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.

The Development of Mental Representation of Numbers 0-10 in Elementary School Children

2019 ◽  
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 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.

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.

Spatial Representation of Time in Backspace

2018 ◽  
Vol 6 (2) ◽  
pp. 154-168
Author(s):  
Nicole Schwan ◽  
Peter Brugger ◽  
Elisabeth Huberle
Keyword(s):  
Spatial Representation ◽  
Number Line ◽  
Temporal Information ◽  
Numerical Magnitude ◽  
Midsagittal Plane ◽  
Egocentric Reference Frame ◽  
Temporal Domain ◽  
Large Numbers ◽  
The Right ◽  
Processing Mechanisms

Temporal information, numerical magnitude and space extension appear to share common representational mechanisms and be processed similarly in the brain. Evidence comes from the phenomenon of ‘pseudoneglect’, i.e. healthy persons’ orientation asymmetry toward the left side of space. Pseudoneglect is also evident along the mental number line which extends from small numbers on the left to large numbers on the right. In analogy to numbers, time is typically represented on a line extending from the left to the right side. It may thus be no surprise that pseudoneglect has been demonstrated in the temporal domain as well. Besides the perception of the space located anteriorly to our trunk (frontspace), we are able to represent the space behind us, which we cannot visually perceive (backspace). The translational model suggests a mapping of spatially defined information to the ipsilateral side of the egocentric reference frame in front- and backspace, while the rotational concept focuses on a 360° spatial representation around the midsagittal plane of the trunk. At the present stage of investigation, little is known about the representation of temporal information in backspace. In an attempt to fill this gap, we compared duration estimations of auditory stimuli in frontspace and backspace. Healthy right-handers were instructed to judge their duration relative to each other. We found a pseudoneglect-behavior not only in frontspace but also in backspace. The data are discussed in the context of common processing mechanisms for time, numbers and space and favor a translational over a rotational account for the representation of backspace. The results are further discussed with reference to potential consequences for the rehabilitation of hemispatial neglect.

scholarly journals Motion along the mental number line reveals shared representations for numerosity and space

eLife ◽  
2016 ◽  
Vol 5 ◽  
Author(s):  
Caspar M Schwiedrzik ◽  
Benjamin Bernstein ◽  
Lucia Melloni
Keyword(s):  
Reference Frame ◽  
Parietal Cortex ◽  
Visual Motion ◽  
Number Line ◽  
Mental Number Line ◽  
Motion Direction ◽  
Large Numbers ◽  
Cross Adaptation ◽  
The Right ◽  
Numerosity Perception

Perception of number and space are tightly intertwined. It has been proposed that this is due to ‘cortical recycling’, where numerosity processing takes over circuits originally processing space. Do such ‘recycled’ circuits retain their original functionality? Here, we investigate interactions between numerosity and motion direction, two functions that both localize to parietal cortex. We describe a new phenomenon in which visual motion direction adapts nonsymbolic numerosity perception, giving rise to a repulsive aftereffect: motion to the left adapts small numbers, leading to overestimation of numerosity, while motion to the right adapts large numbers, resulting in underestimation. The reference frame of this effect is spatiotopic. Together with the tuning properties of the effect this suggests that motion direction-numerosity cross-adaptation may occur in a homolog of area LIP. ‘Cortical recycling’ thus expands but does not obliterate the functions originally performed by the recycled circuit, allowing for shared computations across domains.

Neural Underpinnings of Numerical and Spatial Cognition: An fMRI Meta-Analysis of Brain Regions Associated with Symbolic Number, Arithmetic, and Mental Rotation

2019 ◽  
Author(s):  
Zachary Hawes ◽  
H Moriah Sokolowski ◽  
Chuka Bosah Ononye ◽  
Daniel Ansari
Keyword(s):  
Mental Rotation ◽  
Parietal Lobe ◽  
Meta Analysis ◽  
Likelihood Estimation ◽  
Brain Regions ◽  
Angular Gyrus ◽  
Number Representation ◽  
Neural Underpinnings ◽  
The Right ◽  
Symbolic Number

