Probability Relations within Response Sequences under Ratio Reinforcement.
01 Apr 1958-Journal of the Experimental Analysis of Behavior (Society for the Experimental Analysis of Behavior)-Vol. 1, Iss: 2, pp 109-121
About: This article is published in Journal of the Experimental Analysis of Behavior.The article was published on 1958-04-01 and is currently open access. It has received 264 citations till now. The article focuses on the topics: Reinforcement.
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TL;DR: There is a fundamental difference between doing educational neuroscience and using neuroscience research results to inform education, and educational neuroscience can expand knowledge about learning, for example, by tracking the normative development of mental representations.
Abstract: — Is educational neuroscience a “bridge too far”? Here, we argue against this negative assessment. We suggest that one major reason for skepticism within the educational community has been the inadequate definition of the potential role and use of neuroscience research in education. Here, we offer a provisional definition for the emerging discipline of educational neuroscience as the study of the development of mental representations. We define mental representations in terms of neural activity in the brain. We argue that there is a fundamental difference between doing educational neuroscience and using neuroscience research results to inform education. While current neuroscience research results do not translate into direct classroom applications, educational neuroscience can expand our knowledge about learning, for example, by tracking the normative development of mental representations. We illustrate this briefly via mathematical educational neuroscience. Current capabilities and limitations of neuroscience research methods are also considered.
132 citations
TL;DR: It is proposed that calculation ability represents a multifactor skill, including verbal, spatial, memory, body knowledge, and executive function abilities, and some general guidelines for the rehabilitation of calculation disturbances are presented.
Abstract: Even though it is generally recognized that calculation ability represents a most important type of cognition, there is a significant paucity in the study of acalculia. In this paper the historical evolution of calculation abilities in humankind and the appearance of numerical concepts in child development are reviewed. Developmental calculation disturbances (developmental dyscalculia) are analyzed. It is proposed that calculation ability represents a multifactor skill, including verbal, spatial, memory, body knowledge, and executive function abilities. A general distinction between primary and secondary acalculias is presented, and different types of acquired calculation disturbances are analyzed. The association between acalculia and aphasia, apraxia and dementia is further considered, and special mention to the so-called Gerstmann syndrome is made. A model for the neuropsychological assessment of numerical abilities is proposed, and some general guidelines for the rehabilitation of calculation disturbances are presented.
125 citations
Cites background from "Probability Relations within Respon..."
...For instance, pigeons can be trained to pick a specific number of times on a board, and rats can be trained to press a lever a certain amount of times to obtain food (Calpadi and Miller, 1988; Koehler, 1951; Mechner, 1958)....
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TL;DR: In the FCN procedure, the speed with which the runs were executed increased with increasing deprivation, although the number of responses in these runs was relatively unaffected, and the pause between reinforcement and the next response shortened.
Abstract: Two procedures were used in an investigation of the effects of deprivation upon counting and timing. Under the first procedure, fixed minimum interval (FMI), the rat received liquid reinforcement every time it pressed bar B after having waited a minimum of 5 sec following a press on bar A. Under the second procedure, fixed consecutive number (FCN), reinforcement was delivered every time the rat pressed bar B following a run of at least four consecutive responses on bar A.
Water deprivation was varied over a set of values ranging from 4 to 56 hr. Deprivation had almost no effect on the waiting time in the FMI procedure, or on the number of responses per run in the FCN procedure. With both procedures, increasing deprivation shortened the pause between reinforcement and the next response. In the FCN procedure, the speed with which the runs were executed increased with increasing deprivation, although the number of responses in these runs was relatively unaffected.
125 citations
TL;DR: The behavioral performance of two rhesus monkeys judging the numerosities 1 to 7 during a delayed match-to-sample task shows similar discrimination performance irrespective of the exact physical appearance of the stimuli, confirming that performance was based on numerical information.
Abstract: Monkeys have been introduced as model organisms to study neural correlates of numerical competence, but many of the behavioral characteristics of numerical judgments remain speculative. Thus, we analyzed the behavioral performance of two rhesus monkeys judging the numerosities 1 to 7 during a delayed match-to-sample task. The monkeys showed similar discrimination performance irrespective of the exact physical appearance of the stimuli, confirming that performance was based on numerical information. Performance declined smoothly with larger numerosities, and reached discrimination threshold at numerosity ''4.'' The nonverbal numerical representations in monkeys were based on analog magnitudes, object tracking process (''subitizing'') could not account for the findings because the continuum of small and large numbers shows a clear Weber fraction signature. The lack of additional scanning eye movements with increasing set sizes, together with indistinguishable neuronal response latencies for neurons with different preferred numerosities, argues for parallel encoding of numerical information. The slight but significant increase in reaction time with increasing numerosities can be explained by task difficulty and consequently time-consuming decision processes. The behavioral results are compared to single-cell recordings from the prefrontal cortex in the same subjects. Models for numerosity discrimination that may account for these results are discussed.
113 citations
Cites background or methods from "Probability Relations within Respon..."
...Mechner (1958) trained rats to perform a certain number of lever presses (4, 8, 12, or 16 lever presses)....
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...Evidence for analog magnitude representations has been reported in other animals as well (Meck & Church, 1983; Mechner, 1958)....
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01 May 2016
TL;DR: The present review identifies substantial commonalities, as well as differences, in these four aspects of numerical development, which include representing increasingly precisely the magnitudes of non-Symbolic numbers, connecting small symbolic numbers to their non-symbolic referents, extending understanding from smaller to larger whole numbers, and accurately representing the magnitude of rational numbers.
Abstract: The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: (1) representing increasingly precisely the magnitudes of non-symbolic numbers, (2) connecting small symbolic numbers to their non-symbolic referents, (3) extending understanding from smaller to larger whole numbers, and (4) accurately representing the magnitudes of rational numbers. The present review identifies substantial commonalities, as well as differences, in these four aspects of numerical development. With both whole and rational numbers, numerical magnitude knowledge is concurrently correlated with, longitudinally predictive of, and causally related to multiple aspects of mathematical understanding, including arithmetic and overall math achievement. Moreover, interventions focused on increasing numerical magnitude knowledge often generalize to other aspects of mathematics. The cognitive processes of association and analogy seem to play especially large roles in this development. Thus, acquisition of numerical magnitude knowledge can be seen as the common core of numerical development.
110 citations
Cites background from "Probability Relations within Respon..."
...This widely accepted hypothesis has roots in psychometrics (Galton, 1880), animal behavior (Mechner, 1958; Platt & Johnson, 1971), and adult cognition research (Moyer & Landauer, 1967; Restle, 1970)....
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References
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340 citations
203 citations
TL;DR: I am indebted to Professor Lighthill for some further illuminating remarks regarding this point and his comments on Heisenberg's Theory of Isotropic Turbulence are highly illuminating.
Abstract: 1 G. K. Batchelor, The Theory of Homogeneous Turbulence (Cambridge: At the University Press, 1954). 2 G. K. Batchelor and A. A. Townsend, \"Decay of Turbulence in the Final Period of Decay,\" Proc. Roy. Soc. London, A, 194, 527-543, 1948. 3 W. Heisenberg, \"Zur statistischen Theorie der Turbulenz,\" Z. Physik, 124, 628-657, 1948. 4W. H. Reid, \"Two Remarks on Heisenberg's Theory of Isotropic Turbulence,\" Quart. Appl. Math. 14, 201-205, 1956. 6 Cf. M. J. Lighthill, Nature, 173, 746, 1954. I am indebted to Professor Lighthill for some further illuminating remarks regarding this point.
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129 citations