Considerable evidence indicates that domain specific knowledge in the form of schemas is the primary factor distinguishing experts from novices in problem‐solving skill. Evidence that conventional problem‐solving activity is not effective in schema acquisition is also accumulating. It is suggested that a major reason for the ineffectiveness of problem solving as a learning device, is that the cognitive processes required by the two activities overlap insufficiently, and that conventional problem solving in the form of means‐ends analysis requires a relatively large (...) amount of cognitive processing capacity which is consequently unavailable for schema acquisition. A computational model and experimental evidence provide support for this contention. Theoretical and practical implications are discussed. (shrink)

A set of hypotheses is formulated for a connectionist approach to cognitive modeling. These hypotheses are shown to be incompatible with the hypotheses underlying traditional cognitive models. The connectionist models considered are massively parallel numerical computational systems that are a kind of continuous dynamical system. The numerical variables in the system correspond semantically to fine-grained features below the level of the concepts consciously used to describe the task domain. The level of analysis is intermediate between those of symbolic cognitive models (...) and neural models. The explanations of behavior provided are like those traditional in the physical sciences, unlike the explanations provided by symbolic models. Higher-level analyses of these connectionist models reveal subtle relations to symbolic models. Parallel connectionist memory and linguistic processes are hypothesized to give rise to processes that are describable at a higher level as sequential rule application. At the lower level, computation has the character of massively parallel satisfaction of soft numerical constraints; at the higher level, this can lead to competence characterizable by hard rules. Performance will typically deviate from this competence since behavior is achieved not by interpreting hard rules but by satisfying soft constraints. The result is a picture in which traditional and connectionist theoretical constructs collaborate intimately to provide an understanding of cognition. (shrink)

We show how an epistemology informed by cognitive science promises to shed light on an ancient problem in the philosophy of mathematics: the problem of exactness. The problem of exactness arises because geometrical knowledge is thought to concern perfect geometrical forms, whereas the embodiment of such forms in the natural world may be imperfect. There thus arises an apparent mismatch between mathematical concepts and physical reality. We propose that the problem can be solved by emphasizing the ways in which the (...) brain can transform and organize its perceptual intake. It is not necessary for a geometrical form to be perfectly instantiated in order for perception of such a form to be the basis of a geometrical concept. (shrink)

: This paper discusses how Herbert Simon's initial interest in decision making became transformed into a focus on understanding human problem solving in response to the concrete conditions of the Cold War and the practical goals of the military. In particular, it suggests a connection between the seachange in Simon's interest and his shift in patronage. As a result, Simon is portrayed as a component of the scientific-military World War II cyborg that further evolved during the Cold War. Moving from (...) decision making to problem solving, Simon's cyborg science not only required large sums of money, but also managed to acquire these. (shrink)

A set of hypotheses is formulated for a connectionist approach to cognitive modeling. These hypotheses are shown to be incompatible with the hypotheses underlying traditional cognitive models. The connectionist models considered are massively parallel numerical computational systems that are a kind of continuous dynamical system. The numerical variables in the system correspond semantically to fine-grained features below the level of the concepts consciously used to describe the task domain. The level of analysis is intermediate between those of symbolic cognitive models (...) and neural models. The explanations of behavior provided are like those traditional in the physical sciences, unlike the explanations provided by symbolic models. (shrink)

A set of hypotheses is formulated for a connectionist approach to cognitive modeling. These hypotheses are shown to be incompatible with the hypotheses underlying traditional cognitive models. The connectionist models considered are massively parallel numerical computational systems that are a kind of continuous dynamical system. The numerical variables in the system correspond semantically to fine-grained features below the level of the concepts consciously used to describe the task domain. The level of analysis is intermediate between those of symbolic cognitive models (...) and neural models. The explanations of behavior provided are like those traditional in the physical sciences, unlike the explanations provided by symbolic models.Higher-level analyses of these connectionist models reveal subtle relations to symbolic models. Parallel connectionist memory and linguistic processes are hypothesized to give rise to processes that are describable at a higher level as sequential rule application. At the lower level, computation has the character of massively parallel satisfaction of soft numerical constraints; at the higher level, this can lead to competence characterizable by hard rules. Performance will typically deviate from this competence since behavior is achieved not by interpreting hard rules but by satisfying soft constraints. The result is a picture in which traditional and connectionist theoretical constructs collaborate intimately to provide an understanding of cognition. (shrink)

