scholarly journals The SNARC effect: A preregistered study on the interaction of horizontal,vertical, and sagittal spatial-numerical associations

2021 ◽  
Author(s):  
Sara Aleotti ◽  
Stefano Massaccesi ◽  
Konstantinos Priftis
Keyword(s):  
Ad Hoc ◽  
Three Dimensional ◽  
Number Line ◽  
Mental Number Line ◽  
Snarc Effect ◽  
Large Numbers ◽  
The Right

Small numbers are processed faster through left-sided than right-sided responses, whereas large numbers are processed faster through right-sided than left-sided responses (i.e., the Spatial-numerical Association of Response Codes [SNARC] effect). This effect suggests that small numbers are represented on the left side of space, whereas large numbers are represented on the right side of space, along a mental number line. The SNARC effect has been widely investigated along the horizontal Cartesian axis (i.e., left-right). Aleotti et al. (2020), however, have shown that the SNARC effect could also be observed along the vertical (i.e., small numbers-down side vs. large numbers-up side) and the sagittal axis (i.e., small numbers-near side vs. large numbers-far side). Here, we investigated whether the three Cartesian axes could interact to elicit the SNARC effect. Participants were asked to decide whether a centrally presented Arabic digit was odd or even. Responses were collected through an ad hoc-made response box on which the SNARC effect could be compatible for one, two, or three Cartesian axes. The results showed that the higher the number of SNARC-compatible Cartesian axes, the stronger the SNARC effect. We suggest that numbers are represented in a three-dimensional number space defined by interacting Cartesian axes.

Linkages between Number Concepts, Spatial Thinking, and Directionality of Writing: The SNARC Effect and the REVERSE SNARC Effect in English and Arabic Monoliterates, Biliterates, and Illiterate Arabic Speakers

2005 ◽  
Vol 5 (1-2) ◽  
pp. 165-190 ◽  
Author(s):  
Samar Zebian
Keyword(s):  
Number Line ◽  
Mental Number Line ◽  
Snarc Effect ◽  
Writing System ◽  
Cultural Artifact ◽  
Arabic Speakers ◽  
Association Response ◽  
Numeric Cognition ◽  
The Right ◽  
First Time

AbstractThe current investigations coordinate math cognition and cultural approaches to numeric thinking to examine the linkages between numeric and spatial processes, and how these linkages are modified by the cultural artifact of writing. Previous research in the adult numeric cognition literature has shown that English monoliterates have a spatialised mental number line which is oriented from left-to-right with smaller magnitudes associated with the left side of space and larger magnitudes are associated with the right side of space. These associations between number and space have been termed the Spatial Numeric Association Response Code Effect (SNARC effect, Dehaene, 1992). The current study investigates the spatial orientation of the mental number line in the following groups: English monoliterates, Arabic monoliterates who use only the right-left writing system, Arabic-English biliterates, and illiterate Arabic speakers who only read numerals. Current results indicate, for the first time, a Reverse SNARC effect for Arabic monoliterates, such that the mental number line had a right-to-left directionality. Furthermore, a weakened Reverse SNARC was observed for Arabic-English biliterates, and no effect was observed among Illiterate Arabic speakers. These findings are especially notable since left-right biases are neurologically supported and are observed in pre-literate children regardless of which writing system is used by adults. The broader implications of how cultural artifacts affect basic numeric cognition will be discussed.

Time course of overt attentional shifts in mental arithmetic: Evidence from gaze metrics

2018 ◽  
Vol 71 (4) ◽  
pp. 1009-1019 ◽  
Author(s):  
Nicolas Masson ◽  
Clément Letesson ◽  
Mauro Pesenti
Keyword(s):  
Time Course ◽  
Mental Arithmetic ◽  
Number Line ◽  
Detection Task ◽  
Mental Number Line ◽  
Large Numbers ◽  
Attentional Shifts ◽  
Addition And Subtraction ◽  
The Right ◽  
Target Detection Task

