We investigate the use of external visual representations in probability problem solving. Twenty-... more We investigate the use of external visual representations in probability problem solving. Twenty-six students enrolled in an introductory statistics course for social sciences graduate students (post-baccalaureate) solved eight probability problems in a structured interview format. Results show that students spontaneously use self- generated external visual representations while solving probability problems. The types of visual representations used include: reorganization of the given information, pictures, novel schematic representations, trees, outcome listings, contingency tables, and Venn diagrams. The frequency of use of each of these different external visual representations depended on the type of probability problem being solved. We interpret these findings as showing that problem solvers attempt to select representations appropriate to the problem structure, and that the appropriateness of the representation is determined by the problem’s underlying schema. First published ...
Most neural network (NN) models of human category learning use a gradient-based learning method, ... more Most neural network (NN) models of human category learning use a gradient-based learning method, which assumes that locally-optimal changes are made to model parameters on each learning trial. This method tends to under predict variability in individual-level cognitive processes. In addition many recent models of human category learning have been criticized for not being able to replicate rapid changes in categorization accuracy and attention processes observed in empirical studies. In this paper we introduce stochastic learning algorithms for NN models of human category learning and show that use of the algorithms can result in (a) rapid changes in accuracy and attention allocation, and (b) different learning trajectories and more realistic variability at the individual-level.
This study investigated the use of schema-specific diagrams in probability problem solving. Gradu... more This study investigated the use of schema-specific diagrams in probability problem solving. Graduate students enrolled in an introductory probability and statistics course solved four probability problems, with and without instructor-provided diagram hints. Participants’ solutions were examined and coded for correctness, use of provided diagrams, and use of student-generated external visual representations. Results show that provided diagram hints helped low-ability students on all but the most difficult problem, while high-ability students were aided by diagrams on the most difficult problem. Implications for the use of diagrams in the development of problem solving proficiency are discussed.
Proceedings of the Twenty-Fourth Annual Conference of the Cognitive Science Society, Apr 24, 2019
Gluck & Myers, 1993) to see how they account for selective attention in category learning. Such c... more Gluck & Myers, 1993) to see how they account for selective attention in category learning. Such comparisons may usefully augment comparisons of the models' classification accuracy.
Keeping track of things as they move in space and time is a task common to scientists, marketers,... more Keeping track of things as they move in space and time is a task common to scientists, marketers, spies, coaches, and more. Visualizations of complex information aid drawing inferences and conclusions but there are many ways to represent data. Here we show that the kinds of inferences people draw depend on the kind of visualization, boxes in tables or lines in graphs. Lines link and boxes contain; they both direct attention and create meaning.
A number of neural network models of categorization have been proposed. The models differ notably... more A number of neural network models of categorization have been proposed. The models differ notably in the types of internal representation used (e.g. exemplars vs. prototypes; hyperplane vs. hypersphere activation regions). However, many of these NN models of categorization (e.g., ALCOVE) use some form of gradient method for learning. These methods have been successful in reproducing group learning curves, but tend to underpredict variability in individual-level data, for both accuracy and attention allocation measures (Matsuka, 2002). Here, we show that use of a different learning algorithm with a given model can result in different learning trajectories and more realistic variability in individual learning curves, especially for attention allocation. Our proposed algorithm is a form of constrained simulated annealing (Ingber, 1989). Initial parameter sets (dimensional attention weights and network connection weights) are randomly selected. At the beginning of each training epoch, a hypothetical "move" in the parameter space is computed by adjusting each parameter by an independently sampled term. These adjustment terms are drawn from a prespecified distribution (e.g., a Cauchy distribution). The move (i.e., the set of new parameter values) are accepted or rejected, based on the computed relative fit of the new values. Specifically, if the new parameter values result in better fit, they are accepted. If they result in worse fit, they are accepted with some probability P. The adjustment in parameters is very rapid initially, and it gradually decreases over learning blocks.
thought has roots in the spatial world. Abstractions are expressed in the ways things are arrange... more thought has roots in the spatial world. Abstractions are expressed in the ways things are arranged in the world as well as the ways people talk and gesture. Mappings to the page should be better when they are congruent, that is, when the abstract concept matches the spatial one. Congruent mappings can be revealed in people's performance and preferences. Congruence is supported here for visual representations of continuum and category. Congruently mapping a continuous concept, frequency, to a continuous visual variable and mapping a categorical concept, class inclusion, to a categorical visual variable were preferred and lead to better performance than the reverse mappings.
