We present a new model of skilled performance in geometry proof problem solving called the Diagram Configuration model (DC). While previous models plan proofs in a step‐by‐step fashion, we observed that experts plan at a more abstract level: They focus on the key steps and skip the less important ones. DC models this abstract planning behavior by parsing geometry problem diagrams into perceptual chunks, called diagram configurations, which cue relevant schematic knowledge. We provide verbal protocol evidence that DC's schemas correspond (...) with the step‐skipping inferences experts make in their initial planning. We compare DC with other models of geometry expertise and then, in the final section, we discuss more general implications of our research. DC's reasoning has important similarities with Larkin's (1988) display‐based reasoning approach and Johnson‐Laird's (1983) mental model approach. DC's perceptually based schemas are a step towards a unified explanation of (1) experts' superior problem‐solving effectiveness, (2) experts' superior problem‐state memory, and (3) experts' ability, in certain domains, to solve relatively simple problems by pure forward inferencing. We also argue that the particular and efficient knowledge organization of DC challenges current theories of skill acquisition as it presents an end‐state of learning that is difficult to explain within such theories. Finally, we discuss the implications of DC for geometry instruction. (shrink)

The appropriate methodology for psychological research depends on whether one is studying mental algorithms or their implementation. Mental algorithms are abstract specifications of the steps taken by procedures that run in the mind. Implementational issues concern the speed and reliability of these procedures. The algorithmic level can be explored only by studying across-task variation. This contrasts with psychology's dominant methodology of looking for within-task generalities, which is appropriate only for studying implementational issues.The implementation-algorithm distinction is related to a number of (...) other “levels” considered in cognitive science. Its realization in Anderson's ACT theory of cognition is discussed. Research at the algorithmic level is more promising because it is hard to make further fundamental scientific progress at the implementational level with the methodologies available. Protocol data, which are appropriate only for algorithm-level theories, provide a richer source than data at the implementational level. Research at the algorithmic level will also yield more insight into fundamental properties of human knowledge because it is the level at which significant learning transitions are defined.The best way to study the algorithmic level is to look for differential learning outcomes in pedagogical experiments that manipulate instructional experience. This provides control and prediction in realistically complex learning situations. The intelligent tutoring paradigm provides a particularly fruitful way to implement such experiments.The implications of this analysis for the issue of modularity of mind, the status of language, research on human/computer interaction, and connectionist models are also examined. (shrink)

The commentaries on our article encourage us to believe that researchers are beginning to take seriously the goal of achieving the broad adequacy that Newell aspired to. The commentators offer useful elaborations to the criteria we suggested for the Newell Test. We agree with many of the commentators that classical connectionism is too restrictive to achieve this broad adequacy, and that other connectionist approaches are not so limited and can deal with the symbolic components of thought. All these approaches, including (...) ACT-R, need to accept the idea that progress in science is a matter of better approximating these goals, and it is premature to be making judgments of true or false. (shrink)

Newell proposed that cognitive theories be developed in an effort to satisfy multiple criteria and to avoid theoretical myopia. He provided two overlapping lists of 13 criteria that the human cognitive architecture would have to satisfy in order to be functional. We have distilled these into 12 criteria: flexible behavior, real-time performance, adaptive behavior, vast knowledge base, dynamic behavior, knowledge integration, natural language, learning, development, evolution, and brain realization. There would be greater theoretical progress if we evaluated theories by a (...) broad set of criteria such as these and attended to the weaknesses such evaluations revealed. To illustrate how theories can be evaluated we apply these criteria to both classical connectionism and the ACT-R theory. The strengths of classical connectionism on this test derive from its intense effort in addressing empirical phenomena in such domains as language and cognitive development. Its weaknesses derive from its failure to acknowledge a symbolic level to thought. In contrast, ACT-R includes both symbolic and subsymbolic components. The strengths of the ACT-R theory derive from its tight integration of the symbolic component with the subsymbolic component. Its weaknesses largely derive from its failure, as yet, to adequately engage in intensive analyses of issues related to certain criteria on Newell's list. Key Words: cognitive architecture; connectionism; hybrid systems; language; learning; symbolic systems. (shrink)

