scholarly journals Learning to run the number line: the development of attentional shifts during single‐digit arithmetic

2020 ◽  
Vol 1477 (1) ◽  
pp. 79-90
Author(s):  
Andrea Díaz‐Barriga Yáñez ◽  
Auriane Couderc ◽  
Léa Longo ◽  
Annabelle Merchie ◽  
Hanna Chesnokova ◽  
...  
Keyword(s):  
Number Line ◽  
Single Digit ◽  
Attentional Shifts

scholarly journals Not toeing the number line for simple arithmetic: Two large-n conceptual replications of Mathieu et al. (Cognition, 2016, Experiment 1)

2021 ◽  
Vol 7 (3) ◽  
pp. 248-258 ◽  
Author(s):  
Jamie I. D. Campbell ◽  
Yalin Chen ◽  
Maham Azhar
Keyword(s):  
Number Line ◽  
Operation Condition ◽  
Single Digit ◽  
Simple Arithmetic ◽  
Position Effects ◽  
Large N ◽  
Addition And Subtraction ◽  
Mixed Operation ◽  
The Right ◽  
The University

We conducted two conceptual replications of Experiment 1 in Mathieu, Gourjon, Couderc, Thevenot, and Prado (2016, https://doi.org/10.1016/j.cognition.2015.10.002). They tested a sample of 34 French adults on mixed-operation blocks of single-digit addition (4 + 3) and subtraction (4 – 3) with the three problem elements (O1, +/-, O2) presented sequentially. Addition was 34 ms faster if O2 appeared 300 ms after the operation sign and displaced 5° to the right of central fixation, whereas subtraction was 19 ms faster when O2 was displaced to the left. Replication Experiment 1 (n = 74 recruited at the University of Saskatchewan) used the same non-zero addition and subtraction problems and trial event sequence as Mathieu et al., but participants completed blocks of pure addition and pure subtraction followed by the mixed-operation condition used by Mathieu et al. Addition RT showed a 32 ms advantage with O2 shifted rightward relative to leftward but only in mixed-operation blocks. There was no effect of O2 position on subtraction RT. Experiment 2 (n = 74) was the same except mixed-operation blocks occurred before the pure-operation blocks. There was an overall 13 ms advantage with O2 shifted right relative to leftward but no interaction with operation or with mixture (i.e., pure vs mixed operations). Nonetheless, the rightward RT advantage was statistically significant for both addition and subtraction only in mixed-operation blocks. Taken together with the robust effects of mixture in Experiment 1, the results suggest that O2 position effects in this paradigm might reflect task specific demands associated with mixed operations.

The fractions SNARC revisited: Processing fractions on a consistent mental number line

2018 ◽  
Vol 71 (8) ◽  
pp. 1761-1770 ◽  
Author(s):  
Elizabeth Y Toomarian ◽  
Edward M Hubbard
Keyword(s):  
Number Line ◽  
Mental Number Line ◽  
Snarc Effect ◽  
Spatial Representations ◽  
Comparison Task ◽  
Single Digit ◽  
Magnitude Processing ◽  
Number Comparison ◽  
Within Subjects ◽  
Solid Foundation

The ability to understand fractions is key to establishing a solid foundation in mathematics, yet children and adults struggle to comprehend them. Previous studies have suggested that these struggles emerge because people fail to process fraction magnitude holistically on the mental number line (MNL), focusing instead on fraction components. Subsequent studies have produced evidence for default holistic processing but examined only magnitude processing, not spatial representations. We explored the spatial representations of fractions on the MNL in a series of three experiments. Experiment 1 replicated Bonato et al.; 30 naïve undergraduates compared unit fractions (1/1-1/9) to 1/5, resulting in a reverse SNARC (Spatial-Numerical Association of Response Codes) effect. Experiment 2 countered potential strategic biases induced by the limited set of fractions used by Bonato et al. by expanding the stimulus set to include all irreducible, single-digit proper fractions and asked participants to compare them against 1/2. We observed a classic SNARC effect, completely reversing the pattern from Experiment 1. Together, Experiments 1 and 2 demonstrate that stimulus properties dramatically impact spatial representations of fractions. In Experiment 3, we demonstrated within-subjects reliability of the SNARC effect across both a fractions and whole number comparison task. Our results suggest that adults can indeed process fraction magnitudes holistically, and that their spatial representations occur on a consistent MNL for both whole numbers and fractions.

Running the number line: Rapid shifts of attention in single-digit arithmetic

Cognition ◽  
2016 ◽  
Vol 146 ◽  
pp. 229-239 ◽  
Author(s):  
Romain Mathieu ◽  
Audrey Gourjon ◽  
Auriane Couderc ◽  
Catherine Thevenot ◽  
Jérôme Prado
Keyword(s):  
Number Line ◽  
Single Digit

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.

scholarly journals Working memory and number line representations in single-digit addition: Approximate versus exact, nonsymbolic versus symbolic

2015 ◽  
Vol 68 (6) ◽  
pp. 1148-1167 ◽  
Author(s):  
Iro Xenidou-Dervou ◽  
Menno van der Schoot ◽  
Ernest C. D. M. van Lieshout
Keyword(s):  
Working Memory ◽  
Number Line ◽  
Single Digit