Probability matching in sequential prediction tasks is argued to occur because participants impli... more Probability matching in sequential prediction tasks is argued to occur because participants implicitly adopt the unrealistic goal of perfect prediction of sequences. Biases in the understanding of randomness then lead them to generate mixed rather than pure sequences of predictions in attempting to achieve this goal. In Study 1, N = 350 participants predicted 100 trials of a binary-outcome event. Two factors were manipulated: probability bias (the outcomes were equiprobable or distributed with a 75 %-25 % bias), and goal type-namely, whether single-trial predictions or the perfect prediction of four-trial sequences was emphasized and rewarded. As we hypothesized, predicting sequences led to more probability-matching behavior than did predicting single trials, for both the bias and no-bias conditions. In Study 1B, we added a control condition to distinguish the effects of the grouped presentation of trials from the effects of sequence-level perfect-prediction rewards. The results sup...
Quarterly Journal of Experimental Psychology, 2008
In two empirical studies of attention allocation during category learning, we investigate the ide... more In two empirical studies of attention allocation during category learning, we investigate the idea that category learners learn to allocate attention optimally across stimulus dimensions. We argue that “optimal” patterns of attention allocation are model or process specific, that human learners do not always optimize attention, and that one reason they fail to do so is that under certain conditions the cost of information retrieval or use may affect the attentional strategy adopted by learners. We empirically investigate these issues using a computer interface incorporating an “information-board” display that collects detailed information on participants’ patterns of attention allocation and information search during learning trials. Experiment 1 investigated the effects on attention allocation of distributing perfectly diagnostic features across stimulus dimensions versus within one dimension. The overall pattern of viewing times supported the optimal attention allocation hypothesi...
Proximity data can be represented by an extended tree, which generalizes traditional trees by inc... more Proximity data can be represented by an extended tree, which generalizes traditional trees by including marked segments that correspond to overlapping dusters. An extended tree is a graphical representation of the distinctive features model. A computer program (EXTREE) that constructs extended trees is described and applied to several sets of conceptual and perceptual proximity data.
The category utility hypothesis holds that categories are useful because they can be used to pred... more The category utility hypothesis holds that categories are useful because they can be used to predict the features of instances and that the categories that tend to survive and become preferred in a culture (basic-level categories) are those that best improve the category users' ability to perform this function. Starting from this hypothesis, a quantitative measure of the utility of a category is derived. Application to the special case of substitutive attributes is described. The measure is used successfully to predict the basic level in applications to data from hierarchies of natural categories and from hierarchies of artificial categories used in category-learning experiments. The relationship of the measure to previously proposed indicators of the basic level is discussed, as is its relation to certain concepts from information theory. Categorization is one of the most basic cognitive functions. Why is the ability to categorize events or objects important to an organism? An obvious answer to this question is that categories are important because they often have functional significance for the organism. Another familiar answer is that grouping objects into categories allows for efficient storage of information about these groups of objects. One purpose of this article is to explore connections between these two answers regarding the utility of categories. The idea that categories serve certain functions for the organism raises the possibility that some categories fulfill these functions better than others. The clearest evidence that certain natural categories are "better" than others stems from the work on "basic-level" categories (Mervis & Rosch, 1981; Rosch, Mervis, Gray, Johnson, & Boyes-Braem, 1976). A basic-level category is one that is preferred by people over its superordinate and subordinate categories. For example, when shown a picture of a particular object, most people will identify it as a chair rather than as furniture or a kitchen chair. From this and other evidence, chair is considered to be a basic-level category for most people. A variety of empirical phenomena demonstrates the superiority of basic-level categories (Mervis & Rosch, 1981). As suggested above, when people are shown an object, they tend to name it at the basic level (Rosch et al, 1976). In recognition tasks, people recognize basic-level objects faster than either subordinates or superordinates (Jolicoeur, Gluck, & Kosslyn, 1984; Rosch et al., 1976). Basic-level names generally have arisen earlier in the development of languages (Berlin, Breedlove, & Raven, 1973), and basic categories are used earlier in the naming and other behavior of young children (Anglin, 1977; Brown, Many people have provided us with suggestions, criticisms, and comments on this work over the last 6 years. However, we must especially thank Pat Langley and Doug Fisher for their early and continuing encouragement. Doug Fisher's own research has contributed to our understanding of many of the issues discussed here. We also thank three anonymous reviewers for their insightful and detailed feedback.
