Automaticity for numerical magnitude of two-digit Arabic numbers in children

Children's comparison of different-length numbers: Managing different attributes in multidigit number processing

In everyday life the comparison of numbers usually occurs between numbers with different numbers of digits. However, experimental research here is scarce. Recent research has shown that adults respond faster to congruent pairs (the initial digit in the number with more digits is larger, e.g., 2384 vs. 107) than to incongruent pairs (the initial digit is larger in the number with fewer digits, e.g., 2675 vs. 398). This has been interpreted as support for the processing of multiple attributes in parallel and against serial accounts. The current research asked whether there is a change in the relevance of these attributes as school grades increase. School-age children from the second to sixth grades (N = 206) were presented with pairs of numbers that had either the same number of digits (3 vs. 3 or 4 vs. 4) or a different number of digits (3 vs. 4). In this latter condition, the stimuli, matched by distance, could be either length/digit congruent (e.g., 2384 vs. 107) or length/digit incongruent (e.g., 2675 vs. 398). Linear mixed models showed a length/digit congruity effect from second graders. Interestingly, in the response time measure, congruity interacted with school grade and the side in which the larger number of the pair was presented. Whereas these results support a model that considers number comparison as a process that weighs different attributes in parallel, it is also argued that developmental changes are associated with differences in the level of automatization of the componential skills involved in the comparison.

The neural differences of arithmetic verification performance depend on math skill: Evidence from event-related potential

AIM

Math skill is a basic need for an individual, as a career prospect. However, little is known about early brain processes of arithmetic between individuals with different math skill. Therefore, we questioned the modulation of the amplitude of an early negative component by math skill level in an arithmetic verification paradigm using event-related potential (ERP).

METHODS

Thirty-six right-handed participants were assigned in two groups of high- and low-performing students. Their electroencephalogram was recorded while they completed an arithmetic verification task. Simple arithmetic operands were made by random digits from 1 to 9. Addition and subtraction operations were equally used in correct and incorrect responses. The accuracy scores, reaction times, and peak amplitude of the negativity in 200-400 ms time window were analyzed.

RESULTS

The high-performing group showed significantly higher response speeds, and they were more accurate than the low-performing group. The group × region interaction effect was significant. The high-performing group showed a significantly greater negativity, particularly in parietal region, while the low-performing group showed a significantly deeper negativity in frontal and prefrontal region. In the low-performing group, there were significant peak amplitude differences between the anterior and posterior areas. However, such differences were not detected in the high-performing group.

CONCLUSION

Students with different mathematical performance showed distinct patterns in early processing of arithmetic verification, as reflected by differences in negativity at 200-400 ms at anterior and posterior. This suggests that ERPs could be used to differentiate math mastery at neural level which is beneficial in educational and clinical contexts.

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

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.

Single-digit Arabic numbers do not automatically activate magnitude representations in adults or in children: evidence from the symbolic same-different task

We investigated whether the mere presentation of single-digit Arabic numbers activates their magnitude representations using a visually-presented symbolic same-different task for 20 adults and 15 children. Participants saw two single-digit Arabic numbers on a screen and judged whether the numbers were the same or different. We examined whether reaction time in this task was primarily driven by (objective or subjective) perceptual similarity, or by the numerical difference between the two digits. We reasoned that, if Arabic numbers automatically activate magnitude representations, a numerical function would best predict reaction time; but if Arabic numbers do not automatically activate magnitude representations, a perceptual function would best predict reaction time. Linear regressions revealed that a perceptual function, specifically, subjective visual similarity, was the best and only significant predictor of reaction time in adults and in children. These data strongly suggest that, in this task, single-digit Arabic numbers do not necessarily automatically activate magnitude representations in adults or in children. As the first study to date to explicitly study the developmental importance of perceptual factors in the symbolic same-different task, we found no significant differences between adults and children in their reliance on perceptual information in this task. Based on our findings, we propose that visual properties may play a key role in symbolic number judgements.

My brain knows numbers! - an ERP study of preschoolers' numerical knowledge

This study investigated brain activity in numerical processing at early stages of development. Brain activity of preschoolers was measured while they performed a numerical Stroop task. Participants were asked to decide which of two digits was numerically or physically larger. Behavioral distance and size congruity effects (SiCEs) were found. However, a reverse facilitation was observed, where responses to neutral trials were faster than to congruent ones. The event-related potentials data showed the expected distance effect at occipitoparietal scalp areas. Moreover, conflict was related to effects both at frontal and parietal scalp areas. In addition, there was a difference between the timing of the interference compared to the facilitation components in the SiCE. In parietal scalp areas, facilitation was significant in an early time window and interference was significant at a later time window. This is consistent with the idea that facilitation and interference are separate processes. Our findings indicate that children as young as 5–6 years old can automatically process the numerical meaning of numerals. In addition, our findings are consistent with the idea that, children might use both frontal and parietal areas in order to process irrelevant numerical information.

Automatic and intentional number processing both rely on intact right parietal cortex: a combined FMRI and neuronavigated TMS study

Practice and training usually lead to performance increase in a given task. In addition, a shift from intentional toward more automatic processing mechanisms is often observed. It is currently debated whether automatic and intentional processing is subserved by the same or by different mechanism(s), and whether the same or different regions in the brain are recruited. Previous correlational evidence provided by behavioral, neuroimaging, modeling, and neuropsychological studies addressing this question yielded conflicting results. Here we used transcranial magnetic stimulation (TMS) to compare the causal influence of disrupting either left or right parietal cortex during automatic and intentional numerical processing, as reflected by the size congruity effect and the numerical distance effect, respectively. We found a functional hemispheric asymmetry within parietal cortex with only the TMS-induced right parietal disruption impairing both automatic and intentional numerical processing. In contrast, disrupting the left parietal lobe with TMS, or applying sham stimulation, did not affect performance during automatic or intentional numerical processing. The current results provide causal evidence for the functional relevance of right, but not left, parietal cortex for intentional, and automatic numerical processing, implying that at least within the parietal cortices, automatic, and intentional numerical processing rely on the same underlying hemispheric lateralization.

Individual differences in children's mathematical competence are related to the intentional but not automatic processing of Arabic numerals

In recent years, there has been an increasing focus on the role played by basic numerical magnitude processing in the typical and atypical development of mathematical skills. In this context, tasks measuring both the intentional and automatic processing of numerical magnitude have been employed to characterize how children's representation and processing of numerical magnitude changes over developmental time. To date, however, there has been little effort to differentiate between different measures of 'number sense'. The aim of the present study was to examine the relationship between automatic and intentional measures of magnitude processing as well as their relationships to individual differences in children's mathematical achievement. A group of 119 children in 1st and 2nd grade were tested on the physical size congruity paradigm (automatic processing) as well as the number comparison paradigm to measure the ratio effect (intentional processing). The results reveal that measures of intentional and automatic processing are uncorrelated with one another, suggesting that these tasks tap into different levels of numerical magnitude processing in children. Furthermore, while children's performance on the number comparison paradigm was found to correlate with their mathematical achievement scores, no such correlations could be obtained for any of the measures typically derived from the physical size congruity task. These findings therefore suggest that different tasks measuring 'number sense' tap into different levels of numerical magnitude representation that may be unrelated to one another and have differential predictive power for individual differences in mathematical achievement.