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Shen J, He H, Wu B, Zhou J. Influence of different spatial representations on the SNARC effect for letters: Electrophysiological evidence. Q J Exp Psychol (Hove) 2023; 76:2613-2628. [PMID: 37021368 DOI: 10.1177/17470218231167056] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/07/2023]
Abstract
Studies have previously demonstrated that different spatial representations may affect the spatial-numerical association of response codes (SNARC) effect for numbers; however, limited studies have assessed the SNARC effect for letters. In this study, event-related potentials (ERPs) were used to measure the influence of two spatial representation modes (ruler and clock) on the SNARC effect. The ruler produced a SNARC-like effect; i.e., the left hand reacted faster than the right to the letters that appeared before N in the alphabet; the right hand reacted faster than the left to the letters that appeared after N, whereas the clock produced a reverse SNARC effect. In addition, the ERP data showed that the SNARC-like effect for letters in both representations induced significant activation in the frontal and parietal regions, indicating that the same brain areas are involved in processing letters and numbers in terms of spatial dimensions. This study further identified the conditions for the SNARC effect and proved that the SNARC effect is attributed to the simultaneous participation of brain regions for sequence and spatial information processing.
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Affiliation(s)
- Jie Shen
- Faculty of Education, Department of Educational Psychology, Center for Educational Neuroscience, East China Normal University, China
| | - Hua He
- Faculty of Education, Soochow University, China
| | - Bin Wu
- Faculty of Education, Department of Educational Psychology, Center for Educational Neuroscience, East China Normal University, China
| | - Jiaxian Zhou
- Faculty of Education, Department of Educational Psychology, Center for Educational Neuroscience, East China Normal University, China
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2
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Tillman KA, Fukuda E, Barner D. Children gradually construct spatial representations of temporal events. Child Dev 2022; 93:1380-1397. [PMID: 35560030 DOI: 10.1111/cdev.13780] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
English-speaking adults often recruit a "mental timeline" to represent events from left-to-right (LR), but its developmental origins are debated. Here, we test whether preschoolers prefer ordered linear representations of events and whether they prefer culturally conventional directions. English-speaking adults (n = 85) and 3- to 5-year-olds (n = 513; 50% female; ~47% white, ~35% Latinx, ~18% other; tested 2016-2018) were told three-step stories and asked to choose which of two image sequences best illustrated them. We found that 3- and 4-year-olds chose ordered over unordered sequences, but preferences between directions did not emerge until at least age 5. Together, these results show that children conceptualize time linearly early in development but gradually acquire directional preferences (e.g., for LR).
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Affiliation(s)
- Katharine A Tillman
- Department of Psychology, The University of Texas at Austin, Austin, Texas, USA
| | - Eren Fukuda
- Department of Psychology, University of Wisconsin-Madison, Madison, Wisconsin, USA
| | - David Barner
- Department of Psychology, University of California, San Diego, San Diego, California, USA.,Department of Linguistics, University of California, San Diego, San Diego, California, USA
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3
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Cheung CN. When A is greater than B: Interactions between magnitude and serial order. Conscious Cogn 2021; 97:103259. [PMID: 34971865 DOI: 10.1016/j.concog.2021.103259] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2021] [Revised: 12/02/2021] [Accepted: 12/04/2021] [Indexed: 11/17/2022]
Abstract
Processing ordinal information is an important aspect of cognitive ability, yet the nature of such ordinal representations remains largely unclear. Previously, it has been suggested that ordinal position is coded as magnitude, but this claim has not yet received direct empirical support. This study examined the nature of ordinal representations using a Stroop-like letter order judgment task. If ordinal position is coded as magnitude, then letter ordering and font size should interact. Experiments 1 and 2 identified a significant interaction between letter size and ordering. Specifically, a facilitation effect was observed for alphabetically ordered sequences with decreasing font size (e.g., B C D). This suggests an overlap in the mechanisms for order and magnitude processing. The finding also suggests that earlier ranks may be represented as "more" in such a magnitude-based code, and vice versa for later ranks.