Extending the Mental Number Line

2011 ◽  
Vol 219 (1) ◽  
pp. 3-22 ◽  
Author(s):  
Hans-Christoph Nuerk ◽  
Korbinian Moeller ◽  
Elise Klein ◽  
Klaus Willmes ◽  
Martin H. Fischer
Keyword(s):  
Everyday Life ◽  
Number Line ◽  
Mental Number Line ◽  
Number Processing ◽  
First Year ◽  
Digit Number ◽  
Single Digit ◽  
Comprehensive Review ◽  
Cognitive Research ◽  
Current Review

Multi-digit number processing is ubiquitous in our everyday life – even in school, multi-digit numbers are computed from the first year onward. Yet, many problems children and adults have are about the relation of different digits (for instance with fractions, decimals, or carry effects in multi-digit addition). Cognitive research has mainly focused on single-digit processing, and there is no comprehensive review of the different multi-digit number processing types and effects. The current review aims to fill this gap. First, we argue that effects observed in single-digit tasks cannot simply be transferred to multi-digit processing. Next, we list 16 effect types and processes which are specific for multi-digit number processing. We then discuss the development of multi-digit number processing, its neurocognitive correlates, its cultural or language-related modulation, and finally some models for multi-digit number processing. We finish with conclusions and perspectives about where multi-digit number processing research may or should be heading in following years.

scholarly journals Cerebellar degeneration selectively disrupts continuous mental operations

2020 ◽  
Author(s):  
Samuel D. McDougle ◽  
Jonathan Tsay ◽  
Benjamin Pitt ◽  
Maedbh King ◽  
William Saban ◽  
...  
Keyword(s):  
Mental Rotation ◽  
Computational Models ◽  
Mental Representations ◽  
Number Line ◽  
Cerebellar Degeneration ◽  
Control Group ◽  
Single Digit ◽  
General Role ◽  
Mental Operations ◽  
Discrete Representations

ABSTRACTInspired by computational models of how the cerebellum supports the coordination of movement, we propose a novel hypothesis to specify constraints on how this subcortical structure contributes to higher-level cognition. Specifically, we propose that the cerebellum helps facilitate dynamic continuous transformations of mental representations (CoRT). To test this hypothesis, we compared the performance of individuals with cerebellar degeneration (CD) on tasks that entail continuous movement-like mental operations with tasks that entail more discrete mental operations. In the first pair of experiments, individuals with CD were impaired on a mental rotation task, showing a slower rate of mental rotation compared to control participants. In contrast, the rate at which they scanned discrete representations in visual working memory was similar to that observed in the control group. In the second pair of experiments, we turned to mathematical cognition as a test of the generality of the CoRT hypothesis. Individuals with CD were selectively impaired in adding single-digit numbers, a task hypothesized to entail a mental operation involving continuous transformations along a mental number line. In contrast, their rate of performing arithmetic operations thought to involve retrieval from a look-up table was unimpaired. These results, obtained in disparate task domains, suggest a general role for the cerebellum in coordinating dynamic transformations in mental space, paralleling key features of computational theories concerning the cerebellum’s role in coordinated movement.

The Number Line And Mental Arithmetic

1990 ◽  
Vol 38 (4) ◽  
pp. 44-46
Author(s):  
Theodore E. Kurland
Keyword(s):  
Mental Arithmetic ◽  
Number Line ◽  
Single Digit ◽  
Addition And Subtraction

Some students have easily recognized difficulties with addition and subtraction. Some have no trouble adding or subtracting single-digit numbers when the sums are less than ten (7 + 2, 5 + 4, etc.) but have to resort to their fingers for sums greater than ten (7 + 5, 8 + 6, etc.). Other students have no difficulty adding numbers whose sums are greater than ten, such as 7 + 5, but have difficulty determining their differences, like 12 − 7. Finally, some students have no difficulty adding 7 + 5 or 8 + 4 but cannot mentall y add 17 + 5 or 18 + 4 or recognize the connection between the sum of singledigit numbers and numbers inc reased by orders of ten. Any one or a combination of these difficulties may appear when students compute; moreover, these problems will continue to plague them, curtailing their confidence and development in mathematics and mental arithmetic.

scholarly journals Finger Tracking Reveals the Covert Stages of Mental Arithmetic

Open Mind ◽  
2017 ◽  
Vol 1 (1) ◽  
pp. 30-41 ◽  
Author(s):  
Pedro Pinheiro-Chagas ◽  
Dror Dotan ◽  
Manuela Piazza ◽  
Stanislas Dehaene
Keyword(s):  
Mental Arithmetic ◽  
Number Line ◽  
Mental Number Line ◽  
Correct Result ◽  
Single Digit ◽  
Absolute Value ◽  
Transient Activation ◽  
Novel Method ◽  
Finger Tracking ◽  
The Right

We introduce a novel method capable of dissecting the succession of processing stages underlying mental arithmetic, thus revealing how two numbers are transformed into a third. We asked adults to point to the result of single-digit additions and subtractions on a number line, while their finger trajectory was constantly monitored. We found that the two operands are processed serially: the finger first points toward the larger operand, then slowly veers toward the correct result. This slow deviation unfolds proportionally to the size of the smaller operand, in both additions and subtractions. We also observed a transient operator effect: a plus sign attracted the finger to the right and a minus sign to the left and a transient activation of the absolute value of the subtrahend. These findings support a model whereby addition and subtraction are computed by a stepwise displacement on the mental number line, starting with the larger number and incrementally adding or subtracting the smaller number.

Sign in / Sign up

Export Citation Format

Share Document