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 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.

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.

The SNARC effect does not imply a mental number line

Cognition ◽  
2008 ◽  
Vol 108 (1) ◽  
pp. 263-270 ◽  
Author(s):  
Seppe Santens ◽  
Wim Gevers
Keyword(s):  
Number Line ◽  
Mental Number Line ◽  
Snarc Effect

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.

The fractions SNARC revisited: Processing fractions on a consistent mental number line

2018 ◽  
Vol 71 (8) ◽  
pp. 1761-1770 ◽  
Author(s):  
Elizabeth Y Toomarian ◽  
Edward M Hubbard
Keyword(s):  
Number Line ◽  
Mental Number Line ◽  
Snarc Effect ◽  
Spatial Representations ◽  
Comparison Task ◽  
Single Digit ◽  
Magnitude Processing ◽  
Number Comparison ◽  
Within Subjects ◽  
Solid Foundation

The ability to understand fractions is key to establishing a solid foundation in mathematics, yet children and adults struggle to comprehend them. Previous studies have suggested that these struggles emerge because people fail to process fraction magnitude holistically on the mental number line (MNL), focusing instead on fraction components. Subsequent studies have produced evidence for default holistic processing but examined only magnitude processing, not spatial representations. We explored the spatial representations of fractions on the MNL in a series of three experiments. Experiment 1 replicated Bonato et al.; 30 naïve undergraduates compared unit fractions (1/1-1/9) to 1/5, resulting in a reverse SNARC (Spatial-Numerical Association of Response Codes) effect. Experiment 2 countered potential strategic biases induced by the limited set of fractions used by Bonato et al. by expanding the stimulus set to include all irreducible, single-digit proper fractions and asked participants to compare them against 1/2. We observed a classic SNARC effect, completely reversing the pattern from Experiment 1. Together, Experiments 1 and 2 demonstrate that stimulus properties dramatically impact spatial representations of fractions. In Experiment 3, we demonstrated within-subjects reliability of the SNARC effect across both a fractions and whole number comparison task. Our results suggest that adults can indeed process fraction magnitudes holistically, and that their spatial representations occur on a consistent MNL for both whole numbers and fractions.

scholarly journals The SNARC Effect in the Processing of Second-Language Number Words: Further Evidence for Strong Lexico-Semantic Connections

2008 ◽  
Vol 61 (3) ◽  
pp. 444-458 ◽  
Author(s):  
Jolien De Brauwer ◽  
Wouter Duyck ◽  
Marc Brysbaert
Keyword(s):  
Second Language ◽  
Number Line ◽  
Snarc Effect ◽  
Left Hand ◽  
Number Words ◽  
Number Magnitude ◽  
Large Numbers ◽  
Word Translation ◽  
New Evidence ◽  
Semantic Mediation

We present new evidence that word translation involves semantic mediation. It has been shown that participants react faster to small numbers with their left hand and to large numbers with their right hand. This SNARC (spatial-numerical association of response codes) effect is due to the fact that in Western cultures the semantic number line is oriented from left (small) to right (large). We obtained a SNARC effect when participants had to indicate the parity of second-language (L2) number words, but not when they had to indicate whether L2 number words contained a particular sound. Crucially, the SNARC effect was also obtained in a translation verification task, indicating that this task involved the activation of number magnitude.

scholarly journals The SNARC effect is associated with worse mathematical intelligence and poorer time estimation

2018 ◽  
Vol 5 (8) ◽  
pp. 172362 ◽  
Author(s):  
Peter Kramer ◽  
Paola Bressan ◽  
Massimo Grassi
Keyword(s):  
Spatial Ability ◽  
Mathematical Reasoning ◽  
Time Estimation ◽  
Number Line ◽  
Mental Number Line ◽  
Spatial Extent ◽  
Snarc Effect ◽  
Spatial Skills ◽  
Large Sample ◽  
Within Subjects

Interactions between the ways we process space, numbers and time may arise from shared and innate generic magnitude representations. Alternatively or concurrently, such interactions could be due to the use of physical magnitudes, like spatial extent, as metaphors for more abstract ones, like number and duration. That numbers might be spatially represented along a mental number line is suggested by the SNARC effect: faster left-side responses to small single digits, like 1 or 2, and faster right-side responses to large ones, like 8 or 9. Previously, we found that time estimation predicts mathematical intelligence and speculated that it may predict spatial ability too. Here, addressing this issue, we test—on a relatively large sample of adults and entirely within subjects—the relationships between (a) time: proficiency at producing and evaluating durations shorter than one second, (b) space: the ability to mentally rotate objects, (c) numbers: mathematical reasoning skills, and (d) space–number associations: the SNARC effect. Better time estimation was linked to greater mathematical intelligence and better spatial skills. Strikingly, however, stronger associations between space and numbers predicted worse mathematical intelligence and poorer time estimation.

Cognitive Representation of Negative Numbers

2003 ◽  
Vol 14 (3) ◽  
pp. 278-282 ◽  
Author(s):  
Martin H. Fischer
Keyword(s):  
Number Line ◽  
Mental Number Line ◽  
Phylogenetic Hypothesis ◽  
Cognitive Representation ◽  
Negative Numbers ◽  
Number Representations

To understand negative numbers, must we refer to positive number representations (the phylogenetic hypothesis), or do we acquire a negative mental number line (the ontogenetic hypothesis)? In the experiment reported here, participants made lateralized button responses to indicate the larger of two digits from the range -9 to 9. Digit pairs were displayed spatially congruent or incongruent with either a phylogenetic or an ontogenetic mental number line. The pattern of decision latencies suggests that negative numbers become associated with left space, thus supporting the ontogenetic view.

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 Linear representation of pitch height in the SMARC effect

2018 ◽  
Vol 27 (3) ◽  
pp. 437-452 ◽  
Author(s):  
Valter Prpić ◽  
Dražen Domijan
Keyword(s):  
Linear Representation ◽  
Number Line ◽  
Mental Number Line ◽  
Snarc Effect ◽  
Pitch Height ◽  
Direct Mapping ◽  
Response Alternatives ◽  
Bottom Left ◽  
Response Execution ◽  
Different Origins

The Spatial-Musical Association of Response Codes (SMARC) effect consists in faster and more accurate responses to low (vs. high) pitched tones when they are executed in the bottom/left (vs. top/right) space. This phenomenon has many similarities with the Spatial-Numerical Association of Response Codes (SNARC) effect which, however, has been more extensively investigated and theoretically debated. The first theoretical account of the SNARC effect suggests the existence of a direct mapping between the position of a number on a mental number line and the external space of response execution. Conversely, following accounts claim that numbers are automatically categorized in two opposing categories (e.g., small vs. large) and then associated to response alternatives (left vs. right). A modified task, consisting in unimanual close/far responses relative to a reference key, has been employed to disentangle between the opposite theoretical accounts of the SNARC effect. However, this modified task has never been applied to pitch height and currently there are no specific theoretical accounts for the SMARC effect. The aim of this study is to fill this gap of knowledge. Contrary to what has been found for numbers, our data are more in line with the "direct mapping" account and suggests a linear representation of pitch height. Our data suggest that SNARC and SMARC effects might have different origins and might require different theoretical accounts.

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