Processing numbers induces shifts of spatial attention in probe detection tasks, with small numbers orienting attention to the left and large numbers to the right side of space. This has been interpreted as supporting the concept of a mental number line with number magnitudes ranging from left to right, from small to large numbers. Recently, the investigation of this spatial-numerical link has been extended to mental arithmetic with the hypothesis that solving addition or subtraction problems might induce attentional displacements, rightward or leftward, respectively. At the neurofunctional level, the activations elicited by the solving of additions have been shown to resemble those induced by rightward eye movements. However, the possible behavioural counterpart of these activations has not yet been observed. Here, we investigated overt attentional shifts with a target detection task primed by addition and subtraction problems (2-digit ± 1-digit operands) in participants whose gaze orientation was recorded during the presentation of the problems and while calculating. No evidence of early overt attentional shifts was observed while participants were hearing the first operand, the operator or the second operand, but they shifted their gaze towards the right during the solving step of addition problems. These results show that gaze shifts related to arithmetic problem solving are elicited during the solving procedure and suggest that their functional role is to access, from the first operand, the representation of the result.

scholarly journals Registered Replication Report on Fischer, Castel, Dodd, and Pratt (2003)

2020 ◽  
Vol 3 (2) ◽  
pp. 143-162 ◽  
Author(s):  
Lincoln J. Colling ◽  
Dénes Szűcs ◽  
Damiano De Marco ◽  
Krzysztof Cipora ◽  
Rolf Ulrich ◽  
...  
Keyword(s):  
Mathematics Anxiety ◽  
Number Line ◽  
Mental Number Line ◽  
Snarc Effect ◽  
Moderating Effects ◽  
Mathematics Fluency ◽  
Finger Counting ◽  
Large Numbers ◽  
Number Representations ◽  
And Mathematics

The attentional spatial-numerical association of response codes (Att-SNARC) effect (Fischer, Castel, Dodd, & Pratt, 2003)—the finding that participants are quicker to detect left-side targets when the targets are preceded by small numbers and quicker to detect right-side targets when they are preceded by large numbers—has been used as evidence for embodied number representations and to support strong claims about the link between number and space (e.g., a mental number line). We attempted to replicate Experiment 2 of Fischer et al. by collecting data from 1,105 participants at 17 labs. Across all 1,105 participants and four interstimulus-interval conditions, the proportion of times the effect we observed was positive (i.e., directionally consistent with the original effect) was .50. Further, the effects we observed both within and across labs were minuscule and incompatible with those observed by Fischer et al. Given this, we conclude that we failed to replicate the effect reported by Fischer et al. In addition, our analysis of several participant-level moderators (finger-counting habits, reading and writing direction, handedness, and mathematics fluency and mathematics anxiety) revealed no substantial moderating effects. Our results indicate that the Att-SNARC effect cannot be used as evidence to support strong claims about the link between number and space.

scholarly journals Motion along the mental number line reveals shared representations for numerosity and space

eLife ◽  
2016 ◽  
Vol 5 ◽  
Author(s):  
Caspar M Schwiedrzik ◽  
Benjamin Bernstein ◽  
Lucia Melloni
Keyword(s):  
Reference Frame ◽  
Parietal Cortex ◽  
Visual Motion ◽  
Number Line ◽  
Mental Number Line ◽  
Motion Direction ◽  
Large Numbers ◽  
Cross Adaptation ◽  
The Right ◽  
Numerosity Perception

Perception of number and space are tightly intertwined. It has been proposed that this is due to ‘cortical recycling’, where numerosity processing takes over circuits originally processing space. Do such ‘recycled’ circuits retain their original functionality? Here, we investigate interactions between numerosity and motion direction, two functions that both localize to parietal cortex. We describe a new phenomenon in which visual motion direction adapts nonsymbolic numerosity perception, giving rise to a repulsive aftereffect: motion to the left adapts small numbers, leading to overestimation of numerosity, while motion to the right adapts large numbers, resulting in underestimation. The reference frame of this effect is spatiotopic. Together with the tuning properties of the effect this suggests that motion direction-numerosity cross-adaptation may occur in a homolog of area LIP. ‘Cortical recycling’ thus expands but does not obliterate the functions originally performed by the recycled circuit, allowing for shared computations across domains.