Where and under what conditions do spatial and numerical skills converge and diverge in the brain? To address this question, we conducted a meta-analysis of brain regions associated with basic symbolic number processing, arithmetic, and mental rotation. We used Activation Likelihood Estimation (ALE) to construct quantitative meta-analytic maps synthesizing results from 86 neuroimaging papers (~ 30 studies/cognitive process). All three cognitive processes were found to activate bilateral parietal regions in and around the intraparietal sulcus (IPS); a finding consistent with shared processing accounts. Numerical and arithmetic processing were associated with overlap in the left angular gyrus, whereas mental rotation and arithmetic both showed activity in the middle frontal gyri. These patterns suggest regions of cortex potentially more specialized for symbolic number representation and domain-general mental manipulation, respectively. Additionally, arithmetic was associated with unique activity throughout the fronto-parietal network and mental rotation was associated with unique activity in the right superior parietal lobe. Overall, these results provide new insights into the intersection of numerical and spatial thought in the human brain.

scholarly journals Comparison of the accuracy of intraoral scans between complete-arch scan and quadrant scan

2020 ◽  
Vol 21 (1) ◽  
Author(s):  
Youn-Gyeong Moon ◽  
Kyung-Min Lee
Keyword(s):  
Third Molar ◽  
Careful Consideration ◽  
Missing Teeth ◽  
Posterior Teeth ◽  
Anterior Teeth ◽  
Posterior Quadrant ◽  
Left Posterior ◽  
The Right ◽  
Best Fit ◽  
Posterior Area

Abstract Objective To compare the accuracy of complete-arch scans and quadrant scans obtained using a direct chairside intraoral scanner. Material and methods Intraoral scans were obtained from 20 adults without missing teeth except for the third molar. Maxillary and mandibular complete-arch scans were carried out, and 4 quadrant scans for each arch were performed to obtain right posterior, right anterior, left anterior, and left posterior quadrant scans. Complete-arch scans and quadrant scans were compared with corresponding model scans using best-fit surface-based registration. Shell/shell deviations were computed for complete-arch scans and quadrant scans and compared between the complete-arch scans and each quadrant scans. In addition, shell/shell deviations were calculated also for each individual tooth in complete-arch scans to evaluate factors which influence the accuracy of intraoral scans. Results Complete-arch scans showed relatively greater errors (0.09 ~ 0.10 mm) when compared to quadrant scans (0.05 ~ 0.06 mm). The errors were greater in the maxillary scans than in the mandibular scans. The evaluation of errors for each tooth showed that the errors were greater in posterior teeth than in anterior teeth. Comparing the right and left errors, the right side posterior teeth showed a more substantial variance than the left side in the mandibular scans. Conclusion The scanning accuracy has a difference between complete-arch scanning and quadrant scanning, particularly in the posterior teeth. Careful consideration is needed to avoid scanning inaccuracy for maxillary or mandibular complete-arch, particularly in the posterior area because a complete-arch scan might have potential error than a quadrant scan.

Chalastospora gossypii in a Maine Coon cat: case report and literature review

2021 ◽  
pp. 104063872110222
Author(s):  
Samantha M. Norris ◽  
Paula A. Schaffer ◽  
Noah B. Bander
Keyword(s):  
Soft Tissue ◽  
Needle Aspiration ◽  
Tissue Mass ◽  
Large Numbers ◽  
Formalin Fixed Paraffin ◽  
Formalin Fixed Paraffin Embedded ◽  
Soft Tissue Masses ◽  
Subcutaneous Mass ◽  
The Right ◽  
A Minor

A 15-y-old castrated male Maine Coon cat was evaluated for an ulcerated soft tissue mass on the right hindlimb that had been observed for 4 mo and had grown rapidly. A 3 × 3 cm soft, raised, amorphous, and ulcerated subcutaneous mass was observed on the lateral right metatarsus. In-house cytology via fine-needle aspiration was nondiagnostic. Incisional biopsy of the mass and further staging was declined, and amputation was elected. The amputated limb was submitted for histopathology, which revealed severe chronic nodular granulomatous dermatitis and multifocal granulomatous popliteal lymphadenitis with large numbers of intralesional fungal hyphae. Fungal PCR and sequencing on formalin-fixed, paraffin-embedded tissue identified Chalastospora gossypii. No adjunctive therapy was elected at the time. The patient has done well clinically 1 y post-operatively. C. gossypii is a rare microfungus found worldwide and is considered a minor pathogen of several plants. To our knowledge, infection by this fungus has not been reported previously in veterinary species. Features in our case are comparable to other mycotic infections. Nodular granulomatous mycotic dermatitis and cellulitis, although uncommon, should be a differential for soft tissue masses in veterinary species; C. gossypii is a novel isolate.

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 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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