This article investigates the potential of fMRI to test assumptions about different components in models of complex cognitive tasks. If the components of a model can be associated with specific brain regions, one can make predictions for the temporal course of the BOLD response in these regions. An event‐locked procedure is described for dealing with temporal variability and bringing model runs and individual data trials into alignment. Statistical methods for testing the model are described that deal with the scan‐to‐scan correlations (...) in the errors of measurement of the BOLD signal. This approach is illustrated using a “sacrificial” ACT‐R model that involves mapping 6 modules onto 6 brain regions in an experiment from concerned with equation solving. The model's visual encoding predicted the BOLD response in the fusiform gyrus, its controlled retrieval predicted the BOLD response in the lateral inferior prefrontal cortex, and its subgoal setting predicted the BOLD response in the anterior cingulate cortex. On the other hand, its motor programming failed to predict anticipatory activation in the motor cortex, its representational changes failed to predicted the pattern of activity in the posterior parietal cortex, and its procedural component failed to predict an initial spike in caudate. The results illustrate the power of such data to direct the development of a theory of complex problem solving, both at the level of a specific task model as well as at the level of the cognitive architecture. (shrink)

Perhaps no other population exposes the clinician to more moral and legal dilemmas than clients with an HIV-positive diagnosis. What does the therapist do about the HIV positive patient who is having sex with unnamed partners and refuses to stop? What should be said in end-of-life decisions? What of the adolescent who is HIV positive but whose guardian does not wish the youth to be informed of his status?

We present an account of processing capacity in the ACT-R theory. At the symbolic level, the number of chunks in the current goal provides a measure of relational complexity. At the subsymbolic level, limits on spreading activation, measured by the attentional parameter W, provide a theory of processing capacity, which has been applied to performance, learning, and individual differences data.

This article describes the Adaptive Control of Thought–Rational (ACT–R) cognitive architecture (Anderson et al., 2004; Anderson & Lebiere, 1998) and its detailed application to the learning of algebraic symbol manipulation. The theory is applied to modeling the data from a study by Qin, Anderson, Silk, Stenger, & Carter (2004) in which children learn to solve linear equations and perfect their skills over a 6‐day period. Functional MRI data show that: (a) a motor region tracks the output of (...) equation solutions, (b) a prefrontal region tracks the retrieval of declarative information, (c) a parietal region tracks the transformation of mental representations of the equation, (d) an anterior cingulate region tracks the setting of goal information to control the information flow, and (e) a caudate region tracks the firing of productions in the ACT–R model. The article concludes with an architectural comparison of the competence children display in this task and the competence that monkeys have shown in tasks that require manipulations of sequences of elements. (shrink)

Can the output of human cognition be predicted from the assumption that it is an optimal response to the information-processing demands of the environment? A methodology called rational analysis is described for deriving predictions about cognitive phenomena using optimization assumptions. The predictions flow from the statistical structure of the environment and not the assumed structure of the mind. Bayesian inference is used, assuming that people start with a weak prior model of the world which they integrate with experience to develop (...) stronger models of specific aspects of the world. Cognitive performance maximizes the difference between the expected gain and cost of mental effort. Memory performance can be predicted on the assumption that retrieval seeks a maximal trade-off between the probability of finding the relevant memories and the effort required to do so; in categorization performance there is a similar trade-off between accuracy in predicting object features and the cost of hypothesis formation; in casual inference the trade-off is between accuracy in predicting future events and the cost of hypothesis formation; and in problem solving it is between the probability of achieving goals and the cost of both external and mental problem-solving search. The implemention of these rational prescriptions in neurally plausible architecture is also discussed. (shrink)

An experiment was performed to investigate the effects of practice and spacing on retention of Japanese–English vocabulary paired associates. The relative benefit of spacing increased with increased practice and with longer retention intervals. Data were fitted with an activation‐based memory model, which proposes that each time an item is practiced it receives an increment of strength but that these increments decay as a power function of time. The rate of decay for each presentation depended on the activation at the time (...) of the presentation. This mechanism limits long‐term benefits from further practice at higher levels of activation and produces the spacing effect and its observed interactions with practice and retention interval. The model was compared with another model of the spacing effect (Raaijmakers, 2003) and was fit to some results from the literature on spacing and memory. (shrink)