The Development of the Mental Representation of Numbers 0-10 in Elementary School Children

2020 ◽  
Author(s):  
Anat Feldman ◽  
Michael Shmueli ◽  
Dror Dotan ◽  
Joseph Tzelgov ◽  
Andrea Berger
Keyword(s):  
Sixth Grade ◽  
Number Line ◽  
Number Representation ◽  
Large Numbers ◽  
Position Task ◽  
Sigmoidal Curve ◽  
Anchor Points ◽  
The Right ◽  
Line P ◽  
Best Fit

In recent years, there has been growing interest in the development of mental number line (MNL) representation examined using a number-to-position task. In the present study, we investigated the development of number representation on a 0-10 number line using a computerized version of the number-to-position task on a touchscreen, with restricted response time; 181 children from first through sixth grade were tested. We found that the pattern of estimated number position on the physical number line was best fit by the sigmoidal curve function–which was characterized by underestimation of small numbers and overestimation of large numbers–and that the breakpoint changed with age. Moreover, we found that significant developmental leaps in MNL representation occurred between the first and second grades and again between the second and third grades, which was reflected in the establishment of the right endpoint and the number 5 as anchor points, yielding a more accurate placement of other numbers along the number line.

The role of visual experience for spatial numerical associations

2012 ◽  
Vol 25 (0) ◽  
pp. 222 ◽  
Author(s):  
Michael J. Proulx ◽  
Achille Pasqualotto ◽  
Shuichiro Taya
Keyword(s):  
Visual Experience ◽  
Opposite Effect ◽  
Random Number Generation ◽  
Number Line ◽  
Mental Number Line ◽  
Generation Task ◽  
Congenitally Blind ◽  
Left And Right ◽  
The Right

The topographic representation of space interacts with the mental representation of number. Evidence for such number–space relations have been reported in both synaesthetic and non-synaesthetic participants. Thus far most studies have only examined related effects in sighted participants. For example, the mental number line increases in magnitude from left to right in sighted individuals (Loetscher et al., 2008, Curr. Biol.). What is unclear is whether this association arises from innate mechanisms or requires visual experience early in life to develop in this way. Here we investigated the role of visual experience for the left to right spatial numerical association using a random number generation task in congenitally blind, late blind, and blindfolded sighted participants. Participants orally generated numbers randomly whilst turning their head to the left and right. Sighted participants generated smaller numbers when they turned their head to the left than to the right, consistent with past results. In contrast, congenitally blind participants generated smaller numbers when they turned their head to the right than to the left, exhibiting the opposite effect. The results of the late blind participants showed an intermediate profile between that of the sighted and congenitally blind participants. Visual experience early in life is therefore necessary for the development of the spatial numerical association of the mental number line.

scholarly journals Leaning to the Left Makes the Eiffel Tower Seem Smaller

2011 ◽  
Vol 22 (12) ◽  
pp. 1511-1514 ◽  
Author(s):  
Anita Eerland ◽  
Tulio M. Guadalupe ◽  
Rolf A. Zwaan
Keyword(s):  
Number Line ◽  
Mental Number Line ◽  
Body Posture ◽  
Wii Balance Board ◽  
Quantitative Estimates ◽  
Line Theory ◽  
Within Subjects ◽  
The Right ◽  
Balance Board

In two experiments, we investigated whether body posture influences people’s estimation of quantities. According to the mental-number-line theory, people mentally represent numbers along a line with smaller numbers on the left and larger numbers on the right. We hypothesized that surreptitiously making people lean to the right or to the left would affect their quantitative estimates. Participants answered estimation questions while standing on a Wii Balance Board. Posture was manipulated within subjects so that participants answered some questions while they leaned slightly to the left, some questions while they leaned slightly to the right, and some questions while they stood upright. Crucially, participants were not aware of this manipulation. Estimates were significantly smaller when participants leaned to the left than when they leaned to the right.

scholarly journals Critical Time Course of Right Frontoparietal Involvement in Mental Number Space

2013 ◽  
Vol 25 (3) ◽  
pp. 465-483 ◽  
Author(s):  
Elena Rusconi ◽  
Martynas Dervinis ◽  
Frederick Verbruggen ◽  
Christopher D. Chambers
Keyword(s):  
Time Course ◽  
Posterior Parietal Cortex ◽  
Inferior Frontal Gyrus ◽  
Critical Time ◽  
Single Pulse ◽  
Random Order ◽  
Number Line ◽  
Sampling Interval ◽  
Snarc Effect ◽  
Large Numbers

