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.

scholarly journals On the Genesis of Spatial-Numerical Associations: Evolutionary and Cultural Factors Co- Construct the Mental Number Line

2018 ◽  
Author(s):  
Elizabeth Y Toomarian ◽  
Edward M. Hubbard
Keyword(s):  
Human Brain ◽  
Empirical Work ◽  
Number Line ◽  
Cultural Factors ◽  
Mental Number Line ◽  
Future Research ◽  
Cognitive Representation ◽  
Theoretical Frameworks ◽  
Educational Implications ◽  
Line P

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.

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.

Extending the Mental Number Line—How Do Negative Numbers Contribute?

Perception ◽  
10.1068/p7081 ◽  
2012 ◽  
Vol 41 (11) ◽  
pp. 1323-1335 ◽  
Author(s):  
Y u Zhang ◽  
Xuqun You
Keyword(s):  
Number Line ◽  
Mental Number Line ◽  
Holistic Processing ◽  
Negative Numbers ◽  
Absolute Value ◽  
Low Level ◽  
Task Requirements ◽  
Context Dependent ◽  
And Task

Previous studies suggest that there is an association between positive numbers and space; however, there is less agreement for negative numbers. The main purpose of the present study was to investigate the nature of the processing and representation of negative numbers, and the association between negative numbers and space. Results of the two experiments show that low-level processing (perception) of negative numbers can induce spatial shifts of attention. Whether this is caused by their numerical value or absolute value depends on the numerical context and task requirements, indicating that there are both components and holistic processing, and representation for negative numbers. The representation is automatically associated with leftward space; the coding and representation of the mental number line is adaptable to the specific numerical context and task requirements. The mental number line, therefore, can extend to the left side of zero, thus supporting the context-dependent view.

Moving on Down the (Mental Number) Line

2012 ◽  
Author(s):  
David Landy ◽  
Zachary J. Davis ◽  
Brian M. Guay ◽  
Megan L. Delaunay ◽  
Arthur Charlesworth ◽  
...  
Keyword(s):  
Number Line ◽  
Mental Number Line

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 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 Sharing a mental number line across individuals? The role of body position and empathy in joint numerical cognition

2018 ◽  
Vol 72 (7) ◽  
pp. 1732-1740 ◽  
Author(s):  
Matthias Hartmann ◽  
Martin H Fischer ◽  
Fred W Mast
Keyword(s):  
Numerical Cognition ◽  
Body Position ◽  
Random Number Generation ◽  
Number Line ◽  
Mental Number Line ◽  
Response Level ◽  
Spatial Reference ◽  
Mediating Role ◽  
Spatial Reference Frame

A growing body of research shows that the human brain acts differently when performing a task together with another person than when performing the same task alone. In this study, we investigated the influence of a co-actor on numerical cognition using a joint random number generation (RNG) task. We found that participants generated relatively smaller numbers when they were located to the left (vs. right) of a co-actor (Experiment 1), as if the two individuals shared a mental number line and predominantly selected numbers corresponding to their relative body position. Moreover, the mere presence of another person on the left or right side or the processing of numbers from loudspeaker on the left or right side had no influence on the magnitude of generated numbers (Experiment 2), suggesting that a bias in RNG only emerged during interpersonal interactions. Interestingly, the effect of relative body position on RNG was driven by participants with high trait empathic concern towards others, pointing towards a mediating role of feelings of sympathy for joint compatibility effects. Finally, the spatial bias emerged only after the co-actors swapped their spatial position, suggesting that joint spatial representations are constructed only after the spatial reference frame became salient. In contrast to previous studies, our findings cannot be explained by action co-representation because the consecutive production of numbers does not involve conflict at the motor response level. Our results therefore suggest that spatial reference coding, rather than motor mirroring, can determine joint compatibility effects. Our results demonstrate how physical properties of interpersonal situations, such as the relative body position, shape seemingly abstract cognition.

scholarly journals Reversing the Manual Digit Bias in Two-Digit Number Comparison

2017 ◽  
Vol 64 (3) ◽  
pp. 191-204 ◽  
Author(s):  
Thomas J. Faulkenberry ◽  
Alexander Cruise ◽  
Samuel Shaki
Keyword(s):  
Numerical Cognition ◽  
Number Line ◽  
Number Representation ◽  
Digit Number ◽  
Computer Mouse ◽  
Number Comparison ◽  
Number Representations ◽  
Mouse Movements ◽  
Embodied Representation ◽  
Fixed Standard

Abstract. Though recent work in numerical cognition has supported a strong tie between numerical and spatial representations (e.g., a mental number line), less is known about such ties in multi-digit number representations. Along this line, Bloechle, Huber, and Moeller (2015) found that pointing positions in two-digit number comparison were biased leftward toward the decade digit. Moreover, this bias was reduced in unit-decade incompatible pairs. In the present study, we tracked computer mouse movements as participants compared two-digit numbers to a fixed standard (55). Similar to Bloechle et al. (2015) , we found that trajectories exhibited a leftward bias that was reduced for unit-decade incompatible comparisons. However, when positions of response labels were reversed, the biases reversed. That is, we found a rightward bias for compatible pairs that was reduced for incompatible pairs. This result calls into question a purely embodied representation of place value structure and instead supports a competition model of two-digit number representation.

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