The representational space of numerical magnitude: Illusions of length

2008 ◽  
Vol 61 (10) ◽  
pp. 1496-1514 ◽  
Author(s):  
Maria-Dolores De Hevia ◽  
Luisa Girelli ◽  
Emanuela Bricolo ◽  
Giuseppe Vallar
Keyword(s):  
Mental Representation ◽  
Number Line ◽  
Numerical Magnitude ◽  
Numerical Representation ◽  
Reproduction Task ◽  
The Core ◽  
Spatial Extension ◽  
Representational Space ◽  
Spatial Resources ◽  
Cognitive Illusion

In recent years, a growing amount of evidence concerning the relationships between numerical and spatial representations has been interpreted, by and large, in favour of the mental number line hypothesis—namely, the analogue continuum where numbers are spatially represented (Dehaene, 1992; Dehaene, Piazza, Pinel, & Cohen, 2003). This numerical representation is considered the core of number meaning and, accordingly, needs to be accessed whenever numbers are semantically processed. The present study explored, by means of a length reproduction task, whether besides the activation of lateralized spatial codes, numerical processing modulates the mental representation of a horizontal spatial extension. Mis-estimations of length induced by Arabic numbers are interpreted in terms of a cognitive illusion, according to which the elaboration of magnitude information brings about an expansion or compression of the mental representation of spatial extension. These results support the hypothesis that visuo-spatial resources are involved in the representation of numerical magnitude.

Developmental Dyscalculia in Adults: Beyond Numerical Magnitude Impairment

2017 ◽  
Vol 51 (6) ◽  
pp. 600-611 ◽  
Author(s):  
Alice De Visscher ◽  
Marie-Pascale Noël ◽  
Mauro Pesenti ◽  
Valérie Dormal
Keyword(s):  
Mental Representation ◽  
Healthy Adults ◽  
Numerical Magnitude ◽  
Developmental Dyscalculia ◽  
Common System ◽  
The Core ◽  
Magnitude Processing ◽  
Core Deficit ◽  
Face Categorization ◽  
Numerical Magnitudes

Numerous studies have tried to identify the core deficit of developmental dyscalculia (DD), mainly by assessing a possible deficit of the mental representation of numerical magnitude. Research in healthy adults has shown that numerosity, duration, and space share a partly common system of magnitude processing and representation. However, in DD, numerosity processing has until now received much more attention than the processing of other non-numerical magnitudes. To assess whether or not the processing of non-numerical magnitudes is impaired in DD, the performance of 15 adults with DD and 15 control participants was compared in four categorization tasks using numerosities, lengths, durations, and faces (as non-magnitude-based control stimuli). Results showed that adults with DD were impaired in processing numerosity and duration, while their performance in length and face categorization did not differ from controls’ performance. Our findings support the idea of a nonsymbolic magnitude deficit in DD, affecting numerosity and duration processing but not length processing.

Spatial Cues Affect Mental Number Line Bisections

2010 ◽  
Vol 57 (4) ◽  
pp. 315-319 ◽  
Author(s):  
Michael E. R. Nicholls ◽  
Alissandra M. McIlroy
Keyword(s):  
Attentional Bias ◽  
Neural Circuits ◽  
Mental Representations ◽  
Physical Space ◽  
Number Line ◽  
Mental Number Line ◽  
Numerical Magnitude ◽  
Spatial Cues ◽  
Representational Space ◽  
High Level

Numerical magnitude is coded left-to-right along a mental number line (MNL). The MNL can be distorted by an attentional bias directed to the left side, known as pseudoneglect – making the left of the MNL appear longer. We investigated whether this distortion can be corrected using spatial cues. Participants (n = 17) made forced-choice discriminations of relative numerical length while spatial cues were presented to the left, right, and both sides. Overall, participants overestimated the leftward length of the MNL, consistent with the effect of pseudoneglect. The bias was present for left- and neutral-cues, but was eliminated by right-cues. The results demonstrate that low-level manipulation of attention in physical space affects attention for high-level mental representations. The effect of cueing may reflect common activation of overlapping neural circuits that are thought to underlie attention in physical and representational space.

EXPRESS: Spatial-numerical associations from a novel paradigm support the Mental Number Line account

2021 ◽  
pp. 174702182110087
Author(s):  
Lauren Aulet ◽  
Sami R Yousif ◽  
Stella Lourenco
Keyword(s):  
Memory Task ◽  
Verbal Working Memory ◽  
Number Line ◽  
Mental Number Line ◽  
Task Demands ◽  
Numerical Magnitude ◽  
The Novel ◽  
Alternative Account ◽  
Subject Design ◽  
Multiple Tasks

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 judgments and/or categorical responses. In the novel ‘Where was The Number?’ task, no explicit numerical judgments 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.

