Numerical capacities as domain-specific predictors beyond early mathematics learning: a longitudinal study

Form perception is a cognitive correlate of the relation between subitizing ability and math performance

"Subitizing" defines a phenomenon whereby approximately four items can be quickly and accurately processed. Studies have shown the close association between subitizing and math performance, however, the mechanism for the association remains unclear. The present study was conducted to investigate whether form perception assessed on a serial figure matching task is a potential non-numerical mechanism between subitizing ability and math performance. Three-hundred and seventy-three Chinese primary school students completed four kinds of dot comparison tasks, serial figure matching task, math performance tasks (including three arithmetic computation tasks and math word problem task), and other cognitive tasks as their general cognitive abilities were observed as covariates. A series of hierarchical regression analyses showed that after controlling for age, gender, nonverbal matrix reasoning, and visual tracking, subitizing comparison (subitizing vs. subitizing, subitizing vs. estimation) still contributed to simple addition or simple subtraction but not to complex subtraction ability or math word problem. After taking form perception as an additional control variable, the predictive power of different dot comparison conditions disappeared. A path model also showed that form perception fully mediates the relation between numerosity comparison (within and beyond the subitizing range) and arithmetic performance. These findings support the claim that form perception is a non-numerical cognitive correlate of the relation between subitizing ability and math performance (especially arithmetic computation).

Impaired large numerosity estimation and intact subitizing in developmental dyscalculia

It is believed that the approximate estimation of large sets and the exact quantification of small sets (subitizing) are supported by two different systems, the Approximate Number System (ANS) and Object Tracking System (OTS), respectively. It is a current matter of debate whether they are both impaired in developmental dyscalculia (DD), a specific learning disability in symbolic number processing and calculation. Here we tackled this question by asking 32 DD children and 32 controls to perform a series of tasks on visually presented sets, including exact enumeration of small sets as well as comparison of large, uncountable sets. In children with DD, we found poor sensitivity in processing large numerosities, but we failed to find impairments in the exact enumeration of sets within the subitizing range. We also observed deficits in visual short-term memory skills in children with dyscalculia that, however, did not account for their low ANS acuity. Taken together, these results point to a dissociation between quantification skills in dyscalculia, they highlight a link between DD and low ANS acuity and provide support for the notion that DD is a multifaceted disability that covers multiple cognitive skills.

Perceptual subitizing and conceptual subitizing in Williams syndrome and Down syndrome: Insights from eye movements

BACKGROUND AND AIMS

Mathematical difficulties in individuals with Williams Syndrome (WS) and in individuals with Down Syndrome (DS) are well-established. Perceptual subitizing and conceptual subitizing are domain-specific precursors of mathematical achievement in typically developing (TD) population. This study employed, for the first time, eye-tracking methodology to investigate subitizing abilities in WS and DS.

METHODS AND PROCEDURES

Twenty-five participants with WS and 24 participants with DS were compared to a younger group of TD children (n = 25) matched for mental age. Participants were asked to enumerate one to six dots arranged either in a dice or a random pattern.

OUTCOMES AND RESULTS

Accuracy rates and analyses of reaction time showed no significant differences between the clinical groups (WS and DS) and the control group, suggesting that all participants used the same processes to perform the enumeration task in the different experimental conditions. Analyses of the eye movements showed that both individuals with WS and individuals with DS were using inefficient scanning strategies when counting. Moreover, analyses of the eye movements showed significantly shorter fixation duration in participants with DS compared to the control group in all the experimental conditions.

CONCLUSIONS AND IMPLICATIONS

The current study provides evidence that individuals with WS and individuals with DS perform both perceptual subitizing and conceptual subitizing. Moreover, our results suggest a fixation instability in DS group that does not affect their performance when subitizing but might explain their low accuracy rates when counting. Findings are discussed in relation to previous studies and the impact for intervention programmes to improve counting and symbolic mathematical abilities in these populations.

Subitizing and counting impairments in children with developmental coordination disorder

Developmental coordination disorder (DCD) interferes with academic achievement and daily life, and is associated with persistent academic difficulties, in particular within mathematical learning. In the present study, we aimed to study numerical cognition using an approach that taps very basic numerical processes such as subitizing and counting abilities in DCD. We used a counting task and a subitizing task in forty 7-10 years-old children with or without DCD. In both tasks, children were presented with arrays of one to eight dots and asked to name aloud the number of dots as accurately and quickly as possible. In the subitizing task, dots were presented during 250 ms whereas in the counting task they stayed on the screen until the participants gave a verbal response. The results showed that children with DCD were less accurate and slower in the two enumeration tasks (with and without a time limit), providing evidence that DCD impairs both counting and subitizing. These impairments might have a deleterious impact on the ability to improve the acuity of the Approximate Number System through counting, and thus could play a role in the underachievement of children with DCD in mathematics.