Much of cognitive psychology focuses on effects measured in tens of milliseconds while significant educational outcomes take tens of hours to achieve. The task of bridging this gap is analyzed in terms of Newell's (1990) bands of cognition—the Biological, Cognitive, Rational, and Social Bands. The 10 millisecond effects reside in his Biological Band while the significant learning outcomes reside in his Social Band. The paper assesses three theses: The Decomposition Thesis claims that learning occurring at the Social Band can be (...) reduced to learning occurring at lower bands. The Relevance Thesis claims that instructional outcomes at the Social Band can be improved by paying attention to cognition at the lower bands. The Modeling Thesis claims that cognitive modeling provides a basis for bridging between events on the small scale and desired outcomes on the large scale. The unit-task level, at the boundary of the Cognitive and Rational Bands, is useful for assessing these theses. There is good evidence for all three theses in efforts that bridge from the unit-task level to educational applications. While there is evidence for the Decomposition Thesis all the way down to the 10 millisecond level, more work needs to be done to establish the Relevance Thesis and particularly the Modeling Thesis at the lower levels. (shrink)

Memory should make more available things that are more likely to be needed. Across multiple environmental domains, it has been shown that such a system would match qualitatively the memory effects involving repetition, delay, and spacing (Schooler & Anderson, 2017). To obtain data of sufficient size to study how detailed patterns of past appearance predict probability of being needed again, we examined the patterns with which words appear in large two data sets: tweets from popular sources and comments on (...) popular subreddits. The two data sets show remarkably similar statistics, which are also consistent with earlier, smaller studies of environmental statistics. None of a candidate set of mathematical models of memory do well at predicting the observed patterns in these environments. A new model of human memory based on the environmental model proposed by Anderson and Milson (1989) did better at predicting the environmental data and a wide range of behavioral studies that measure memory availability by probability of recall and speed of retrieval. A critical variable in this model was range, the span of time over which an item occurs, which was discovered in mining the environmental data. These results suggest that theories of memory can be guided by mining of the statistical structure of the environment. (PsycInfo Database Record (c) 2023 APA, all rights reserved). (shrink)

LAS is a program that acquires augmented transition network (ATN) grammars. It requires as data sentences of the language and semantic network representatives of their meaning. In acquiring the ATN grammars, it induces the word classes of the language, the rules of formation for sentences, and the rules mapping sentences onto meaning. The induced ATN grammar can be used both for sentence generation and sentence comprehension. Critical to the performance of the program are assumptions that it makes about the relation (...) between sentence structure and surface structure (the graph deformation condition), about when word classes may be formed and when ATN networks may be merged, and about the structure of noun phrases. These assumptions seem to be good heuristics which are largely true for natural languages although they would not be true for many nonnatural languages. Provided these assumptions are satisfied LAS seems capable of learning any context‐free language. (shrink)

Six leading experts speak about the future of cognitive science.

Multi-voxel pattern recognition techniques combined with Hidden Markov models can be used to discover the mental states that people go through in performing a task. The combined method identifies both the mental states and how their durations vary with experimental conditions. We apply this method to a task where participants solve novel mathematical problems. We identify four states in the solution of these problems: Encoding, Planning, Solving, and Respond. The method allows us to interpret what participants are doing on individual (...) problem-solving trials. The duration of the planning state varies on a trial-to-trial basis with novelty of the problem. The duration of solution stage similarly varies with the amount of computation needed to produce a solution once a plan is devised. The response stage similarly varies with the complexity of the answer produced. In addition, we identified a number of effects that ran counter to a prior model of the task. Thus, we were able to decompose the overall problem-solving time into estimates of its components and in way that serves to guide theory. (shrink)

We studied collaborative skill acquisition in a dynamic setting with the game Co-op Space Fortress. While gaining expertise, the majority of subjects became increasingly consistent in the role they adopted without being able to communicate. Moreover, they acted in anticipation of the future task state. We constructed a collaborative skill acquisition model in the cognitive architecture ACT-R that reproduced subject skill acquisition trajectory. It modeled role adoption through reinforcement learning and predictive processes through motion extrapolation and learned relevant control parameters (...) using both a reinforcement learning procedure and a new to ACT-R supervised learning procedure. This is the first integrated cognitive model of collaborative skill acquisition and, as such, gives us valuable insights into the multiple cognitive processes that are involved in learning to collaborate. (shrink)

