Four experiments explored participants' understanding of the abstract principles goincipl coinci simulatios o coulat adaptive systems. Experiments 1, 2, and 3shoBU better transfero abstract principlesacroc simulatioA that were relatively dissimilar, and that this e#ect was dueto participantswho perfocip relativelypolat o the initialsimulatioB In Experiment 4, participantsshoic better abstract understandingo asimulatio when it was depicted withcohA@CU rather than idealized graphical elements.Homents fo pom perfos.Aq/ the idealizedversio o the simulatio transferred betterto a newsimulatio gomulat by the same abstractioU The results are interpreted in termso cosAq6BP--A between abstract and codAP)U coAP)U@/A o thesimulatio)/ Individualsproi toiv coivid coividual tendto oodAPU abstractioH whenconA)C@ pro)C@qUA o superficial similarities are salient.

Working memory resources are needed for processing and maintenance of information during cognitive tasks. Many models have been developed to capture the effects of limited working memory resources on performance. However, most of these models do not account for the finding that different individuals show different sensitivities to working memory demands, and none of the models predicts individual subjects' patterns of performance. We propose a computational model that accounts for differences in working memory capacity in terms of a quantity called source activation, which is used to maintain goal-relevant information in an available state. We apply this model to capture the working memory effects of individual subjects at a fine level of detail across two experiments. This, we argue, strengthens the interpretation of source activation as working memory capacity. 2001 Cognitive Science Society, Inc. All rights reserved.

This article presents five principles of learning, derived from cognitive theory and supported by empirical results in cognitive psychology. To bridge the gap between theory and practice, each of these principles is transformed into a practical guideline and exemplified in a real teaching context. It is argued that this approach of putting cognitive theory into practice can offer several benefits to statistics education: a means for explaining and understanding why reform efforts work; a set of guidelines that can help instructors make well-informed design decisions when implementing these reforms; and a framework for generating new and effective instructional innovations

If strategy shifts speed up performance, learning curves should show discontinuities where such shifts occur. Relatively smooth curves appear consistently in the literature, however. To explore this incongruity, we examined learning when multiple strategies were used. We plotted power law learning curves for aggregated data from four mental arithmetic experiments and then plotted similar curves separately for each participant and strategy. We then evaluated the fits achieved by each group of curves. In all four experiments, plotting separately by strategy produced significantly better fits to individual participants' data than did plotting a single power function. We conclude that improvement of solution time is better explained by practice on a strategy than by practice on a task, and that careful assessment of trial-by-trial changes in strategy can improve understanding of the effects of practice on learning.

Most accounts of the Stroop effect (Stroop, 1935) emphasize its negative aspect, namely, that in particular situations, processing of an irrelevant stimulus dimension interferes with participants ’ performance of the instructed task. In contrast, this paper emphasizes the fact that, even with that interference, participants actually can (and usually do) exert enough control to perform the instructed task. An Adaptive Control of Thought–Rational (ACT–R) model of the Stroop task interprets this as a kind of learned strategic control. Specifically, the concept of utility is applied to the two processes that compete in the Stroop task, and a utility-learning mechanism serves to update the corresponding utility values according to experience and hence influence the competition. This model both accounts for various extant Stroop results and makes novel predictions about when people can reduce their susceptibility to Stroop interference. These predictions are tested in three experiments that involve a double-response variant of the Stroop task.

Two experiments examine how participants vary in their approach to solving an orientation task. Verbal reports from untrained participants in a pilot study revealed that some participants used a strategy based on mental imagery, while others used verbal descriptions to do the task. The two experiments presented here involved training participants to perform the orientation task using one of these strategies. Participants ’ performance, measured by response time and eye movements, differed as a function of strategy. An ACT-R model of the task that uses the strategies provides a validation of the proposed mechanisms, producing a close fit to both the response time and eye movement data. The model's success is achieved, in part, by performing all aspects of the task, from processing the information on the screen to making responses. Overall, the results indicate that strategic variability is an important feature of human performance on such tasks.

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Cognitive development on certain tasks (e.g., the balance scale task) is characterized by periods of relative stable, rule-like but suboptimal behavior that occur in a fixed order and alternate with short transition periods. Many models have been developed to capture the developmental phenomena associated with the balance scale task. However, most of these models do not account for important phenomena as discontinuous transitions or rely on questionable assumptions, and none of the models is able to predict improvement in behavior without feedback. We propose a computational model that is implemented in ACT-R and is based on the evaluation of success of applied knowledge structures combined with a mechanism to construct new knowledge by searching for differences in the presented balance scale problems. This model accounts for the empirical phenomena, including learning without feedback as is common in developmental tasks.

We describe a theory of quantitative representations and processes that makes novel predictions about student problem-solving and learning during the transition from arithmetic to algebraic competence or "early algebra". Our Early Algebra Problem Solving (EAPS) theory comes in the form of a cognitive model within the ACT-R cognitive architecture. As a "pedagogical domain theory", our EAPS theory can be used to make sense of the pattern of difficulties and successes students experience in early algebra problem solving and learning. In particular, the theory provides an explanation for the surprising result that algebra students perform better on certain word problems than on equivalent equations (Koedinger & Nathan, 2000; Nathan & Koedinger, 2000). It also makes explicit the knowledge and knowledge selection processes behind student strategies and errors and provides a theoretical tool for psychologists and mathematics educators to both productively generate and accurately evaluate hypotheses about early algebra learning and instruction. We have abstracted our development process into six model-building constraints that may be appropriate for creating cognitive models of problem solving in other domains.

From Ebbinghaus onward psychology has seen an enormous amount of research invested in the study of learning and memory. This research has produced a steady stream of results and, with a few "mini-revolutions " along the way, a steady increase in our understanding of how knowledge is acquired, retained, retrieved, and utilized. Throughout this history there has been a concern with the relationship of this research to its obvious application to education. The first author has written two textbooks (Anderson, 1995a, 1995b) summarizing some of this research. In both textbooks he has made efforts to identify the implications of this research for education. However, he left both textbooks feeling very dissatisfied-- that the intricacy of research and theory on the psychological side was not showing through in the intricacy of educational application. One finds in psychology many claims of relevance of cognitive psychology research for education. However, these claims are loose and vague and contrast sharply with the crisp theory and results that exist in the field. To be able to rigorously understand what the implications are of cognitive psychology research one needs a rigorous theory that bridges the gap between the detail of the laboratory experiment and the scale of the educational enterprise. This chapter is based on the ACT-R theory