For patients with borderline personality disorder, separations from significant figures in their ... more For patients with borderline personality disorder, separations from significant figures in their lives, including therapists, are thought to be particularly painful. According to clinical wisdom, these patients manifest aggressive and self-destructive behavior around the time of separation. However, virtually no empirical studies have been conducted to test these beliefs. In this study, the behaviors of a sample of 41 inpatients with borderline personality disorder were recorded and analyzed to determine what, if any, effect their therapists' vacations had on target behaviors, including acting up, self-destructive behaviors, and somatic complaints. Results indicated significant variations in the rates of acting up and somatic complaints before, during, and after therapist vacations. No significant variations were observed in the rate of self-destructive behaviors, failing to support the commonly held belief that self-destructive acts in borderline patients may be especially prevalent around therapist vacations. Possible reasons for the pattern of findings are discussed, as are the implications for clinical practice. Patients with borderline personality disorder are believed to react strongly to separations from significant figures in their lives, including therapists. According Requests for reprints should be sent to
We investigate the role of external inscriptions, particularly those of a spatial or visual natur... more We investigate the role of external inscriptions, particularly those of a spatial or visual nature, in the solution of probability word problems. We define a taxonomy of external visual representations used in probability problem solving that includes pictures, spatial reorganization of the given information, outcome listings, contingency tables, Venn diagrams, trees, and novel graphical representations. We also propose a process model for probability problem solving (PPS) and use it as a framework to better understand how and why external visual representations are used. In a study of 34 novice probability problem solvers, participants worked to solve six probability word problems covering six probability subtopics. Both written and verbal structured interview protocols were analyzed to investigate when and how external visual representations are spontaneously used by problem solvers. Analyses of the coded transcripts showed that participants' probability problem-solving efforts move through the stages of PPS in a sequential but not always linear manner, sometimes exhibiting iterated attempts to represent the problem mathematically and to find a solution strategy. Results showed that use of specific external visual representations was associated with specific probability topics, and that certain choices of representation are associated with higher rates of solution success. These findings suggest that an external visual representation can facilitate probability problem solving, but only when an appropriate representation is chosen. Finally, we present evidence to show that external visual representations are usually created and first used during the stages of representing the problem mathematically and finding a solution strategy. However, pictures are often created during the initial stage of problem text understanding, and tables are sometimes created during computation of the solution. Visualization has long been thought to play an important role in mathematics problem solving (e.g., Hadamard, 1945). When mathematical problems are especially difficult, or when solutions must be shared with others, problem solvers may externalize these visualizations by making inscriptions on paper or other media (e.g.
Proceedings of the Workshop on Probability …, 1985
In designing an intelligent system that must be able to explain its reasoning to a human user, or... more In designing an intelligent system that must be able to explain its reasoning to a human user, or to provide generalizations that the human user finds reasonable, it may be useful to take into consideration psychological data on what types of concepts and categories people ...
A large-scale, multi-year, randomized study compared learning activities and outcomes for hands-o... more A large-scale, multi-year, randomized study compared learning activities and outcomes for hands-on, remotely-operated, and simulation-based educational laboratories in an undergraduate engineering course. Students (N ¼ 458) worked in small-group lab teams to perform two experiments involving stress on a cantilever beam. Each team conducted the experiments in one of three lab formats (hands-on, remotely-operated, or simulation-based), collecting data either individually or as a team. Lab format and data-collection mode showed an interaction, such that for the hands-on lab format learning outcomes were higher when the lab team collected data sets working as a group rather than individually collecting data sets to be combined later, while for remotely-operated labs individual data collection was best. The pattern of time spent on various lab-related activities suggests that working with real instead of simulated data may induce higher levels of motivation. The results also suggest that learning with computermediated technologies can be improved by careful design and coordination of group and individual activities.