Neuropsychological, neurophysiological, and neuroimaging studies suggest that right frontoparietal circuits may be necessary for the processing of mental number space, also known as the mental number line (MNL). Here we sought to specify the critical time course of three nodes that have previously been related to MNL processing: right posterior parietal cortex (rPPC), right FEF (rFEF), and right inferior frontal gyrus (rIFG). The effects of single-pulse TMS delivered at 120% distance-adjusted individual motor threshold were investigated in 21 participants, within a window of 0–400 msec (sampling interval = 33 msec) from the onset of a central digit (1–9, 5 excluded). Pulses were delivered in a random order and with equal probability at each time point, intermixed with noTMS trials. To analyze whether and when TMS interfered with MNL processing, we fitted bimodal Gaussian functions to the observed data and measured effects on changes in the Spatial–Numerical Association of Response Codes (SNARC) effect (i.e., an advantage for left- over right-key responses to small numbers and right- over left-key responses to large numbers) and in overall performance efficiency. We found that, during magnitude judgment with unimanual key-press responses, TMS reduced the SNARC effect in the earlier period of the fitted functions (∼25–60 msec) when delivered over rFEF (small and large numbers) and rIFG (small numbers); TMS further reduced the SNARC effect for small numbers in a later period when delivered to rFEF (∼200 msec). In contrast, TMS of rPPC did not interfere with the SNARC effect but generally reduced performance for small numbers and enhanced it for large numbers, thus producing a pattern reminiscent of “neglect” in mental number space. Our results confirm the causal role of an intact right frontoparietal network in the processing of mental number space. They also indicate that rPPC is specifically tied to explicit number magnitude processing and that rFEF and rIFG contribute to interfacing mental visuospatial codes with lateralized response codes. Overall, our findings suggest that both ventral and dorsal frontoparietal circuits are causally involved and functionally connected in the mapping of numbers to space.

scholarly journals Leaning to the left makes the Eiffel tower seem smaller: Posture-modulated estimation

2017 ◽  
Author(s):  
Anita Eerland ◽  
Tulio M. Guadalupe ◽  
Rolf Antonius Zwaan
Keyword(s):  
Number Line ◽  
Mental Number Line ◽  
Body Posture ◽  
Wii Balance Board ◽  
Quantitative Estimates ◽  
Line Theory ◽  
Within Subjects ◽  
The Right ◽  
Balance Board

In two experiments, we investigated whether body posture influences people’s estimation of quantities. According to the mental-number-line theory, people mentally represent numbers along a line with smaller numbers on the left and larger numbers on the right. We hypothesized that surreptitiously making people lean to the right or to the left would affect their quantitative estimates. Participants answered estimation questions while standing on a Wii Balance Board. Posture was manipulated within subjects so that participants answered some questions while they leaned slightly to the left, some questions while they leaned slightly to the right, and some questions while they stood upright. Crucially, participants were not aware of this manipulation. Estimates were significantly smaller when participants leaned to the left than when they leaned to the right.

Mathematics and TMS

2012 ◽  
Author(s):  
Elena Rusconi ◽  
Carlo Umiltà
Keyword(s):  
Transcranial Magnetic Stimulation ◽  
Magnetic Stimulation ◽  
Right Hemisphere ◽  
Parietal Lobe ◽  
Brain Activation ◽  
Number Line ◽  
Mathematical Cognition ◽  
Mental Number Line ◽  
The Right ◽  
The Relationship

This article introduces the relationship between mathematical cognition and transcranial magnetic stimulation (TMS). The mental number line is located in the parietal lobe. Studies employing TMS have explored issues related to the mental number line. This article reviews the studies centered on the magnitude code. The results show that even though the parietal activation is nearly always present in both hemispheres, it is often asymmetric, being greater in the right hemisphere when quantification of nonverbal and nonsymbolic material is required. Neuropsychological studies confirm the relation between the magnitude code and the parietal lobe. The extent to which number-related processes are number specific, and the extent to which they overlap with other aspects of spatial or magnitude representation, is currently a burgeoning area of research. Current work is aimed to disrupt numerical processes and observe concomitant changes in brain activation.

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