scholarly journals Reversing the manual digit bias in two-digit number comparison

2016 ◽  
Author(s):  
Thomas J. Faulkenberry
Keyword(s):  
Numerical Cognition ◽  
Number Line ◽  
Number Representation ◽  
Digit Number ◽  
Computer Mouse ◽  
Number Comparison ◽  
Number Representations ◽  
Mouse Movements ◽  
Embodied Representation ◽  
Fixed Standard

Though recent work in numerical cognition has supported the embodiment of number representations (e.g., a mental number line), little is known about the embodiment of 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.

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.

The Effect of External Representations on Numeric Tasks

2005 ◽  
Vol 58 (5) ◽  
pp. 817-838 ◽  
Author(s):  
Jiajie Zhang ◽  
Hongbin Wang
Keyword(s):  
Cognitive Processes ◽  
Numerical Cognition ◽  
Process Models ◽  
External Information ◽  
External Representations ◽  
Comparison Task ◽  
Digit Number ◽  
Internal Representations ◽  
Number Comparison ◽  
Number Representations

This article explores the effect of external representations on numeric tasks. Through several minor modifications on the previously reported two-digit number comparison task, we obtained different results. Rather than holistic comparison, we found parallel comparison. We argue that this difference was a reflection of different representational forms: The comparison was based on internal representations in previous studies but on external representations in our present study. This representational effect is discussed under a framework of distributed number representations. We propose that in numerical tasks involving external representations, numbers should be considered as distributed representations, and the behaviour in these tasks should be considered as the interactive processing of internal and external information through the interplay of perceptual and cognitive processes. We suggest that theories of number representations and process models of numerical cognition should consider external representations as an essential component.

scholarly journals Empirical and Theoretical Studies on Number Comparison: Design Parameters and Research Questions

Scientifica ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Meltem Ballan
Keyword(s):  
Research Question ◽  
Distance Effect ◽  
Number Line ◽  
Design Parameters ◽  
Number Representation ◽  
Sensory Representation ◽  
Number Comparison ◽  
Universal Approach ◽  
Research Questions ◽  
Size Congruity Effect

For well over one-hundred years, several key factors have been well established in the study of number comparison, including mental number line, numerical distance effect, and effect of sensory representation on number processing. The purpose of this article is to put some of these studies together to discuss design parameters and research questions addressed in the mental number comparison studies. Most of the studies discuss sensory representation and abstract number representation as well as degree of their interaction. In order to give the different views on a particular research question, the author classified studies under the related research questions. For example, Stroop and size congruity effect studies are addressed under this title chronologically. It was very clear that the design parameters and research question might change the interpretation of a task. It may be time to shift attention from the question of the interaction degree of sensory representation and abstract representation to a larger scope. The larger scope would be to understand the differences and similarities between different groups using a universal approach.

scholarly journals Task instructions modulate unit-decade binding in two-digit number representation

2018 ◽  
Author(s):  
Thomas J. Faulkenberry ◽  
Alexander Cruise ◽  
Samuel Shaki
Keyword(s):  
Compatibility Effect ◽  
Task Instruction ◽  
Late Response ◽  
Number Representation ◽  
Digit Number ◽  
Task Instructions ◽  
Computer Mouse ◽  
Task Requirements ◽  
Mere Presence ◽  
The Given

Previous studies have found decomposed processes, as well as holistic processes, in the representation of two-digit numbers. The present study investigated the influence of task instruction on such processes. Participants completed both magnitude and parity tasks in one of three instructional conditions, where they were asked to either consider two-digit numbers as a whole or to focus on one specific digit. In two experiments, we found that when participants were asked to consider the two digits as an integrated number, they always exhibited a unit-decade compatibility effect, indicating a failure of selective attention on the digit relevant to the given task. However, the mere presence of the neighboring digit is not a sufficient condition for the compatibility effect: when participants were explicitly asked to process a specific digit, their success/failure to selectively ignore the irrelevant digit depended on task requirements. Further, computer mouse tracking indicated that the locus of the compatibility effect was related to late response-related processing. The results signify the deep involvement of top-down processes in unit-decade binding for two-digit number representation.

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.

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 Tracking the continuous dynamics of numerical processing: A brief review and editorial

2018 ◽  
Author(s):  
Thomas J. Faulkenberry ◽  
Matthias Witte ◽  
Matthias Hartmann
Keyword(s):  
Numerical Cognition ◽  
Mental Arithmetic ◽  
Special Section ◽  
Past Research ◽  
Number Processing ◽  
Hand Tracking ◽  
Single Digit ◽  
Future Directions ◽  
Numerical Processing ◽  
Computer Mouse

Many recent studies in numerical cognition have moved beyond the use of purely chronometric techniques in favor of methods which track the continuous dynamics of numerical processing. Two examples of such techniques include eye tracking and hand tracking (or computer mouse tracking). To reflect this increased concentration on continuous methods, we have collected a group of 5 articles that utilize these techniques to answer some contemporary questions in numerical cognition. In this editorial, we discuss the two paradigms and provide a brief review of some of the work in numerical cognition that has profited from the use of these techniques. For both methods, we discuss the past research through the frameworks of single digit number processing, multidigit number processing, and mental arithmetic processing. We conclude with a discussion of the papers that have been contributed to this special section and point to some possible future directions for researchers interested in tracking the continuous dynamics of numerical processing.

Multi-digit Number Processing

2014 ◽  
Author(s):  
Hans-Christoph Nuerk ◽  
Korbinian Moeller ◽  
Klaus Willmes
Keyword(s):  
Numerical Cognition ◽  
Distance Effect ◽  
Number Processing ◽  
Place Value ◽  
Digit Number ◽  
Single Digit ◽  
Numerical Development ◽  
Conceptual Distinction ◽  
Place Identification

Only recently the focus in numerical cognition research has considered multi-digit number processing as a relatively new and yet understudied domain in mathematical cognition. In this chapter: (i) we argue that single-digit number processing is not sufficient to understand multi-digit number processing; (ii) provide an overview on which representations and effects have been investigated for multi-digit numbers; (iii) suggest a conceptual distinction between place-identification, place-value activation, and place-value computation; (iv) identify language influences on multi-digit number processing along that conceptual distinction; and (v) argue that for numerical development indices of multi-digit number processing may be more suitable predictors of later arithmetical performance than classical single-digit measure such as the distance effect or non-numerical variables (e.g., working memory). In the final section, we summarize the important issues in multi-digit number processing, outline future directions and try to encourage readers to contribute to a new, exciting, yet understudied domain of numerical cognition.

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