Collaborators generally coordinate their activities through communication, during which they read... more Collaborators generally coordinate their activities through communication, during which they readily negotiate a shared lexicon for activity-related objects. This social-pragmatic activity both recruits and affects cognitive and social-cognitive processes ranging from selective attention to perspective taking. We ask whether negotiating reference also facilitates category learning or might private verbalization yield comparable facilitation? Participants in three referential conditions learned to classify imaginary creatures according to combinations of functional features-nutritive and destructive-that implicitly defined four categories. Remote partners communicated in the Dialogue condition. In the Monologue condition, participants recorded audio descriptions for their own later use. Controls worked silently. Dialogue yielded better category learning, with wider distribution of attention. Monologue offered no benefits over working silently. We conclude that negotiating reference compels collaborators to find communicable structure in their shared activity; this social-pragmatic constraint accelerates category learning and likely provides much of the benefit recently ascribed to learning labeled categories.
Artificial Intelligence for Engineering Design, Analysis and Manufacturing, 2010
Fixation prevents the associations that are bridges to new designs. The inability to see alternat... more Fixation prevents the associations that are bridges to new designs. The inability to see alternative solutions, or even to see how to map known solutions onto current problems, is a particularly acute problem in the design of software-intensive systems. Here, we explored two related ways of liberating fixated thinking: abstracting and rerepresenting. Although both techniques helped designers generate original ideas, not all the added ideas fit the problem constraints. We discuss ways the results might be used to generate reflective design aids that help designers to first generate original ideas and later prune them.
In two simulation studies, we compare the attention learning predictions of three well-known adap... more In two simulation studies, we compare the attention learning predictions of three well-known adaptive network models of category learning: ALCOVE, RASHNL, and SUSTAIN. The simulation studies use novel stimulus structures designed to explore the effects of predictor diagnosticity and independence, and differentiate the models regarding their tendencies to learn simple rules versus exemplar-based representations for categories. An interesting phenomenon is described in which the models (especially SUSTAIN and RASHNL) learn to attend to a completely nondiagnostic constant dimension.
We investigate the use of external visual representations in probability problem solving. Twenty-... more We investigate the use of external visual representations in probability problem solving. Twenty-six students enrolled in an introductory statistics course for social sciences graduate students (post-baccalaureate) solved eight probability problems in a structured interview format. Results show that students spontaneously use self- generated external visual representations while solving probability problems. The types of visual representations used include: reorganization of the given information, pictures, novel schematic representations, trees, outcome listings, contingency tables, and Venn diagrams. The frequency of use of each of these different external visual representations depended on the type of probability problem being solved. We interpret these findings as showing that problem solvers attempt to select representations appropriate to the problem structure, and that the appropriateness of the representation is determined by the problem’s underlying schema. First published ...
Most neural network (NN) models of human category learning use a gradient-based learning method, ... more Most neural network (NN) models of human category learning use a gradient-based learning method, which assumes that locally-optimal changes are made to model parameters on each learning trial. This method tends to under predict variability in individual-level cognitive processes. In addition many recent models of human category learning have been criticized for not being able to replicate rapid changes in categorization accuracy and attention processes observed in empirical studies. In this paper we introduce stochastic learning algorithms for NN models of human category learning and show that use of the algorithms can result in (a) rapid changes in accuracy and attention allocation, and (b) different learning trajectories and more realistic variability at the individual-level.
This study investigated the use of schema-specific diagrams in probability problem solving. Gradu... more This study investigated the use of schema-specific diagrams in probability problem solving. Graduate students enrolled in an introductory probability and statistics course solved four probability problems, with and without instructor-provided diagram hints. Participants’ solutions were examined and coded for correctness, use of provided diagrams, and use of student-generated external visual representations. Results show that provided diagram hints helped low-ability students on all but the most difficult problem, while high-ability students were aided by diagrams on the most difficult problem. Implications for the use of diagrams in the development of problem solving proficiency are discussed.
Proceedings of the Twenty-Fourth Annual Conference of the Cognitive Science Society, Apr 24, 2019
Gluck & Myers, 1993) to see how they account for selective attention in category learning. Such c... more Gluck & Myers, 1993) to see how they account for selective attention in category learning. Such comparisons may usefully augment comparisons of the models' classification accuracy.
