Preverbal and verbal counting and computation.
TL;DR: The preverbal system of counting and arithmetic reasoning revealed by experiments on numerical representations in animals is described and a model of the fact retrieval process accounts for the salient features of the reaction time differences and error patterns revealed by experiment on mental arithmetic.
About: This article is published in Cognition.The article was published on 1992-01-01. It has received 1190 citations till now. The article focuses on the topics: Mathematical ability & Subitizing.
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Book•
01 Jan 2000
TL;DR: The relationship between the structural and physiological mechanisms of the brain/nervous system has been studied in this paper, from the molecular level up to that of human consciousness, and contributions cover one of the most fascinating areas of science.
Abstract: Shows the many advances in the field of cognitive neurosciences. From the molecular level up to that of human consciousness, the contributions cover one of the most fascinating areas of science - the relationship between the structural and physiological mechanisms of the brain/nervous system.
1,531 citations
01 Jan 2000
TL;DR: From the molecular level up to that of human consciousness, the contributions cover one of the most fascinating areas of science - the relationship between the structural and physiological mechanisms of the brain/nervous system.
1,512 citations
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TL;DR: Practical work in cognitive science and empirical work in memory and language comprehension are reviewed that suggest that it may be possible to investigate connections between topics as disparate as infantile amnesia and mental-model theory.
Abstract: Let's start from scratch in thinking about what memory is for, and consequently, how it works. Suppose that memory and conceptualization work in the service of perception and action. In this case, conceptualization is the encoding of patterns of possible physical interaction with a three-dimensional world. These patterns are constrained by the structure of the environment, the structure of our bodies, and memory. Thus, how we perceive and conceive of the environment is determined by the types of bodies we have. Such a memory would not have associations. Instead, how concepts become related (and what it means to be related) is determined by how separate patterns of actions can be combined given the constraints of our bodies. I call this combination "mesh." To avoid hallucination, conceptualization would normally be driven by the environment, and patterns of action from memory would play a supporting, but automatic, role. A significant human skill is learning to suppress the overriding contribution of the environment to conceptualization, thereby allowing memory to guide conceptualization. The effort used in suppressing input from the environment pays off by allowing prediction, recollective memory, and language comprehension. I review theoretical work in cognitive science and empirical work in memory and language comprehension that suggest that it may be possible to investigate connections between topics as disparate as infantile amnesia and mental-model theory.
1,509 citations
TL;DR: Six-month-old infants discriminate between large sets of objects on the basis of numerosity when other extraneous variables are controlled, provided that the sets to be discriminated differ by a large ratio.
1,276 citations
Cites background from "Preverbal and verbal counting and c..."
...Most investigators who grant numerical representations to infants have proposed that infants possess the same sense of approximate number as do other animals and human adults ( Gallistel & Gelman, 1992; Wynn, 1995, 1996, 1998)....
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...Most investigators who grant numerical representations to infants have proposed that infants possess the same sense of approximate number as do other animals and human adults (Gallistel & Gelman, 1992; Wynn, 1995, 1996, 1998)....
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TL;DR: This work studied numerical cognition in speakers of Mundurukú, an Amazonian language with a very small lexicon of number words, and implies a distinction between a nonverbal system of number approximation and a language-based counting system for exact number and arithmetic.
Abstract: Is calculation possible without language ? Or is the human ability for arithmetic dependent on the language faculty ? To clarify the relation between language and arithmetic, we studied numerical cognition in speakers of munduruku, an Amazonian language with a very small lexicon of numbers words. Our results imply a distinction between a non-verbal system of number approximation and a language-based counting system for exact number and arithmetic.
1,089 citations
References
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TL;DR: This paper showed an adult chimpanzee a series of videotaped scenes of a human actor struggling with a variety of problems, some of which were simple, such as bananas vertically or horizontally out of reach, behind a box, and so forth; others were more complex, involving an actor unable to extricate himself from a locked cage, shivering because of a malfunctioning heater, or unable to play a phonograph because it was unplugged.