An analysis of student learning with the LISP tutor indicates that while LISP is complex, learning it is simple. The key to factoring out the complexity of LISP is to monitor the learning of the 500 productions in the LISP tutor which describe the programming skill. The learning of these productions follows the power‐law learning curve typical of skill acquisition. There is transfer from other programming experience to the extent that this programming experience involves the same productions. Subjects appear to (...) differ only on the general dimensions of how well they acquire the productions and how well they retain the productions. Instructional manipulations such as remediation, content of feedback, and timing of feedback are effective to the extent they give students more practice programming, and explain to students why correct solutions work. (shrink)

Open‐ended tasks can be decomposed into the three levels of Newell's Cognitive Band: the Unit‐Task level, the Operation level, and the Deliberate‐Act level. We analyzed the video game Co‐op Space Fortress at these levels, reporting both the match of a cognitive model to subject behavior and the use of electroencephalogram (EEG) to track subject cognition. The Unit Task level in this game involves coordinating with a partner to kill a fortress. At this highest level of the Cognitive Band, there is (...) a good match between subject behavior and the model. The EEG signals were also strong enough to track when Unit Tasks succeeded or failed. The intermediate Operation level in this task involves legs of flight to achieve a kill. The EEG signals associated with these operations are much weaker than the signals associated with the Unit Tasks. Still, it was possible to reconstruct subject play with much better than chance success. There were significant differences in the leg behavior of subjects and models. Model behavior did not provide a good basis for interpreting a subject's behavior at this level. At the lowest Deliberate‐Act level, we observed overlapping key actions, which the model did not display. Such overlapping key actions also frustrated efforts to identify EEG signals of motor actions. We conclude that the Unit‐task level is the appropriate level both for understanding open‐ended tasks and for using EEG to track the performance of open‐ended tasks. (shrink)

The Dictionary of World Philosophy covers the diverse and challenging terminology, concepts, schools and traditions of the vast field of world philosophy. Providing an extremely comprehensive resource and an essential point of reference in a complex and expanding field of study the Dictionary covers all major subfields of the discipline. Key features: * Cross-references are used to highlight interconnections and the cross-cultural diffusion and adaptation of terms which has taken place over time * The user is led from specific terms (...) to master entries which provide valuable historical and cultural context * Each master entry is followed by at least two suggestions for further reading on the subject, creating a substantial bibliography of world philosophy * References extend beyond philosophy to related areas such as cognitive science, computer science, language and physics Subdisciplines covered include: * aesthetics * ethics * sociopolitical philosophy * the philosophy of law * epistemology * logic * the philosophy of science * the philosophy of mind * the philosophy of culture and history * metaphysics * the philosophy of religion Entries are drawn from West Africa, Arabic, Chinese, Indian, Japanese, Jewish, Korean, Latin American, Maori and Native American philosophy including the important and so far largely neglected instance of Pre-Hispanic thought: Nahua philosophy. (shrink)

Previous research on scientific reasoning has shown that it involves a diverse set of skills. Yet, little is known about generality or domain specificity of those skills, an important issue in theories of expertise and in attempts to automate scientific reasoning skills. We present a study designed to test what kinds of skills psychologists actually use in designing and interpreting experiments and contrast expertise within a particular research area with general expertise at designing and interpreting experiments. The results suggest that (...) psychologists use many domain‐general skills in their experimentation and that bright and motivated Carnegie Mellon undergraduates are missing many of these skills. We believe that these results have important implications for psychological and artificial intelligence models of expertise, as well as educational implications in the domain of science instruction. (shrink)

This article describes the path‐mapping theory of how humans integrate analogical mapping and general problem solving. The theory posits that humans represent analogs with declarative roles, map analogs by lower‐level retrieval of analogous role paths, and coordinate mappings with higher‐level organizational knowledge. Implemented in the ACT‐R cognitive architecture, the path‐mapping theory enables models of analogical mapping behavior to incorporate and interface with other problem‐solving knowledge. Path‐mapping models thus can include task‐specific skills such as encoding analogs or generating responses, and can (...) make behavioral predictions at the level of real‐world metrics such as latency or correctness. We show that the path‐mapping theory can successfully account for the major phenomena addressed by previous theories of analogy. We also describe a path‐mapping model that can account for subjects' incremental eye‐movement and typing behavior in a story‐mapping task. We discuss extensions and implications of this work to other areas of analogy and problem‐solving research. (shrink)