Keeping track of things as they move in space and time is a task common to scientists, marketers,... more Keeping track of things as they move in space and time is a task common to scientists, marketers, spies, coaches, and more. Visualizations of complex information aid drawing inferences and conclusions but there are many ways to represent data. Here we show that the kinds of inferences people draw depend on the kind of visualization, boxes in tables or lines in graphs. Lines link and boxes contain; they both direct attention and create meaning.
A number of neural network models of categorization have been proposed. The models differ notably... more A number of neural network models of categorization have been proposed. The models differ notably in the types of internal representation used (e.g. exemplars vs. prototypes; hyperplane vs. hypersphere activation regions). However, many of these NN models of categorization (e.g., ALCOVE) use some form of gradient method for learning. These methods have been successful in reproducing group learning curves, but tend to underpredict variability in individual-level data, for both accuracy and attention allocation measures (Matsuka, 2002). Here, we show that use of a different learning algorithm with a given model can result in different learning trajectories and more realistic variability in individual learning curves, especially for attention allocation. Our proposed algorithm is a form of constrained simulated annealing (Ingber, 1989). Initial parameter sets (dimensional attention weights and network connection weights) are randomly selected. At the beginning of each training epoch, a hypothetical "move" in the parameter space is computed by adjusting each parameter by an independently sampled term. These adjustment terms are drawn from a prespecified distribution (e.g., a Cauchy distribution). The move (i.e., the set of new parameter values) are accepted or rejected, based on the computed relative fit of the new values. Specifically, if the new parameter values result in better fit, they are accepted. If they result in worse fit, they are accepted with some probability P. The adjustment in parameters is very rapid initially, and it gradually decreases over learning blocks.
thought has roots in the spatial world. Abstractions are expressed in the ways things are arrange... more thought has roots in the spatial world. Abstractions are expressed in the ways things are arranged in the world as well as the ways people talk and gesture. Mappings to the page should be better when they are congruent, that is, when the abstract concept matches the spatial one. Congruent mappings can be revealed in people's performance and preferences. Congruence is supported here for visual representations of continuum and category. Congruently mapping a continuous concept, frequency, to a continuous visual variable and mapping a categorical concept, class inclusion, to a categorical visual variable were preferred and lead to better performance than the reverse mappings.
Probability matching in sequential prediction tasks is argued to occur because participants impli... more Probability matching in sequential prediction tasks is argued to occur because participants implicitly adopt the unrealistic goal of perfect prediction of sequences. Biases in the understanding of randomness then lead them to generate mixed rather than pure sequences of predictions in attempting to achieve this goal. In Study 1, N = 350 participants predicted 100 trials of a binary-outcome event. Two factors were manipulated: probability bias (the outcomes were equiprobable or distributed with a 75 %-25 % bias), and goal type-namely, whether single-trial predictions or the perfect prediction of four-trial sequences was emphasized and rewarded. As we hypothesized, predicting sequences led to more probability-matching behavior than did predicting single trials, for both the bias and no-bias conditions. In Study 1B, we added a control condition to distinguish the effects of the grouped presentation of trials from the effects of sequence-level perfect-prediction rewards. The results sup...
Quarterly Journal of Experimental Psychology, 2008
In two empirical studies of attention allocation during category learning, we investigate the ide... more In two empirical studies of attention allocation during category learning, we investigate the idea that category learners learn to allocate attention optimally across stimulus dimensions. We argue that “optimal” patterns of attention allocation are model or process specific, that human learners do not always optimize attention, and that one reason they fail to do so is that under certain conditions the cost of information retrieval or use may affect the attentional strategy adopted by learners. We empirically investigate these issues using a computer interface incorporating an “information-board” display that collects detailed information on participants’ patterns of attention allocation and information search during learning trials. Experiment 1 investigated the effects on attention allocation of distributing perfectly diagnostic features across stimulus dimensions versus within one dimension. The overall pattern of viewing times supported the optimal attention allocation hypothesi...
