Development Of Numerical Cognition Research Articles

Neurodevelopmental differences in task-evoked number network connectivity: Comparing symbolic and nonsymbolic number discrimination in children and adults

Numerical cognition can take place in multiple representational formats, such as Arabic digits (e.g., 1), verbal number words (e.g., “two”), and nonsymbolic (e.g., •••) numerical magnitude. Basic numerical discrimination abilities are key factors underlying the development of arithmetic abilities, acting as an important developmental precursor of adult-level numeracy. While prior research has begun to detail the neural correlates associated with basic numerical discrimination skills in different representational formats, the interactions between functional neural circuits are less understood. A growing body of evidence suggests that the functional networks recruited by number discrimination tasks differ between children and adults, which may provide valuable insights into the development of numerical cognition. To this end, we posed two questions: how do the interactions between functional circuits associated with number processing differ in children and adults? Are differences in functional network connectivity modulated by numerical representational codes? A theoretically motivated 22 ROI analysis indicated significant functional connectivity differences between children and adults across all three codes. Adults demonstrated sparser and more consistent connectivity patterns across codes, indicative of developmental domain-specialization for number processing. Although neural activity in children and adults is similar, the functional connectivity supporting number processing appears subject to substantial developmental maturation effects.

PC020 / #794 THE EFFECTS OF ANODAL TRANSCRANIAL DIRECT CURRENT STIMULATION OVER RIGHT PARIETAL AND PREFRONTAL CORTICES ON NUMERICAL COGNITION: E-POSTER VIEWING

Non-invasive brain stimulation (NIBS) is used in basic cognitive science to establish causal models of the relationships between specific neural regions and cognition. In the field of numerical cognition, Transcranial Direct Current Stimulation (tDCS) applied to parietal and prefrontal cortex produce neuromodulatory effects, which translate into measurable behavioral effects affecting magnitude processing (Schroeder, 2017). The improvement of the number sense during early childhood is the foundation for the further development of numerical cognition and mathematical skills.

Understanding the Effects of Transcranial Electrical Stimulation in Numerical Cognition: A Systematic Review for Clinical Translation.

Atypical development of numerical cognition (dyscalculia) may increase the onset of neuropsychiatric symptoms, especially when untreated, and it may have long-term detrimental social consequences. However, evidence-based treatments are still lacking. Despite plenty of studies investigating the effects of transcranial electrical stimulation (tES) on numerical cognition, a systematized synthesis of results is still lacking. In the present systematic review (PROSPERO ID: CRD42021271139), we found that the majority of reports (20 out of 26) showed the effectiveness of tES in improving both number (80%) and arithmetic (76%) processing. In particular, anodal tDCS (regardless of lateralization) over parietal regions, bilateral tDCS (regardless of polarity/lateralization) over frontal regions, and tRNS (regardless of brain regions) strongly enhance number processing. While bilateral tDCS and tRNS over parietal and frontal regions and left anodal tDCS over frontal regions consistently improve arithmetic skills. In addition, tACS seems to be more effective than tDCS at ameliorating arithmetic learning. Despite the variability of methods and paucity of clinical studies, tES seems to be a promising brain-based treatment to enhance numerical cognition. Recommendations for clinical translation, future directions, and limitations are outlined.

Bidirectional Mapping Between the Symbolic Number System and the Approximate Number System.

Previous studies have discussed the symmetry of bidirectional mapping between approximate number system (ANS) and symbolic number system (SNS). However, these studies neglected the essential significance of bidirectional mapping in the development of numerical cognition. That is, with age, the connection strength between the ANS and SNS in ANS-SNS mapping could be higher than that in SNS-ANS mapping. Therefore, this study attempted to explore the symmetry of bidirectional mapping by examining whether the connection between the ANS and SNS is the same. Using two types of dot array materials (extensive and intensive) and sequence priming paradigms, this study found a stable negative priming effect in the ANS-SNS priming task, but no priming effect in the SNS-ANS priming task. In addition, although sensory cues (extensive and intensive) could affect performance in the ANS-SNS mapping task, these cues did not affect performance in the ANS-SNS priming task. In general, this study provides valuable insight into the symmetry of bidirectional mapping.