This research presents a computer model called EUREKA that begins with novice‐like strategies and knowledge organizations for solving physics word problems and acquires features of knowledge organizations and basic approaches that characterize experts in this domain. EUREKA learns a highly interrelated network of problem‐type schemas with associated solution methodologies. Initially, superficial features of the problem statement form the basis for both the problem‐type schemas and the discriminating features that organize them in the P‐MOP (Problem Memory Organization Packet) network. As EUREKA (...) solves more problems, the content of the schemas and the discriminating features change to reflect more fundamental physics principles. This changing network allows EUREKA to shift from a novicelike means‐ends strategy to a more expertlike “knowledge development” strategy in which the presence of abstract concepts are triggered by problem features. In this model, the strategy shift emerges as a natural consequence of the evolving expertlike organization of problem‐type schemos. EUREKA captures many of the descriptive models of novice expert differences, and also suggests a number of empirically testable assumptions regarding problem‐solving strategies and the representation of problem‐solving knowledge. (shrink)

Mathematical explanations are poorly understood. Although mathematicians seem to regularly suggest that some proofs are explanatory whereas others are not, none of the philosophical accounts of what such claims mean has become widely accepted. In this paper we explore Wilkenfeld’s suggestion that explanations are those sorts of things that generate understanding. By considering a basic model of human cognitive architecture, we suggest that existing accounts of mathematical explanation are all derivable consequences of Wilkenfeld’s ‘functional explanation’ proposal. We therefore argue that (...) the explanatory criteria offered by earlier accounts can all be thought of as features that make it more likely that a mathematical proof will generate understanding. On the functional account, features such as characterising properties, unification, and salience correlate with explanatoriness, but they do not define explanatoriness. (shrink)

This paper describes Peirce's systems of logic diagrams, focusing on the so-called ''existential'' graphs, which are equivalent to the first-order predicate calculus. It analyses their implications for the nature of mental representations, particularly mental models with which they have many characteristics in common. The graphs are intended to be iconic, i.e., to have a structure analogous to the structure of what they represent. They have emergent logical consequences and a single graph can capture all the different ways in which a (...) possibility can occur. Mental models share these properties. But, as the graphs show, certain aspects of propositions cannot be represented in an iconic or visualisable way. They include negation, and the representation of possibilities qua possibilities, which both require representations that do not depend on a perceptual modality. Peirce took his graphs to reveal the fundamental operations of reasoning, and the paper concludes with an analysis of different hypotheses about these operations. (shrink)

The acquisition of expertise in formal problem solving has been assumed to involve either a shift from backwards to forwards inference, or a shift from unguided to guided forwards inference. In a longitudinal study, the acquisition of formal problem-solving expertise was investigated. Participants were tested as novices before undertaking controlled practice in the problem domain which involved transformation rule problems , and were finally tested as experts. The direction of inference in problem solutions was found to be inadequate to describe (...) the strategic differences between novices and experts. Therefore, a new solution coding system was applied, based on atomic components of problem solution. Analysis of novice and expert solutions revealed no systematic strategy in the novice stage solutions were confused and contained unproductive steps and backtracking. Several strategies were found in the expert solutions, but they did not agree with previously reported results. It was therefore proposed that the acquisition of expertise does not involve a change from one specific solution strategy to another, but rather the development of an efficient strategy, which can differ between participants. (shrink)

Young single women's and men's cognitive scripts for the event “a first date” were examined to determine their content and to test for hypothesized differences in behavioral expectations. Participants were asked to list 20 expected actions involved in a first date for a woman and for a man. High agreement among participants was found for the content and sequence of actions that hypothetically would occur on a first date. The respondents listed a total of 19 different actions for women, and (...) 27 for men. The scripts for women and men differed significantly. The scripts for women emphasized the private sphere ; the scripts for men focused on control of the public domain. Gender roles were more prevalent in experienced daters' scripts. The results indicate that young adults' interpersonal scripts for dating maintain the traditional gender-power ratio. (shrink)

In spite of the wide variety of approaches to ethics training it is still debatable which approach has the highest potential to enhance professionals’ integrity. The current effort assesses a novel curriculum that focuses on metacognitive reasoning strategies researchers use when making sense of day-to-day professional practices that have ethical implications. The evaluated trainings effectiveness was assessed by examining five key sensemaking processes, such as framing, emotion regulation, forecasting, self-reflection, and information integration that experts and novices apply in ethical decision-making. (...) Mental models of trained and untrained graduate students, as well as faculty, working in the field of physical sciences were compared using a think-aloud protocol 6 months following the ethics training. Evaluation and comparison of the mental models of participants provided further validation evidence for sensemaking training. Specifically, it was found that trained students applied metacognitive reasoning strategies learned during training in their ethical decision-making that resulted in complex mental models focused on the objective assessment of the situation. Mental models of faculty and untrained students were externally-driven with a heavy focus on autobiographical processes. The study shows that sensemaking training has a potential to induce shifts in researchers’ mental models by making them more cognitively complex via the use of metacognitive reasoning strategies. Furthermore, field experts may benefit from sensemaking training to improve their ethical decision-making framework in highly complex, novel, and ambiguous situations. (shrink)