Proximity data can be represented by an extended tree, which generalizes traditional trees by inc... more Proximity data can be represented by an extended tree, which generalizes traditional trees by including marked segments that correspond to overlapping dusters. An extended tree is a graphical representation of the distinctive features model. A computer program (EXTREE) that constructs extended trees is described and applied to several sets of conceptual and perceptual proximity data.
The category utility hypothesis holds that categories are useful because they can be used to pred... more The category utility hypothesis holds that categories are useful because they can be used to predict the features of instances and that the categories that tend to survive and become preferred in a culture (basic-level categories) are those that best improve the category users' ability to perform this function. Starting from this hypothesis, a quantitative measure of the utility of a category is derived. Application to the special case of substitutive attributes is described. The measure is used successfully to predict the basic level in applications to data from hierarchies of natural categories and from hierarchies of artificial categories used in category-learning experiments. The relationship of the measure to previously proposed indicators of the basic level is discussed, as is its relation to certain concepts from information theory. Categorization is one of the most basic cognitive functions. Why is the ability to categorize events or objects important to an organism? An obvious answer to this question is that categories are important because they often have functional significance for the organism. Another familiar answer is that grouping objects into categories allows for efficient storage of information about these groups of objects. One purpose of this article is to explore connections between these two answers regarding the utility of categories. The idea that categories serve certain functions for the organism raises the possibility that some categories fulfill these functions better than others. The clearest evidence that certain natural categories are "better" than others stems from the work on "basic-level" categories (Mervis & Rosch, 1981; Rosch, Mervis, Gray, Johnson, & Boyes-Braem, 1976). A basic-level category is one that is preferred by people over its superordinate and subordinate categories. For example, when shown a picture of a particular object, most people will identify it as a chair rather than as furniture or a kitchen chair. From this and other evidence, chair is considered to be a basic-level category for most people. A variety of empirical phenomena demonstrates the superiority of basic-level categories (Mervis & Rosch, 1981). As suggested above, when people are shown an object, they tend to name it at the basic level (Rosch et al, 1976). In recognition tasks, people recognize basic-level objects faster than either subordinates or superordinates (Jolicoeur, Gluck, & Kosslyn, 1984; Rosch et al., 1976). Basic-level names generally have arisen earlier in the development of languages (Berlin, Breedlove, & Raven, 1973), and basic categories are used earlier in the naming and other behavior of young children (Anglin, 1977; Brown, Many people have provided us with suggestions, criticisms, and comments on this work over the last 6 years. However, we must especially thank Pat Langley and Doug Fisher for their early and continuing encouragement. Doug Fisher's own research has contributed to our understanding of many of the issues discussed here. We also thank three anonymous reviewers for their insightful and detailed feedback.
For patients with borderline personality disorder, separations from significant figures in their ... more For patients with borderline personality disorder, separations from significant figures in their lives, including therapists, are thought to be particularly painful. According to clinical wisdom, these patients manifest aggressive and self-destructive behavior around the time of separation. However, virtually no empirical studies have been conducted to test these beliefs. In this study, the behaviors of a sample of 41 inpatients with borderline personality disorder were recorded and analyzed to determine what, if any, effect their therapists' vacations had on target behaviors, including acting up, self-destructive behaviors, and somatic complaints. Results indicated significant variations in the rates of acting up and somatic complaints before, during, and after therapist vacations. No significant variations were observed in the rate of self-destructive behaviors, failing to support the commonly held belief that self-destructive acts in borderline patients may be especially prevalent around therapist vacations. Possible reasons for the pattern of findings are discussed, as are the implications for clinical practice. Patients with borderline personality disorder are believed to react strongly to separations from significant figures in their lives, including therapists. According Requests for reprints should be sent to
We investigate the role of external inscriptions, particularly those of a spatial or visual natur... more We investigate the role of external inscriptions, particularly those of a spatial or visual nature, in the solution of probability word problems. We define a taxonomy of external visual representations used in probability problem solving that includes pictures, spatial reorganization of the given information, outcome listings, contingency tables, Venn diagrams, trees, and novel graphical representations. We also propose a process model for probability problem solving (PPS) and use it as a framework to better understand how and why external visual representations are used. In a study of 34 novice probability problem solvers, participants worked to solve six probability word problems covering six probability subtopics. Both written and verbal structured interview protocols were analyzed to investigate when and how external visual representations are spontaneously used by problem solvers. Analyses of the coded transcripts showed that participants' probability problem-solving efforts move through the stages of PPS in a sequential but not always linear manner, sometimes exhibiting iterated attempts to represent the problem mathematically and to find a solution strategy. Results showed that use of specific external visual representations was associated with specific probability topics, and that certain choices of representation are associated with higher rates of solution success. These findings suggest that an external visual representation can facilitate probability problem solving, but only when an appropriate representation is chosen. Finally, we present evidence to show that external visual representations are usually created and first used during the stages of representing the problem mathematically and finding a solution strategy. However, pictures are often created during the initial stage of problem text understanding, and tables are sometimes created during computation of the solution. Visualization has long been thought to play an important role in mathematics problem solving (e.g., Hadamard, 1945). When mathematical problems are especially difficult, or when solutions must be shared with others, problem solvers may externalize these visualizations by making inscriptions on paper or other media (e.g.
