Separable effects of the approximate number system, symbolic number knowledge, and number ordering ability on early arithmetic development

Concepts of order: Why is ordinality processed slower and less accurately for non-consecutive sequences?

Both adults and children are slower at judging the ordinality of non-consecutive sequences (e.g., 1-3-5) than consecutive sequences (e.g., 1-2-3). It has been suggested that the processing of non-consecutive sequences is slower because it conflicts with the intuition that only count-list sequences are correctly ordered. An alternative explanation, however, may be that people simply find it difficult to switch between consecutive and non-consecutive concepts of order during order judgement tasks. Therefore, in adult participants, we tested whether presenting consecutive and non-consecutive sequences separately would eliminate this switching demand and thus improve performance. In contrast with this prediction, however, we observed similar patterns of response times independent of whether sequences were presented separately or together (Experiment 1). Furthermore, this pattern of results remained even when we doubled the number of trials and made participants explicitly aware when consecutive and non-consecutive sequences were presented separately (Experiment 2). Overall, these results suggest slower response times for non-consecutive sequences do not result from a cognitive demand of switching between consecutive and non-consecutive concepts of order, at least not in adults.

Basic Symbolic Number Skills, but Not Formal Mathematics Performance, Longitudinally Predict Mathematics Anxiety in the First Years of Primary School

Mathematical anxiety (MA) and mathematics performance typically correlate negatively in studies of adolescents and adults, but not always amongst young children, with some theorists questioning the relevance of MA to mathematics performance in this age group. Evidence is also limited in relation to the developmental origins of MA and whether MA in young children can be linked to their earlier mathematics performance. To address these questions, the current study investigated whether basic and formal mathematics skills around 4 and 5 years of age were predictive of MA around the age of 7-8. Additionally, we also examined the cross-sectional relationships between MA and mathematics performance in 7-8-year-old children. Specifically, children in our study were assessed in their first (T1; aged 4-5), second (T2; aged 5-6), and fourth years of school (T3; aged 7-8). At T1 and T2, children completed measures of basic numerical skills, IQ, and working memory, as well as curriculum-based mathematics tests. At T3, children completed two self-reported MA questionnaires, together with a curriculum-based mathematics test. The results showed that MA could be reliably measured in a sample of 7-8-year-olds and demonstrated the typical negative correlation between MA and mathematical performance (although the strength of this relationship was dependent on the specific content domain). Importantly, although early formal mathematical skills were unrelated to later MA, there was evidence of a longitudinal relationship between basic early symbolic number skills and later MA, supporting the idea that poorer basic numerical skills relate to the development of MA.

Aprendizaje del conteo y los números naturales en preescolar: una revisión sistemática de la literatura

Aprender a contar cantidades discretas de forma exacta constituye uno de los primeros hitos del desarrollo del conocimiento matemático infantil. En los últimos años, ha habido un extenso debate en torno a cómo ocurre este proceso de aprendizaje en preescolar. La actual investigación tuvo como objetivo conocer las temáticas y preguntas de investigación generales desarrolladas en los últimos cinco años en cuanto al aprendizaje del conteo y los números naturales en preescolar. Para ello, se realizó una revisión sistemática en la que se hizo una indagación en las bases de datos ScienceDirect, EBSCO, Web of Science, SpringerLink, JSTOR y Sage. Se obtuvieron 98 artículos de investigación que fueron examinados mediante análisis de conglomerados y mapas jerárquicos a través de NVIVO 11.0.  Se encontraron cuatro núcleos temáticos (Ideas sobre los procesos cognitivos implicados en la comprensión del número, Representación de magnitudes numéricas, Intervenciones para favorecer el desarrollo de habilidades matemáticas y Aspectos estructurales del número), que muestran el panorama actual de investigación sobre aprendizaje del conteo. Los resultados de este estudio son importantes para delimitar posibles programas futuros de investigación, y pueden ser usados por docentes como insumo para enriquecer los ambientes de aprendizaje de sus aulas de clase.

Number sense: the mediating effect between nonverbal intelligence and children’s mathematical performance

The study explored the mediating effect of number sense between nonverbal intelligence and children’s mathematical performance. The sample consisted of 131 pupils in Shaoxing City of China from grades 1, 3, and 5. The students completed measures of nonverbal intelligence, number sense, basic arithmetic ability, mathematical performance, rapid automatized naming, and working memory. Results show that although all variables significantly relate with each other (all p < .01), only nonverbal intelligence, number sense, and basic arithmetic ability significantly affect children’s mathematical performance (all p < .01). According to multiple-mediation model, nonverbal intelligence significantly predicts children’s mathematical performance through number sense and basic arithmetic ability. These findings suggest that domain-specific mathematical skills play a prominent role in children’s mathematical performance in primary school, rather than domain-general cognitive functions. Educators should pay attention to develop children’s number sense in order to improve children’s mathematical ability.