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Affiliation(s)
- Chi-Ngai Cheung
- Department of Psychology and Criminal Justice, Middle Georgia State University, USA; Jiann-Ping Hsu College of Public Health, Georgia Southern University, USA; Department of Psychology, University of South Florida, USA.
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4
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Aulet LS, Yousif SR, Lourenco SF. Spatial-numerical associations from a novel paradigm support the mental number line account. Q J Exp Psychol (Hove) 2021; 74:1829-1840. [PMID: 33759642 DOI: 10.1177/17470218211008733] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Multiple tasks have been used to demonstrate the relation between numbers and space. The classic interpretation of these directional spatial-numerical associations (d-SNAs) is that they are the product of a mental number line (MNL), in which numerical magnitude is intrinsically associated with spatial position. The alternative account is that d-SNAs reflect task demands, such as explicit numerical judgements and/or categorical responses. In the novel "Where was The Number?" task, no explicit numerical judgements were made. Participants were simply required to reproduce the location of a numeral within a rectangular space. Using a between-subject design, we found that numbers, but not letters, biased participants' responses along the horizontal dimension, such that larger numbers were placed more rightward than smaller numbers, even when participants completed a concurrent verbal working memory task. These findings are consistent with the MNL account, such that numbers specifically are inherently left-to-right oriented in Western participants.
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Affiliation(s)
- Lauren S Aulet
- Department of Psychology, Emory University, Atlanta, GA, USA
| | - Sami R Yousif
- Department of Psychology, Yale University, New Haven, CT, USA
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5
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Does 1 + 1 = 2nd? The relations between children's understanding of ordinal position and their arithmetic performance. J Exp Child Psychol 2019; 187:104651. [PMID: 31352227 DOI: 10.1016/j.jecp.2019.06.004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2018] [Revised: 06/02/2019] [Accepted: 06/07/2019] [Indexed: 11/19/2022]
Abstract
The current study examined the relations between 5- and 6-year-olds' understanding of ordinality and their mathematical competence. We focused specifically on "positional operations," a property of ordinality not contingent on magnitude, in an effort to better understand the unique contributions of position-based ordinality to math development. Our findings revealed that two types of positional operations-the ability to execute representational movement along letter sequences and the ability to update ordinal positions after item insertion or removal-predicted children's arithmetic performance. Nevertheless, these positional operations did not mediate the relation between magnitude processing (as measured by the acuity of the approximate number system) and arithmetic performance. Taken together, these findings suggest a unique role for positional ordinality in math development. We suggest that positional ordinality may aid children in their mental organization of number symbols, which may facilitate solving arithmetic computations and may support the development of novel numerical concepts.
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6
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Buijsman S, Tirado C. Spatial-numerical associations: Shared symbolic and non-symbolic numerical representations. Q J Exp Psychol (Hove) 2019; 72:2423-2436. [PMID: 30931820 DOI: 10.1177/1747021819844503] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
During the last decades, there have been a large number of studies into the number-related abilities of humans. As a result, we know that humans and non-human animals have a system known as the approximate number system that allows them to distinguish between collections based on their number of items, separately from any counting procedures. Dehaene and others have argued for a model on which this system uses representations for numbers that are spatial in nature and are shared by our symbolic and non-symbolic processing of numbers. However, there is a conflicting theoretical perspective in which there are no representations of numbers underlying the approximate number system, but only quantity-related representations. This perspective would then suggest that there are no shared representations between symbolic and non-symbolic processing. We review the evidence on spatial biases resulting from the activation of numerical representations, for both non-symbolic and symbolic tests. These biases may help decide between the theoretical differences; shared representations are expected to lead to similar biases regardless of the format, whereas different representations more naturally explain differences in biases, and thus behaviour. The evidence is not yet decisive, as the behavioural evidence is split: we expect bisection tasks to eventually favour shared representations, whereas studies on the spatial-numerical association of response codes (SNARC) effect currently favour different representations. We discuss how this impasse may be resolved, in particular, by combining these behavioural studies with relevant neuroimaging data. If this approach is carried forward, then it may help decide which of these two theoretical perspectives on number representations is correct.