Proceedings of the Workshop on Probability …, 1985
In designing an intelligent system that must be able to explain its reasoning to a human user, or... more In designing an intelligent system that must be able to explain its reasoning to a human user, or to provide generalizations that the human user finds reasonable, it may be useful to take into consideration psychological data on what types of concepts and categories people ...
A large-scale, multi-year, randomized study compared learning activities and outcomes for hands-o... more A large-scale, multi-year, randomized study compared learning activities and outcomes for hands-on, remotely-operated, and simulation-based educational laboratories in an undergraduate engineering course. Students (N ¼ 458) worked in small-group lab teams to perform two experiments involving stress on a cantilever beam. Each team conducted the experiments in one of three lab formats (hands-on, remotely-operated, or simulation-based), collecting data either individually or as a team. Lab format and data-collection mode showed an interaction, such that for the hands-on lab format learning outcomes were higher when the lab team collected data sets working as a group rather than individually collecting data sets to be combined later, while for remotely-operated labs individual data collection was best. The pattern of time spent on various lab-related activities suggests that working with real instead of simulated data may induce higher levels of motivation. The results also suggest that learning with computermediated technologies can be improved by careful design and coordination of group and individual activities.
Collaborators generally coordinate their activities through communication, during which they read... more Collaborators generally coordinate their activities through communication, during which they readily negotiate a shared lexicon for activity-related objects. This social-pragmatic activity both recruits and affects cognitive and social-cognitive processes ranging from selective attention to perspective taking. We ask whether negotiating reference also facilitates category learning or might private verbalization yield comparable facilitation? Participants in three referential conditions learned to classify imaginary creatures according to combinations of functional features-nutritive and destructive-that implicitly defined four categories. Remote partners communicated in the Dialogue condition. In the Monologue condition, participants recorded audio descriptions for their own later use. Controls worked silently. Dialogue yielded better category learning, with wider distribution of attention. Monologue offered no benefits over working silently. We conclude that negotiating reference compels collaborators to find communicable structure in their shared activity; this social-pragmatic constraint accelerates category learning and likely provides much of the benefit recently ascribed to learning labeled categories.
Artificial Intelligence for Engineering Design, Analysis and Manufacturing, 2010
Fixation prevents the associations that are bridges to new designs. The inability to see alternat... more Fixation prevents the associations that are bridges to new designs. The inability to see alternative solutions, or even to see how to map known solutions onto current problems, is a particularly acute problem in the design of software-intensive systems. Here, we explored two related ways of liberating fixated thinking: abstracting and rerepresenting. Although both techniques helped designers generate original ideas, not all the added ideas fit the problem constraints. We discuss ways the results might be used to generate reflective design aids that help designers to first generate original ideas and later prune them.
In two simulation studies, we compare the attention learning predictions of three well-known adap... more In two simulation studies, we compare the attention learning predictions of three well-known adaptive network models of category learning: ALCOVE, RASHNL, and SUSTAIN. The simulation studies use novel stimulus structures designed to explore the effects of predictor diagnosticity and independence, and differentiate the models regarding their tendencies to learn simple rules versus exemplar-based representations for categories. An interesting phenomenon is described in which the models (especially SUSTAIN and RASHNL) learn to attend to a completely nondiagnostic constant dimension.
Uploads
Papers by James Corter