Numerical processing profiles in children with varying degrees of arithmetical achievement

Recent studies show basic cognitive abilities such as the rapid and precise apprehension of small numerosities in object sets ("subitizing"), verbal counting and numerical magnitude comparison significantly influence the acquisition of arithmetic and continues to modulate more advanced stages of mathematical cognition. Additionally, children with low arithmetic achievement (LAA) and Developmental Dyscalculia (DD) exhibit significant deficits in these cognitive processes. Nevertheless, the different cognitive profiles of children with varying degrees of numerical and arithmetic processing deficits have not been sufficiently characterized, despite its potential relevance to the stimulation of numerical cognition and the design of appropriate intervention strategies. Here, the cognitive profiles of groups of typically developing children, children with low arithmetical achievement and DD, exhibiting typical and atypical subitizing ability were contrasted. The results suggest that relatively independent neurocognitive mechanisms may produce distinct profiles at the behavioral level and suggest children with low arithmetic performance exhibiting atypical subitizing abilities are not only significantly slower, but rely on compensatory mechanisms and strategies compared to typical subitizers. The role of subitizing as a correlate of arithmetic fluency is revised in the light of the present findings.

Longitudinal Brain Development of Numerical Skills in Typically Developing Children and Children with Developmental Dyscalculia

Developmental dyscalculia (DD) is a learning disability affecting the acquisition of numerical-arithmetical skills. Studies report persistent deficits in number processing and aberrant functional activation of the fronto-parietal numerical network in DD. However, the neural development of numerical abilities has been scarcely investigated. The present paper provides a first attempt to investigate behavioral and neural trajectories of numerical abilities longitudinally in typically developing (TD) and DD children. During a study period of 4 years, 28 children (8-11 years) were evaluated twice by means of neuropsychological tests and a numerical order fMRI paradigm. Over time, TD children improved in numerical abilities and showed a consistent and well-developed fronto-parietal network. In contrast, DD children revealed persistent deficits in number processing and arithmetic. Brain imaging results of the DD group showed an age-related activation increase in parietal regions (intraparietal sulcus), pointing to a delayed development of number processing areas. Besides, an activation increase in frontal areas was observed over time, indicating the use of compensatory mechanisms. In conclusion, results suggest a continuation in neural development of number representation in DD, whereas the neural network for simple ordinal number estimation seems to be stable or show only subtle changes in TD children over time.

Reliability and Validity of Nonsymbolic and Symbolic Comparison Tasks in School-Aged Children

Basic numerical processing has been regularly assessed using numerical nonsymbolic and symbolic comparison tasks. It has been assumed that these tasks index similar underlying processes. However, the evidence concerning the reliability and convergent validity across different versions of these tasks is inconclusive. We explored the reliability and convergent validity between two numerical comparison tasks (nonsymbolic vs. symbolic) in school-aged children. The relations between performance in both tasks and mental arithmetic were described and a developmental trajectories' analysis was also conducted. The influence of verbal and visuospatial working memory processes and age was controlled for in the analyses. Results show significant reliability (p < .001) between Block 1 and 2 for nonsymbolic task (global adjusted RT (adjRT): r = .78, global efficiency measures (EMs): r = .74) and, for symbolic task (adjRT: r = .86, EMs: r = .86). Also, significant convergent validity between tasks (p < .001) for both adjRT (r = .71) and EMs (r = .70) were found after controlling for working memory and age. Finally, it was found the relationship between nonsymbolic and symbolic efficiencies varies across the sample's age range. Overall, these findings suggest both tasks index the same underlying cognitive architecture and are appropriate to explore the Approximate Number System (ANS) characteristics. The evidence supports the central role of ANS in arithmetic efficiency and suggests there are differences across the age range assessed, concerning the extent to which efficiency in nonsymbolic and symbolic tasks reflects ANS acuity.

Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: a meta-analysis

Many studies have investigated the association between numerical magnitude processing skills, as assessed by the numerical magnitude comparison task, and broader mathematical competence, e.g. counting, arithmetic, or algebra. Most correlations were positive but varied considerably in their strengths. It remains unclear whether and to what extent the strength of these associations differs systematically between non-symbolic and symbolic magnitude comparison tasks and whether age, magnitude comparison measures or mathematical competence measures are additional moderators. We investigated these questions by means of a meta-analysis. The literature search yielded 45 articles reporting 284 effect sizes found with 17,201 participants. Effect sizes were combined by means of a two-level random-effects regression model. The effect size was significantly higher for the symbolic (r = .302, 95% CI [.243, .361]) than for the non-symbolic (r = .241, 95% CI [.198, .284]) magnitude comparison task and decreased very slightly with age. The correlation was higher for solution rates and Weber fractions than for alternative measures of comparison proficiency. It was higher for mathematical competencies that rely more heavily on the processing of magnitudes (i.e. mental arithmetic and early mathematical abilities) than for others. The results support the view that magnitude processing is reliably associated with mathematical competence over the lifespan in a wide range of tasks, measures and mathematical subdomains. The association is stronger for symbolic than for non-symbolic numerical magnitude processing. So symbolic magnitude processing might be a more eligible candidate to be targeted by diagnostic screening instruments and interventions for school-aged children and for adults.