The Oxford Handbook of Grammatical Number

2021 ◽  
Keyword(s):  
Case Studies ◽  
Mental Representation ◽  
Noun Phrases ◽  
Numeral Classifiers ◽  
Number Marking ◽  
The Core ◽  
Grammatical Number ◽  
The Relationship ◽  
Linguistic Means

This volume offers an overview of current research on grammatical number in language. The chapters Part i of the handbook present foundational notions in the study of grammatical number covering the semantic analyses of plurality, the mass–count distinction, the relationship between number and quantity expressions and the mental representation of number and individuation. The core instance of grammatical number is marking for number distinctions in nominal expressions as in English the book/the books and the chapters in Part ii, Number in the nominal domain, explore morphological, semantic, and syntactic aspects of number marking within noun phrases. The contributions examine morphological marking of number the relationship between syntax and nominal number marking, and the interactions between numeral classifiers with semantic number and number marking. They also address cases of mismatches in form and meaning with respect to number displayed by lexical plurals and collective nouns. The final chapter reviews nominal number processing from the perspective of language pathologies. While number marking on nouns has been the focus of most research on number, number distinctions can also be found in the event domain. Part iii, Number in the event domain, presents an overview of different linguistic means of expressing plurality in the event domain, covering verbal plurality marking, pluractional modifiers of the form Noun preposition Noun, frequency adjectives and dependent indefinites. Part iv provides fifteen case studies examining different aspects of grammatical number marking in a range of typologically diverse languages.

Spatial-numerical associations from a novel paradigm support the mental number line account

2021 ◽  
Author(s):  
Lauren S Aulet ◽  
Sami Ryan Yousif ◽  
Stella F. Lourenco
Keyword(s):  
Memory Task ◽  
Verbal Working Memory ◽  
Number Line ◽  
Mental Number Line ◽  
Task Demands ◽  
Numerical Magnitude ◽  
The Novel ◽  
Alternative Account ◽  
Subject Design ◽  
Multiple Tasks

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 judgments and/or categorical responses. In the novel ‘Where was The Number?’ task, no explicit numerical judgments 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.

Activating, seeking, and creating common ground

2009 ◽  
Vol 17 (2) ◽  
pp. 331-355 ◽  
Author(s):  
Istvan Kecskes ◽  
Fenghui Zhang
Keyword(s):  
Mental Representation ◽  
Common Ground ◽  
A Priori ◽  
Emergent Property ◽  
Shared Knowledge ◽  
Construction Process ◽  
Cognitive Approach ◽  
The Core ◽  
Communicative Process ◽  
Integrated Concept

This paper argues that current pragmatic theories fail to describe common ground in its complexity because they usually retain a communication-as-transfer-between-minds view of language, and disregard the fact that disagreement and egocentrism of speaker-hearers are as fundamental parts of communication as agreement and cooperation. On the other hand, current cognitive research has overestimated the egocentric behavior of the dyads and argued for the dynamic emergent property of common ground while devaluing the overall significance of cooperation in the process of verbal communication. The paper attempts to eliminate this conflict and proposes to combine the two views into an integrated concept of common ground, in which both core common ground (assumed shared knowledge, a priori mental representation) and emergent common ground (emergent participant resource, a post facto emergence through use) converge to construct a dialectical socio-cultural background for communication.
Both cognitive and pragmatic considerations are central to this issue. While attention (through salience, which is the cause for interlocutors’ egocentrism) explains why emergent property unfolds, intention (through relevance, which is expressed in cooperation) explains why presumed shared knowledge is needed. Based on this, common ground is perceived as an effort to converge the mental representation of shared knowledge present as memory that we can activate, shared knowledge that we can seek, and rapport, as well as knowledge that we can create in the communicative process. The socio-cognitive approach emphasizes that common ground is a dynamic construct that is mutually constructed by interlocutors throughout the communicative process. The core and emergent components join in the construction of common ground in all stages, although they may contribute to the construction process in different ways, to different extents, and in different phases of the communicative process.

Order and Magnitude Share a Common Representation in Parietal Cortex

2009 ◽  
Vol 21 (11) ◽  
pp. 2114-2120 ◽  
Author(s):  
Michael S. Franklin ◽  
John Jonides
Keyword(s):  
Distance Effect ◽  
Number Line ◽  
Judgment Task ◽  
Mental Number Line ◽  
Numerical Magnitude ◽  
Intraparietal Sulcus ◽  
Ordinal Information ◽  
Common Representation ◽  
Distance Effects