Can training in the approximate number system improve the informal mathematics ability of preschoolers?

Recent studies show that comparison or arithmetic training in the approximate number system (ANS) can improve the early mathematics ability of preschool children. However, no studies have compared the training effects of ANS comparison training with those of ANS arithmetic training on the early mathematics ability of preschool children. The current study pseudorandomly assigned 87 children aged 4-5 years to one of three training groups (the ANS comparison, ANS arithmetic, and control groups) for 4 weeks of training. The results showed that compared with the control group, the ANS comparison training and ANS arithmetic training equally improved the ANS acuity and informal mathematics ability of preschool children. In addition, the study found that there may be a bidirectional causal relationship between ANS and mathematics in preschoolers, but this relationship needs to be further investigated using longitudinal studies. Taken together, these findings emphasize the importance of ANS-based training in improving preschoolers' ANS acuity and informal mathematics ability before formal school enrollment.

Numerosity Comparison, Estimation and Proportion Estimation Abilities May Predict Numeracy and Cognitive Reflection in Adults

This study explores whether and how different tasks associated with approximate number system (ANS) ability are related to numeracy and cognitive reflection in adults. We conducted an online experiment using a sample of 300 Japanese adults aged 20–39. Participants were given three ANS tasks (numerosity comparison, numerosity estimation, and proportion estimation) as well as Rasch-based numeracy scale and cognitive reflection test, and we tested the correlation among the measures of these tasks. We explored the hypothesis that the typical measures used to gauge ANS ability, numerosity comparison and numerosity estimation may mediate different cognitive mechanisms in adults. We also introduced a task measuring proportion estimation, added because such estimation requires numerosity perception and the ability to map symbolic numerals. Our findings suggest that there is a weak, but significant correlation among the three ANS-related tasks. Moreover, there is a significant relationship between each of these measures and the numeracy and CRT score, suggesting that the ANS-related ability may be associated with higher cognitive abilities such as numeracy and cognitive reflection. In addition, we found that performances on the numerosity and proportion estimation are more clearly related to CRT score than the numerosity comparison task.

The value of structural brain imaging in explaining individual differences in children's arithmetic fluency

How do different measures of brain structure correlate with individual differences in arithmetic fluency? This paper builds on two previously published studies in which individual differences in children's arithmetic fluency were correlated with measures of white (Polspoel et al., 2019) and grey matter (Polspoel et al., 2020) in one sample of children. We combined the brain imaging data of these two studies with measures of cognitive abilities that have been shown to be predictive of arithmetic fluency, i.e., numerical magnitude processing, working memory and rapid automatized naming (RAN). This allowed us to investigate to which extend the observed structural brain imaging measures uniquely correlated with children's arithmetic fluency, on top of each other as well as on top of the abovementioned cognitive variables. Participants were 43 typically developing 9-10-year-olds. All measures were added to a hierarchical multiple regression model. This regression model showed that the white matter integrity of the right inferior longitudinal fasciculus and the cortical complexity of the left postcentral gyrus remained unique predictors of individual differences in arithmetic when the abovementioned cognitive variables were taken into account. This indicates that structural neuroimaging measures can explain individual differences in arithmetic performance that are not merely accounted for by relevant cognitive predictors.

Syntactic priming reveals an explicit syntactic representation of multi-digit verbal numbers

When we say or understand verbal numbers, a major challenge to the cognitive system is the need to process the number's syntactic structure. Several studies showed that number syntax is handled by dedicated processes, however, it is still unclear how precisely these processes operate, whether the number's syntactic structure is represented explicitly, and if it is - what this representation looks like. Here, we used a novel experimental paradigm, syntactic priming of numbers, which can examine in detail the syntactic representation of multi-digit verbal numbers. In each trial, the participants - Arabic-Hebrew bilinguals and Hebrew monolinguals - heard a multi-digit number and responded orally with a random number. The syntactic structure of their responses was similar to that of the targets, showing that they represented the verbal number's syntax. This priming effect was genuinely syntactic, and could not be explained as lexical - repeating words from the target; as phonological - responding with words phonologically-similar to the target; or as a numerical distance effect - producing responses numerically close to the target. The syntactic priming effect was stronger for earlier words in the verbal number and weaker for later words, suggesting that the syntactic representation is capped by working-memory limits. We propose that syntactic priming could become a useful method to examine various aspects of the syntactic representation of numbers.