A probabilistic approach for quantifying children’s subitizing span

The development of enumeration skills over childhood is thought to reflect improvements in both subitizing (for small sets) and serial counting (for larger sets). However, investigations into the contribution of subitizing to advancing mathematics ability are limited by challenges in measuring subitizing capacity across developmental populations. Subitizing capacity in adults is traditionally assessed by calculating the bilinear inflection point for reaction times or accuracy across set sizes, but in children greater variability and dramatic improvements in counting ability introduce problems with this approach. This study demonstrates this limitation in a sample of elementary school children and proposes a novel probabilistic approach to measuring subitizing capacity. This metric captures well-established trends in the development of children’s subitizing. Furthermore, the proposed metric predicts unique variance in symbolic arithmetic ability, corroborating previous research that suggests a foundational role for subitizing in the development of numerical cognition. Findings demonstrate the advantages of a probabilistic approach to determining subitizing capacity in young children and suggest that it may be practically and theoretically well-suited for investigating subitizing and its role in mathematics development.

Size Perception and the Foundation of Numerical Processing

Research in numerical cognition has led to a widely accepted view of the existence of innate, domain-specific, core numerical knowledge that involves the intraparietal sulcus in the brain. Much of this research has revolved around the ability to perceive and manipulate discrete quantities (e.g., enumeration of dots). We question several aspects of this accepted view and suggest that continuous noncountable dimensions might play an important role in the development of numerical cognition. Accordingly, we propose that a relatively neglected aspect of performance—the ability to perceive and evaluate sizes or amounts—might be an important foundation of numerical processing. This ability might even constitute a more primitive system that has been used throughout evolutionary history as the basis for the development of the number sense and numerical abilities.

La cognición del número desde el punto de vista simbólico en educación primaria

Recent investigations indicate that the skills of numerical processing of children at the beginning of Primary Education precede the development of arithmetic in students, in the modes of oral verbal and alphabetical, analogical and written coding in Arabic numerals. The present work aims to study the development of numerical cognition in students of Primary Education. Thus, it presents the results of a sample of 2nd and 3rd grade at this stage, allowing us to show significant differences in performance levels among children when responding to tasks designed to evaluate the numerical processing.

Continuous visual properties of number influence the formation of novel symbolic representations.

Numerical symbols are thought to be mapped onto preexisting nonsymbolic representations of number. A growing body of evidence suggests that nonsymbolic numerical processing is significantly influenced by the associated visual properties of continuous quantity (e.g., surface area, density), but their role in the acquisition of novel symbols is unknown. Forty undergraduate students were trained to associate novel abstract symbols with numerical magnitudes. Half of the symbols were associated with nonsymbolic arrays in which total surface area and numerosity were correlated ("congruent"), and the other symbols were associated with arrays in which total surface area was equated across numerosities ("incongruent"). As numbers are represented in multiple formats (words, digits, nonsymbolic arrays), we also tested whether providing auditory nonword labels facilitated symbol learning. Following training, participants engaged in speeded comparisons of the newly learnt symbols. Comparisons were affected by the ratio between the numerosities associated with each symbol, a characteristic marker of numerical processing. Furthermore, comparisons were hardest for large-ratio comparisons of symbols associated with incongruent area and numerosity pairing during learning. In turn, these findings call for the further investigation of visual parameters on the development of numerical cognition.

The role of indigenous traditional counting systems in children's development of numerical cognition: results from a study in Papua New Guinea

The Government of Papua New Guinea undertook a significant step in developing curriculum reform policy that promoted the use of Indigenous knowledge systems in teaching formal school subjects in any of the country's 800-plus Indigenous languages. The implementation of the Elementary Cultural Mathematics Syllabus is in line with the above curriculum emphasis. Given the aims of the reform, the research reported here investigated the influence of children's own mother tongue (Tok Ples) and traditional counting systems on their development of early number knowledge formally taught in schools. The study involved 272 school children from 22 elementary schools in four provinces. Each child participated in a task-based assessment interview focusing on eight task groups relating to early number knowledge. The results obtained indicate that, on average, children learning their traditional counting systems in their own language spent shorter time and made fewer mistakes in solving each task compared to those taught without Tok Ples (using English and/or the lingua franca, Tok Pisin). Possible reasons accounting for these differences are also discussed.