The role of the intraparietal sulcus (IPS) in the representation of numerical magnitude is well established. Recently, there has also been speculation that the IPS is involved in the representation of ordinal information as well. These claims, however, overlook the fact that all neuroimaging paradigms in which participants make judgments about either magnitude and/or order result in a behavioral distance effect (i.e., the comparison is easier when the stimuli span a greater distance). This leaves open two possibilities: It may be that activation of the IPS is due to the mechanism that yields distance effects, or it may be that the IPS is involved in the representation of information about both magnitude and order. The current study used fMRI to compare a magnitude task in which participants show distance effects to an order-judgment task that yields reverse-distance effects. The results reveal activation of the IPS for both the magnitude and order tasks that is based on participants' strategies as opposed to the actual distance between the numbers. This leads to the conclusion that the IPS represents a mental number line, and that accessing this line can lead to distance effects when participants compare magnitudes and to reverse-distance effects when participants check for order.

scholarly journals The Force of Numbers: Investigating Manual Signatures of Embodied Number Processing

2021 ◽  
Vol 14 ◽  
Author(s):  
Alex Miklashevsky ◽  
Oliver Lindemann ◽  
Martin H. Fischer
Keyword(s):  
Embodied Cognition ◽  
Grip Force ◽  
Numerical Cognition ◽  
Stimulus Presentation ◽  
Number Line ◽  
Number Processing ◽  
New Technique ◽  
Numerical Magnitude ◽  
Left Hand ◽  
Number Magnitude

The study has two objectives: (1) to introduce grip force recording as a new technique for studying embodied numerical processing; and (2) to demonstrate how three competing accounts of numerical magnitude representation can be tested by using this new technique: the Mental Number Line (MNL), A Theory of Magnitude (ATOM) and Embodied Cognition (finger counting-based) account. While 26 healthy adults processed visually presented single digits in a go/no-go n-back paradigm, their passive holding forces for two small sensors were recorded in both hands. Spontaneous and unconscious grip force changes related to number magnitude occurred in the left hand already 100–140 ms after stimulus presentation and continued systematically. Our results support a two-step model of number processing where an initial stage is related to the automatic activation of all stimulus properties whereas a later stage consists of deeper conscious processing of the stimulus. This interpretation generalizes previous work with linguistic stimuli and elaborates the timeline of embodied cognition. We hope that the use of grip force recording will advance the field of numerical cognition research.

scholarly journals Cognitive mediators of US—China differences in early symbolic arithmetic

PLoS ONE ◽  
2021 ◽  
Vol 16 (8) ◽  
pp. e0255283
Author(s):  
John E. Opfer ◽  
Dan Kim ◽  
Lisa K. Fazio ◽  
Xinlin Zhou ◽  
Robert S. Siegler
Keyword(s):  
Standardized Tests ◽  
Number Line ◽  
Chinese Children ◽  
Numerical Magnitude ◽  
Magnitude Comparison ◽  
Cognitive Mediators ◽  
Number Line Estimation ◽  
Mathematics Knowledge ◽  
Us Children ◽  
Symbolic Number

Chinese children routinely outperform American peers in standardized tests of mathematics knowledge. To examine mediators of this effect, 95 Chinese and US 5-year-olds completed a test of overall symbolic arithmetic, an IQ subtest, and three tests each of symbolic and non-symbolic numerical magnitude knowledge (magnitude comparison, approximate addition, and number-line estimation). Overall Chinese children performed better in symbolic arithmetic than US children, and all measures of IQ and number knowledge predicted overall symbolic arithmetic. Chinese children were more accurate than US peers in symbolic numerical magnitude comparison, symbolic approximate addition, and both symbolic and non-symbolic number-line estimation; Chinese and U.S. children did not differ in IQ and non-symbolic magnitude comparison and approximate addition. A substantial amount of the nationality difference in overall symbolic arithmetic was mediated by performance on the symbolic and number-line tests.

“1-2-3”: Is There a Temporal Number Line?

2008 ◽  
Vol 55 (3) ◽  
pp. 143-150 ◽  
Author(s):  
Dana Müller ◽  
Wolf Schwarz
Keyword(s):  
Number Line ◽  
Congruity Effect ◽  
Snarc Effect ◽  
Numerical Magnitude ◽  
Response Hand ◽  
Semantic Congruity ◽  
Left Response ◽  
The Right ◽  
Semantic Congruity Effect

Abstract. Evidence suggests that numbers are intimately related to space ( Dehaene, Bossini, & Giraux, 1993 ; Hubbard, Piazza, Pinel, & Dehaene, 2005 ). Recently, Walsh (2003) suggested that numbers might also be closely related to time. To investigate this hypothesis we asked participants to compare two digits that were presented in a serial manner, i.e., one after another. Temporally ascending digit pairs (such as 2-3) were responded to faster than temporally descending pairs (3-2). This effect was, in turn, qualified by a local SNARC (spatial numerical association of response codes) effect and a local semantic congruity effect (SCE). Moreover, we observed a global numerical SCE only for temporally descending digit pairs. However, we did not observe a global SNARC effect, i.e., an interaction of numerical magnitude and the right/left response hand. We discuss our results in terms of overlearned forward-associations (“1-2-3”) as formed by our ubiquitous cognitive routines to count off objects or events.

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