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

Counteracting Implicit Conflicts by Electrical Inhibition of the Prefrontal Cortex

2016 ◽  
Vol 28 (11) ◽  
pp. 1737-1748 ◽  
Author(s):  
Philipp Alexander Schroeder ◽  
Roland Pfister ◽  
Wilfried Kunde ◽  
Hans-Christoph Nuerk ◽  
Christian Plewnia
Keyword(s):  
Working Memory ◽  
Direct Current ◽  
Transcranial Direct Current Stimulation ◽  
Number Line ◽  
Irrelevant Information ◽  
Snarc Effect ◽  
Direct Current Stimulation ◽  
Magnitude Processing ◽  
Automatic Activation ◽  
Task Irrelevant

Cognitive conflicts and distractions by task-irrelevant information often counteract effective and goal-directed behaviors. In some cases, conflicting information can even emerge implicitly, without an overt distractor, by the automatic activation of mental representations. For instance, during number processing, magnitude information automatically elicits spatial associations resembling a mental number line. This spatial–numerical association of response codes (SNARC) effect can modulate cognitive-behavioral performance but is also highly flexible and context-dependent, which points toward a critical involvement of working memory functions. Transcranial direct current stimulation to the PFC, in turn, has been effective in modulating working memory-related cognitive performance. In a series of experiments, we here demonstrate that decreasing activity of the left PFC by cathodal transcranial direct current stimulation consistently and specifically eliminates implicit cognitive conflicts based on the SNARC effect, but explicit conflicts based on visuospatial distraction remain unaffected. This dissociation is polarity-specific and appears unrelated to functional magnitude processing as classified by regular numerical distance effects. These data demonstrate a causal involvement of the left PFC in implicit cognitive conflicts based on the automatic activation of spatial–numerical processing. Corroborating the critical interaction of brain stimulation and neurocognitive functions, our findings suggest that distraction from goal-directed behavior by automatic activation of implicit, task-irrelevant information can be blocked by the inhibition of prefrontal activity.

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.

Interactivity, Efficiency, and Individual Differences in Mental Arithmetic

2013 ◽  
Vol 60 (4) ◽  
pp. 302-311 ◽  
Author(s):  
Frédéric Vallée-Tourangeau
Keyword(s):  
Working Memory ◽  
Processing Speed ◽  
Mental Arithmetic ◽  
Working Memory Capacity ◽  
Static Condition ◽  
Memory Capacity ◽  
Verbal Protocols ◽  
Attention Switching ◽  
Single Digit ◽  
Set Size

Thinking efficiency was examined in mental arithmetic as a function of the degree of interactivity afforded by the task. Participants carried out single-digit additions, involving either 7 or 11 numbers, as fast and as accurately as possible. They completed the sums in blocks, five from the short 7-number set first, and five from the longer 11-number set second. These sets were interpolated among a series of other tasks that measured numeracy and arithmetic skills, working memory capacity, visuo-spatial processing speed, and attention switching, in such a way as to permit the presentation of the sets twice, once with each of the sums presented on a piece of paper and participants placing their hands flat on the table and once with the sums presented as a set of manipulable tokens. Efficiency was measured as the ratio of performance over time invested. A significant interaction between condition and set size was observed: Efficiency was slightly better in the static condition for short sums but declined substantially relative to the interactive condition for long sums. Twenty-two percent of the variance in efficiency for hard sums in the static condition was explained by arithmetic skills and working memory capacity, whereas 45% of this variance was explained by arithmetic skills, working memory capacity, and attention switching skills in the interactive condition. A separate sample of 17 participants who provided concurrent verbal protocols as they solved the problems revealed that paths to solution and arithmetic strategies were substantially transformed by the opportunity to manipulate tokens.

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

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 Culture-Independent Prerequisites for Early Arithmetic

2018 ◽  
Vol 29 (9) ◽  
pp. 1383-1392 ◽  
Author(s):  
Robert A. Reeve ◽  
Fiona Reynolds ◽  
Jacob Paul ◽  
Brian L. Butterworth
Keyword(s):  
Working Memory ◽  
Cognitive Abilities ◽  
Cultural Practices ◽  
Visuospatial Working Memory ◽  
Single Digit ◽  
Correlation Matrices ◽  
Magnitude Comparison ◽  
Addition Task ◽  
Indigenous Children ◽  
Culture Independent

In numerate societies, early arithmetic development is associated with visuospatial working memory, executive functions, nonverbal intelligence, and magnitude-comparison abilities. To what extent do these associations arise from cultural practices or general cognitive prerequisites? Here, we administered tests of these cognitive abilities (Corsi Blocks, Raven’s Colored Progressive Matrices, Porteus Maze) to indigenous children in remote northern Australia, whose culture contains few counting words or counting practices, and to nonindigenous children from an Australian city. The indigenous children completed a standard nonverbal addition task; the nonindigenous children completed a comparable single-digit addition task. The correlation matrices among variables in the indigenous and nonindigenous children showed similar patterns of relationships, and parallel regression analyses showed that visuospatial working memory was the main predictor of addition performance in both groups. Our findings support the hypothesis that the same cognitive capacities promote competence for learners in both numerate and nonnumerate societies.

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