HOLLAND, KEITH J. HOLYOAK, RICHARD E. NISBETT, and PAUL R. THAGARD [1986]: Induction: Processes of Inference, Learning, and Discovery, The MIT Press, Cambridge, Massachusetts: London, England, xii + 385 pp. ISBN 0-262-08160-1.

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