Abstract: An individual has a theory of mind if he imputes mental states to himself and others. A system of inferences of this kind is properly viewed as a theory because such states are not directly observable, and the system can be used to make predictions about the behavior of others. As to the mental states the chimpanzee may infer, consider those inferred by our own species, for example, purpose or intention, as well as knowledge, belief, thinking, doubt, guessing, pretending, liking, and so forth. To determine whether or not the chimpanzee infers states of this kind, we showed an adult chimpanzee a series of videotaped scenes of a human actor struggling with a variety of problems. Some problems were simple, involving inaccessible food – bananas vertically or horizontally out of reach, behind a box, and so forth – as in the original Kohler problems; others were more complex, involving an actor unable to extricate himself from a locked cage, shivering because of a malfunctioning heater, or unable to play a phonograph because it was unplugged. With each videotape the chimpanzee was given several photographs, one a solution to the problem, such as a stick for the inaccessible bananas, a key for the locked up actor, a lit wick for the malfunctioning heater. The chimpanzee's consistent choice of the correct photographs can be understood by assuming that the animal recognized the videotape as representing a problem, understood the actor's purpose, and chose alternatives compatible with that purpose.
5,979 citations
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TL;DR: Experiments on single, multiple, and concurrent schedules of reinforcement find various correlations between the rate of responding and the rate or magnitude of reinforcement, which can be accounted for by a coherent system of equations.
Abstract: Experiments on single, multiple, and concurrent schedules of reinforcement find various correlations between the rate of responding and the rate or magnitude of reinforcement. For concurrent schedules (i.e., simultaneous choice procedures), there is matching between the relative frequencies of responding and reinforcement; for multiple schedules (i.e., successive discrimination procedures), there are contrast effects between responding in each component and reinforcement in the others; and for single schedules, there are a host of increasing monotonic relations between the rate of responding and the rate of reinforcement. All these results, plus several others, can be accounted for by a coherent system of equations, the most general of which states that the absolute rate of any response is proportional to its associated relative reinforcement.
2,690 citations
Book•
01 Jan 1990
TL;DR: It is argued compellingly that experimental psychologists should begin to view the phenomena of learning within a framework that utilizes as the proper unit of analysis the computation and storage of a quantity, rather than the formation of an association that has been the basis of traditional learning theory.
Abstract: From insects to humans, Charles Gallistel explores the sophisticated computations performed in these ubiquitous but neglected domains of animal learning. How do animals represent space, time, number and rate? From insects to humans, Charles Gallistel explores the sophisticated computations performed in these ubiquitous yet neglected domains of animal learning. He proposes new and imaginative hypotheses about brain and mental processes and provides original insights about animal behavior using a computational-representational framework that is an exciting alternative to traditional associative theories of learning. Gallistel argues compellingly that experimental psychologists should begin to view the phenomena of learning within a framework that utilizes as the proper unit of analysis the computation and storage of a quantity, rather than the formation of an association that has been the basis of traditional learning theory. His approach reveals the formal structure of the environmental relationships that animals master to time and orient their behavior. It clarifies what representations different animals can and cannot compute and the nature of the computations by which animals derive these representations.The author backs up this thesis with studies that encompass a vast range of animal learning: animal navigation (the use of dead reckoning and cognitive maps); the mechanisms of timekeeping in the nervous system; the registration and utilization of time of occurrence (circadian phase) in learned behavior; the learning and use of temporal intervals and of numerosity; the computation of rates of occurrence; modern findings and theories of classical conditioning. Gallistel surveys the experimental literature in zoology, biology, neuroscience, and psychology that bears on those aspects of their environment that animals represent and the computations they perform in constructing and utilizing those representations. He reveals the fundamental role these representations play in learning and memory, and the implications of these findings in the search for the cellular basis of memory. The Organization of Learning is included in the series Learning, Development, and Conceptual Change, edited by Lila Gleitman, Susan Carey, Elissa Newport, and Elizabeth Spelke. A Bradford Book
2,652 citations
2,072 citations
TL;DR: In this paper, the authors focus on the Preschooler and the development of the how-to-count principles, including the counting model, the counting concept, and the Abstraction and Order-Irrelevance Counting Principles.
Abstract: 1. Focus on the Preschooler 2. Training Studies Reconsidered 3. More Capacity Than Meets the Eye: Direct Evidence 4. Number Concepts in the Preschooler? 5. What Numerosities Can the Young Child Represent? 6. How Do Young Children Obtain Their Representations of Numerosity? 7. The Counting Model 8. The Development of the How-To-Count Principles 9. The Abstraction and Order-Irrelevance Counting Principles 10. Reasoning about Number 11. Formal Arithmetic and the Young Child's Understanding of Number 12. What Develops and How Conclusions References Index
1,878 citations