Superior numerical abilities following early visual deprivation

In numerical cognition vision has been assumed to play a predominant role in the elaboration of the numerical representations and skills. However, this view has been recently challenged by the discovery that people with early visual deprivation not only have a semantic numerical representation that shares the same spatial properties with that in sighted people, but also have better numerical estimation skills. Here, we show that blind people's superior numerical abilities can be found in different numerical contexts, whether they are familiar or more general. In particular, we found that blind participants demonstrated better numerical estimation abilities than sighted participants in both an ecologic footstep and an unfamiliar oral verbal production task. Blind participants also tend to show greater working memory skills compared to sighted participants. These findings support the notion that vision is not necessary in the development of numerical cognition and indicate that early visual deprivation may even lead to a general enhancement in numerical estimation abilities. Moreover, they further suggest that blind people's greater numerical skills might be accounted by enhanced high-level cognitive processes, such as working memory.

One language, two number-word systems and many problems: Numerical cognition in the Czech language

Comparing numerical performance between different languages does not only mean comparing different number-word systems, but also implies a comparison of differences regarding culture or educational systems. The Czech language provides the remarkable opportunity to disentangle this confound as there exist two different number-word systems within the same language: for instance, "25" can be either coded in non-inverted order "dvadsetpät" [twenty-five] or in inverted order "pätadvadset" [five-and-twenty]. To investigate the influence of the number-word system on basic numerical processing within one culture, 7-year-old Czech-speaking children had to perform a transcoding task (i.e., writing Arabic numbers to dictation) in both number-word systems. The observed error pattern clearly indicated that the structure of the number-word system determined transcoding performance reliably: In the inverted number-word system about half of all errors were inversion-related. In contrast, hardly any inversion-related errors occurred in the non-inverted number-word system. We conclude that the development of numerical cognition does not only depend on cultural or educational differences, but is indeed related to the structure and transparency of a given number-word system.

Small and large number processing in infants and toddlers with Williams syndrome

Previous studies have suggested that typically developing 6-month-old infants are able to discriminate between small and large numerosities. However, discrimination between small numerosities in young infants is only possible when variables continuous with number (e.g. area or circumference) are confounded. In contrast, large number discrimination is successful even when variables continuous with number are systematically controlled for. These findings suggest the existence of different systems underlying small and large number processing in infancy. How do these develop in atypical syndromes? Williams syndrome (WS) is a rare neurocognitive developmental disorder in which numerical cognition has been found to be impaired in older children and adults. Do impairments of number processing have their origins in infancy? Here this question is investigated by testing the small and large number discrimination abilities of infants and toddlers with WS. While infants with WS were able to discriminate between 2 and 3 elements when total area was confounded with numerosity, the same infants did not discriminate between 8 and 16 elements, when number was not confounded with continuous variables. These findings suggest that a system for tracking the features of small numbers of object (object-file representation) may be functional in WS, while large number discrimination is impaired from an early age onwards. Finally, we argue that individual differences in large number processing in infancy are more likely than small number processing to be predictive of later development of numerical cognition.

Teaching and Learning Fraction and Rational Numbers: The Origins and Implications of Whole Number Bias

Many researchers agree that children's difficulty with fraction and rational numbers is associated with their whole number knowledge, but they disagree on the origin of the whole number bias. This article reviews three explanations of the nature of the bias. These accounts diverge on the questions of whether or not early quantitative representation originates from a numerical-specific cognitive mechanism, and whether or not the early quantitative representation privileges discrete quantity. The review suggests that there does not yet appear to be sufficient evidence to decide among the competing accounts as to the nature of the whole number bias. Yet, in the search for the understanding, two important issues have been brought up with regard to learning and teaching fraction and rational numbers. One question is related to how learning about fraction and rational numbers may be organized in such a way to be less strained for taking advantage of the prior knowledge of whole numbers. The second issue is concerned with what causes the gap between learning number symbols and learning number concepts. These issues have been explored by drawing upon both the accounts of whole number bias and insights from developmental studies, neuropsychological studies, and teaching experiments. The present review of literature has shown that the issues of whole number bias reflect not merely a matter of interference between prior and new knowledge in children's construction of fraction concepts, but a constellation of more general questions with regard to the origin and development of numerical cognition. How the bias is conceptualized therefore has theoretical and instructional significance.