Localization of position within a homogeneous behavior chain: Effects of error contingencies

Platt, John R.; Johnson, David M.

doi:10.1016/0023-9690(71)90020-8

Cited by 203 publications

(127 citation statements)

References 14 publications

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“…If the difference between values of numeral stimuli decreases, then our ability to distinguish them also decreases. These effects, called the distance effect and the size effect, are observed in experiments during the processing of digit numerals (Moyer and Landauer 1967) and in experiments with non-symbolic numerals processed both by people and animals (Whalen et al 1999;Platt and Johnson 1971). These data confirm that neurons which implement representations of numbers located on number axes may be more or less selective.…”

Section: The Point-place Representations Of Numbers On the Mental Numsupporting

confidence: 55%

Representational Structures of Arithmetical Thinking: Part I

Krysztofiak

2015

Axiomathes

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In this paper, representational structures of arithmetical thinking, encoded in human minds, are described. On the basis of empirical research, it is possible to distinguish four types of mental number lines: the shortest mental number line, summation mental number lines, point-place mental number lines and mental lines of exact numbers. These structures may be treated as generative mechanisms of forming arithmetical representations underlying our numerical acts of reference towards cardinalities, ordinals and magnitudes. In the paper, the theoretical framework for a formal model of mental arithmetical representations is constructed. Many competitive conceptions of the mental system responsible for our arithmetical thinking may be unified within the presented framework. The paradigm underlying our research may be interpreted philosophically as a neo-Kantian approach to modeling the mind's representational structures.

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Section: The Point-place Representations Of Numbers On the Mental Numsupporting

confidence: 55%

Representational Structures of Arithmetical Thinking: Part I

Krysztofiak

2015

Axiomathes

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“…When variability was normalized by quantity (to produce a COV), it was found to be constant, as in previous work with animals (e.g. (Platt & Johnson, 1971)). Cordes et al (2001) contrasted this prediction with one derived from the idea of errors made in verbal counting.…”

Section: Appendix a Signatures Of Numerical Processes In The Coefficmentioning

confidence: 71%

Verbal interference suppresses exact numerical representation

Frank

Fedorenko

Lai

et al. 2012

Cognitive Psychology

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Language for number is an important case study of the relationship between language and cognition because the mechanisms of non-verbal numerical cognition are well-understood. When the Pirahã (an Amazonian hunter-gatherer tribe who have no exact number words) are tested in non-verbal numerical tasks, they are able to perform one-to-one matching tasks but make errors in more difficult tasks. Their pattern of errors suggests that they are using analog magnitude estimation, an evolutionarily-and developmentally-conserved mechanism for estimating quantities. Here we show that English-speaking participants rely on the same mechanisms when verbal number representations are unavailable due to verbal interference. Followup experiments demonstrate that the effects of verbal interference are primarily manifest during encoding of quantity information, and-using a new procedure for matching difficulty of interference tasks for individual participants-that the effects are restricted to verbal interference. These results are consistent with the hypothesis that number words are used online to encode, store, and manipulate numerical information. This linguistic strategy complements, rather than altering or replacing, non-verbal representations.

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“…The CV is computed from numerical estimations on single dot collections, as the ratio of the standard deviation of the estimates to their mean: CV = sd / m. The CV is advantageous in comparison to traditional accuracy measures, as it should be constant across numerosities if estimation performance conforms to Weber-Fechner law (see Dehaene, 2003), because the variability of the estimates as measured by their standard deviation should be proportional to the magnitude. Whalen, Gallistel, and Gelman (1999) indeed demonstrated that numerical estimation and number production tasks show scalar variability, by reporting that the CV computed from adult numerical estimates ASSESSING THE APPROXIMATE NUMBER SYSTEM was constant and that it was qualitatively and quantitatively similar to that observed in animal estimation situations (Church & Broadbent, 1990;Platt & Johnson, 1971). More importantly, Whalen and colleagues (1999) argued that such a scalar variability in numerical estimation tasks is actually the signature of a representational system that would conform to the accumulator principle (Meck & Church,1983).…”

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confidence: 65%

Assessing the Approximate Number System: no relation between numerical comparison and estimation tasks

Guillaumé

Gevers

2015

Psychological Research

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Whether our general numerical skills and the mathematical knowledge that we acquire at school are entwined is a debated issue, which many researchers are still striving to investigate.The findings reported in the literature are actually inconsistent; some studies emphasised the existence of a relationship between the acuity of the Approximate Number System (ANS) and arithmetic competence, while some others did not observe any significant correlation. One potential explanation of the discrepancy might stem from the evaluation of the ANS itself. In the present study, we correlated two measures used to index ANS acuity with arithmetic performance. These measures were the Weber fraction (w), computed from a numerical comparison task and the Coefficient of Variation (CV), computed from a numerical estimation task. Arithmetic performance correlated with estimation CV but not with comparison w. We further investigated the meaning of this result by taking the relationship between w and CV into account. We expected a tight relation as both these measures are believed to assess ANS acuity. Crucially however, w and CV did not correlate with each other. Moreover, the value of w was modulated by the congruity of the relation between numerical magnitude and nonnumerical visual cues, potentially accounting for the lack of correlation between the measures. Our findings thus challenge the overuse of w to assess ANS acuity and more generally put into question the relevance of correlating this measure with arithmetic without any deeper understanding of what they are really indexing.Abstract word count: 243 words.

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Localization of position within a homogeneous behavior chain: Effects of error contingencies

Cited by 203 publications

References 14 publications

Representational Structures of Arithmetical Thinking: Part I

Representational Structures of Arithmetical Thinking: Part I

Verbal interference suppresses exact numerical representation

Assessing the Approximate Number System: no relation between numerical comparison and estimation tasks

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