Two separate processes affect the development of the mental number line

Goldman, Ronit; Tzelgov, Joseph; Ben-Shalom, Tamar; Berger, Andrea

doi:10.3389/fpsyg.2013.00317

Cited by 8 publications

(18 citation statements)

References 23 publications

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“…This process was manifested as a modulation of the P3 congruency effect, thus it may be related to higher-order stimuli categorization and evaluation processes thought to be reflected in the P3 (e.g., Kutas et al, 1977 ; McCarthy and Donchin, 1981 ; Kok, 2001 ; Polich, 2007 , 2012 ). Future work is needed to better understand how the end-anchor identification process develops in relation to the analog comparison process ( Goldman et al, 2013 ) as well as characterizing the processing of less salient or prototypical end values by examining upper end values. We conclude that two processes are involved in the processing of numbers: an analog comparison process and an end-anchor identification process.…”

Section: Discussionmentioning

confidence: 99%

The Neural Signatures of Processing Semantic End Values in Automatic Number Comparisons

Pinhas

Buchman

Lavro

et al. 2015

Front. Hum. Neurosci.

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The brain activity associated with processing numerical end values has received limited research attention. The present study explored the neural correlates associated with processing semantic end values under conditions of automatic number processing. Event-related potentials (ERPs) were recorded while participants performed the numerical Stroop task, in which they were asked to compare the physical size of pairs of numbers, while ignoring their numerical values. The smallest end value in the set, which is a task irrelevant factor, was manipulated between participant groups. We focused on the processing of the lower end values of 0 and 1 because these numbers were found to be automatically tagged as the “smallest.” Behavioral results showed that the size congruity effect was modulated by the presence of the smallest end value in the pair. ERP data revealed a spatially extended centro-parieto-occipital P3 that was enhanced for congruent versus incongruent trials. Importantly, over centro-parietal sites, the P3 congruity effect (congruent minus incongruent) was larger for pairs containing the smallest end value than for pairs containing non-smallest values. These differences in the congruency effect were localized to the precuneus. The presence of an end value within the pair also modulated P3 latency. Our results provide the first neural evidence for the encoding of numerical end values. They further demonstrate that the use of end values as anchors is a primary aspect of processing symbolic numerical information.

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Section: Discussionmentioning

confidence: 99%

The Neural Signatures of Processing Semantic End Values in Automatic Number Comparisons

Pinhas

Buchman

Lavro

et al. 2015

Front. Hum. Neurosci.

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“…Beyond the relevant FTT findings (e.g., Reyna, 2012; Reyna & Brainerd, 1991; Reyna et al, 2014), experimental data have shown that subjects prefer to avoid winning nothing in a risky gamble, even if doing so lowers their overall expected value (e.g., the “P max ” strategy of avoiding winning nothing as in Venkatraman & Huettel, 2012; Venkatraman, Payne, Bettman, Luce, & Huettel, 2009). In addition, recent findings show that zero may be encoded into an “end stimulus” category that is separate from how other numbers are encoded (Goldman, Tzelgov, Ben-Shalom, & Berger, 2013; Pinhas & Tzelgov, 2012; Wellman & Miller, 1986), leading Pinhas and Tzelgov (2012) to hypothesize that “0. .…”

Section: Section 3: the Modelmentioning

confidence: 99%

A formal model of fuzzy-trace theory: Variations on framing effects and the Allais Paradox.

2018

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Fuzzy-trace theory assumes that decision-makers process qualitative “gist” representations and quantitative “verbatim” representations in parallel. We develop a lattice model of fuzzy-trace theory that explains both processes. Specifically, the model provides a novel formalization of how: 1) decision-makers encode multiple representations of options in parallel; 2) representations compete or combine so that choices often turn on the simplest representation of encoded gists; and 3) choices between representations are made based on positive vs. negative valences associated with social and moral principles stored in long-term memory (e.g., saving lives is good). The model integrates effects of individual differences in numeracy, metacognitive monitoring and editing, and sensation seeking. We conducted a systematic review of variations on framing effects and the Allais Paradox, both core phenomena of risky decision-making, and tested whether our model could predict observed choices: The model successfully predicted 82 out of 88 (93%) pairs of studies (comparing gain to loss conditions) demonstrating 16 variations on effects, theoretically critical manipulations that eliminate or exaggerate framing effects. When examining these conditions individually, the model successfully predicted 153 (90%) out of 170 eligible studies. Parameters of the model varied in theoretically meaningful ways with differences in numeracy, metacognitive monitoring, and sensation seeking, accounting for risk preferences at the group level. New experiments show similar results at the individual level. The model is also shown to be scientifically parsimonious using standard measures. Relations to current theories, such as Cumulative Prospect Theory, and potential extensions are discussed.

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“…Generally, when analyzing data, the last numerosity is excluded from the analysis due to its known end effect. However, the strong end effect found for numerosity 5 in Experiment 1 (and in Cohen et al.’s (2014) Experiment) might be due to the use of five neighboring fingers, which is the familiar pattern that results from real-world experience of counting with five fingers (see also Goldman, Tzelgov, Ben-Shalom, & Berger, 2013; Pinhas & Tzelgov, 2012). This suggestion can be tested by excluding a one-hand arrangement.…”

Section: Methodsmentioning

confidence: 79%

Effects of Numerosity Range on Tactile and Visual Enumeration

Cohen

Henik

2015

Perception

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Our study explores tactile enumeration using both hands and investigates the effects of numerosity range's (NR) on general enumeration. In Experiment 1, using custom-made vibro-tactile apparatus, we replicated results of Cohen, Naparstek, and Henik (2014, Acta Psychologica, 150C, 26-34) and again found a moderate increase in RT up to four stimuli and then a decrease for five stimuli. In Experiment 2, we used a within participants design and compared NR 1 to 5 and 1 to 10 in tactile and visual enumeration. The results showed that enumeration for NR 5 to 1 was faster than for NR 1 to 10, especially for numerosities four and five. Within NR 1 to 10, in the visual modality the subitizing range was 4, the counting range was from 5 to 9, and there was an end effect of 10 dots. In the tactile modality, when excluding one-hand arrangements, the subitizing range was 2, the counting range was from 3 to 5, there was an acceleration of counting from 5 and on, and there was an end effect for 10 stimuli that was stronger than for 10 visual stimuli. We suggest that NR influences enumeration and that number-hand association (i.e. resulting from finger counting) influences enumeration, resulting in faster counting.

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Two separate processes affect the development of the mental number line

Cited by 8 publications

References 23 publications

The Neural Signatures of Processing Semantic End Values in Automatic Number Comparisons

The Neural Signatures of Processing Semantic End Values in Automatic Number Comparisons

A formal model of fuzzy-trace theory: Variations on framing effects and the Allais Paradox.

Effects of Numerosity Range on Tactile and Visual Enumeration

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