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Affiliation(s)
| | - Carlos Tirado
- 2 Gösta Ekman Laboratory, Department of Psychology, Stockholm University, Stockholm, Sweden
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Kramer P, Bressan P, Grassi M. The SNARC effect is associated with worse mathematical intelligence and poorer time estimation. ROYAL SOCIETY OPEN SCIENCE 2018; 5:172362. [PMID: 30224999 PMCID: PMC6124133 DOI: 10.1098/rsos.172362] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/25/2017] [Accepted: 07/10/2018] [Indexed: 06/08/2023]
Abstract
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.
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Affiliation(s)
- Peter Kramer
- Dipartimento di Psicologia Generale, Università di Padova, Via Venezia 8, 35131 Padova, Italy
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Toomarian EY, Hubbard EM. On the genesis of spatial-numerical associations: Evolutionary and cultural factors co-construct the mental number line. Neurosci Biobehav Rev 2018; 90:184-199. [PMID: 29684402 PMCID: PMC5993626 DOI: 10.1016/j.neubiorev.2018.04.010] [Citation(s) in RCA: 45] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2017] [Revised: 04/11/2018] [Accepted: 04/12/2018] [Indexed: 01/29/2023]
Abstract
Mapping numbers onto space is a common cognitive representation that has been explored in both behavioral and neuroimaging contexts. Empirical work probing the diverse nature of these spatial-numerical associations (SNAs) has led researchers to question 1) how the human brain links numbers with space, and 2) whether this link is biologically vs. culturally determined. We review the existing literature on the development of SNAs and situate that empirical work within cognitive and neuroscientific theoretical frameworks. We propose that an evolutionarily-ancient frontal-parietal circuit broadly tuned to multiple magnitude dimensions provides the phylogenetic substrate for SNAs, while enculturation and sensorimotor experience shape their specific profiles. We then use this perspective to discuss educational implications and highlight promising avenues for future research.
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Affiliation(s)
- Elizabeth Y Toomarian
- Department of Educational Psychology, University of Wisconsin- Madison, 1025 W. Johnson St. Madison, WI, 53706, United States of America.
| | - Edward M Hubbard
- Department of Educational Psychology, University of Wisconsin- Madison, 1025 W. Johnson St. Madison, WI, 53706, United States of America
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Prefrontal neuromodulation reverses spatial associations of non-numerical sequences, but not numbers. Biol Psychol 2017; 128:39-49. [DOI: 10.1016/j.biopsycho.2017.07.008] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2017] [Revised: 07/12/2017] [Accepted: 07/12/2017] [Indexed: 11/20/2022]
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10
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Bonn CD, Cantlon JF. Spontaneous, modality-general abstraction of a ratio scale. Cognition 2017; 169:36-45. [PMID: 28806722 DOI: 10.1016/j.cognition.2017.07.012] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2016] [Revised: 07/26/2017] [Accepted: 07/29/2017] [Indexed: 11/24/2022]
Abstract
The existence of a generalized magnitude system in the human mind and brain has been studied extensively but remains elusive because it has not been clearly defined. Here we show that one possibility is the representation of relative magnitudes via ratio calculations: ratios are a naturally dimensionless or abstract quantity that could qualify as a common currency for magnitudes measured on vastly different psychophysical scales and in different sensory modalities like size, number, duration, and loudness. In a series of demonstrations based on comparisons of item sequences, we demonstrate that subjects spontaneously use knowledge of inter-item ratios within and across sensory modalities and across magnitude domains to rate sequences as more or less similar on a sliding scale. Moreover, they rate ratio-preserved sequences as more similar to each other than sequences in which only ordinal relations are preserved, indicating that subjects are aware of differences in levels of relative-magnitude information preservation. The ubiquity of this ability across many different magnitude pairs, even those sharing no sensory information, suggests a highly general code that could qualify as a candidate for a generalized magnitude representation.
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Affiliation(s)
- Cory D Bonn
- Department of Brain and Cognitive Sciences, 358 Meliora Hall, PO Box 270268, University of Rochester, Rochester, NY 14627-0258, United States.
| | - Jessica F Cantlon
- Department of Brain and Cognitive Sciences, 358 Meliora Hall, PO Box 270268, University of Rochester, Rochester, NY 14627-0258, United States.
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