In this article we propose a theoretical framework of distributed representations and a methodology of representational analysis for the study of distributed cognitive tasks—tasks that require the processing of information distributed across the internal mind and the external environment. The basic principle of distributed representations Is that the representational system of a distributed cognitive task is a set of internal and external representations, which together represent the abstract structure of the task. The basic strategy of representational analysis is to decompose (...) the representation of a hierarchical task into its component levels so that the representational properties at each level can be independently examined. The theoretical framework and the methodology are used to analyze the hierarchical structure of the Tower of Hanoi problem. Based on this analysis, four experiments are designed to examine the representational properties of the Tower of Hanoi. Finally, the nature of external representations is discussed. (shrink)

The present paper analyzes the self‐generated explanations (from talk‐aloud protocols) that “Good” and “Poor” students produce while studying worked‐out examples of mechanics problems, and their subsequent reliance on examples during problem solving. We find that “Good” students learn with understanding: They generate many explanations which refine and expand the conditions for the action parts of the example solutions, and relate these actions to principles in the text. These self‐explanations are guided by accurate monitoring of their own understanding and misunderstanding. Such (...) learning results in example‐independent knowledge and in a better understanding of the principles presented in the text. “Poor” students do not generate sufficient self‐explanations, monitor their learning inaccurately, and subsequently rely heavily on examples. We then discuss the role of self‐explanations in facilitating problem solving, as well as the adequacy of current AI models of explanation‐based learning to account for these psychological findings. (shrink)

This research aims to clarify, by constructing and testing a computer simulation, the use of multiple representations in problem solving, focusing on their role in visual reasoning. The model is motivated by extensive experimental evidence in the literature for the features it incorporates, but this article focuses on the system's structure. We illustrate the model's behavior by simulating the cognitive and perceptual processes of an economics expert as he teaches some well‐learned economics principles while drawing a graph on a blackboard. (...) Data in the experimental literature and concurrent verbal protocols were used to guide construction of a linked production system and parallel network, CaMeRa (Computation with Multiple Representations), that employs a “Mind's Eye” representation for pictorial information, consisting of a bitmap and associated node‐link structures. Propositional list structures are used to represent verbal information and reasoning. Small individual pieces from the different representations are linked on a sequential and temporary basis to form a reasoning and inferencing chain, using visually encoded information recalled to the Mind's Eye from long‐term memory and from cues recognized on an external display. CaMeRa, like the expert, uses the diagrammatic and verbal representations to complement one another, thus exploiting the unique advantages of each. (shrink)

We discuss external and internal graphical and linguistic representational systems. We argue that a cognitive theory of peoples' reasoning performance must account for (a) the logical equivalence of inferences expressed in graphical and linguistic form, and (b) the implementational differences that affect facility of inference. Our theory proposes that graphical representation limit abstraction and thereby aid “processibility”. We discuss the ideas of specificity and abstraction, and their cognitive relevance. Empirical support both comes from tasks which involve the manipulation of external (...) graphics and tasks that do not. For the former, we take Euler's (1772) circles, provide a novel computational reconstruction, show how it captures abstractions, and contrast it with earlier construals and with Johnson‐Laird's (1983) mental models representations. We demonstrate equivalence of the graphical Euler system, and the nongraphical mental models system. For tasks not involving manipulation of external graphics, we discuss text comprehension, and the mental performance of syllogisms. By positing an internal system with the same specificity as Euler's circles, we cover the mental models data, and generate new empirical predictions. Finally, we consider how the architecture of working memory explains why such specific representations are relatively easy to store. (shrink)

The goal of this study was to investigate interindividual differences in learning from worked-out examples with respect to the quality of self-explanations. Restrictions of former studies (e.g., lacking control of time-on-task) were avoided and additional research questions (e.g., reliability and dimensionality of self-explanation characteristics) were addressed. An investigation with 36 university freshmen of education working in individual sessions was conducted. The domain was probability calculus. As predictors of learning, prior knowledge and the quality of self-explanations (thinking aloud protocols) were assessed. (...) A post-test was employed to measure the learning gains as dependent variable. The following main results were obtained. Most self-explanation characteristics can be regarded as relatively stable person characteristics. The interindividual differences in the quality of self-explanations were, however, found to be multidimensional. Most importantly, even when controlling for time-on-task (quantitative aspect), learning gains could be substantially predicted by qualitative differences of self- explanation characteristics. Successful learners tended to employ more principle-based explanations, more anticipative reasoning and more explication of operator-goal combinations. (shrink)

This long-awaited work by prominent Harvard psychologist Stephen Kosslyn integrates a twenty-year research program on the nature of high-level vision and mental ...

Human one‐to‐one tutoring has been shown to be a very effective form of instruction. Three contrasting hypotheses, a tutor‐centered one, a student‐centered one, and an interactive one could all potentially explain the effectiveness of tutoring. To test these hypotheses, analyses focused not only on the effectiveness of the tutors' moves, but also on the effectiveness of the students' construction on learning, as well as their interaction. The interaction hypothesis is further tested in the second study by manipulating the kind of (...) tutoring tactics tutors were permitted to use. In order to promote a more interactive style of dialogue, rather than a didactic style, tutors were suppressed from giving explanations and feedback. Instead, tutors were encouraged to prompt the students. Surprisingly, students learned just as effectively even when tutors were suppressed from giving explanations and feedback. Their learning in the interactive style of tutoring is attributed to construction from deeper and a greater amount of scaffolding episodes, as well as their greater effort to take control of their own learning by reading more. What they learned from reading was limited, however, by their reading abilities. (shrink)