The efficacy of manipulatives versus fingers in supporting young children's addition skills.

Recent empirical investigations have revealed that finger counting is a strategy associated with good arithmetic performance in young children. Fingers could have a special status during development because they operate as external support that provide sensory-motor and kinesthetic affordances in addition to visual input. However, it was unknown whether fingers are more helpful than manipulatives such as tokens during arithmetic problem solving. To address this question, we conducted a study with 93 Vietnamese children (48 girls) aged 4 and 5 years (mean = 58 months, range = 47-63) with high arithmetic and counting skills from families with relatively high socioeconomic status. Their behaviors were observed as they solved addition problems with manipulatives at their disposal. We found that children spontaneously used both manipulatives and fingers to solve the problems. Crucially, their performance was not higher when fingers rather than manipulatives were used (i.e., 70% vs. 81% correct answers, respectively). Therefore, at the beginning of learning, it is possible that, at least for children with high numerical skills, fingers are not the only gateway to efficient arithmetic development and manipulatives might also lead to proficient arithmetic.

Preschoolers' mastery of advanced counting: The best predictor of addition skills 2 years later.

The current study addressed the following question: Among preschoolers' basic numerical abilities, what are the best predictors for the later addition skills? We measured numerical abilities at preschool age and used dominance analysis to determine the dominant predictor for addition skills 2 years later. We tested seven numerical specific predictors (counting, advanced counting, enumeration, Give-N, collection comparison, number-word comparison, and approximate addition). Both quantitative and qualitative aspects (accuracy, strategy choice, and fluency) of addition skills were measured. The results show that the predictor weights for addition skills were 39% (counting), 37% (advanced counting), and 25% (collection comparison). We concluded that counting ability and especially advanced counting measured in early preschool is the most robust predictor of addition skills 2 years later (even after controlling for global cognitive abilities). This study generalized the previous findings found for Western children to Vietnamese preschoolers (N = 157, Mage = 4.8 years); extended and highlighted the role of advanced counting (count from a number other than 1) to later addition performance, mature strategy, and calculation fluency; and suggested further implications.

Early visual deprivation does not prevent the emergence of basic numerical abilities in blind children.

Studies involving congenitally blind adults shows that visual experience is not a mandatory prerequisite for the emergence of efficient numerical abilities. It remains however unknown whether blind adults developed lifelong strategies to compensate for the absence of foundations vision would provide in infancy. We therefore assessed basic numerical abilities in blind and sighted children of 6 to 13 years old. We also assessed verbal and spatial working memory abilities and their relationship with mental arithmetic in both groups. Blind children showed similar or better numerical abilities as compared to the sighted. Blind children also outperformed their sighted peers in every task assessing verbal working memory and demonstrated a similar spatial span. The correlation between arithmetic and the spatial sketchpad was stronger in blind relative to sighted children while the correlations between arithmetic and the other two components (the central executive and the phonological loop) were not affected by early visual experience. Our data suggest that early blindness does not impair the development of basic numerical competencies in children but influences the associations between arithmetic and some working memory subcomponents.

Toward an integrative model accounting for typical and atypical development of visuospatial short-term memory.

The origin of visuospatial short-term memory (STM) impairment is poorly investigated and is generally considered to be the result of a more global visuospatial deficit. However, previous studies suggest an important influence of two elements on performance in visuospatial STM tasks, the mode of presentation (i.e., simultaneous and sequential), and the visuospatial arrangement (structured vs. unstructured). With regards to a recent proposal, the aim of this study was to examine the development of the two modes of presentation and the visuospatial arrangement of visuospatial information in STM in a hundred typically developing participants aged from 4 years old to adults. Moreover, we also examined how the model explains the pattern of visuospatial STM deficit in two neurodevelopmental syndromes with different profiles in terms of STM abilities, namely Williams syndrome and Down syndrome. We found distinct performance for sequential and simultaneous presentation only from 11 years old with better performance in simultaneous than in sequential presentation mode and a sensitivity to visuospatial arrangement that increases with age. Both syndromes presented deficits at different levels, people with Williams syndrome for visuospatial arrangement and with Down syndrome for simultaneous visuospatial information in STM. The results demonstrate the importance to consider the influence of preexisting visuospatial knowledge on STM abilities. A two processing route model of STM is an interesting framework to interpret the different results.

Transparent number-naming system gives only limited advantage for preschooler's numerical development: Comparisons of Vietnamese and French-speaking children.

Several cross-sectional studies have suggested that the transparency of the number-naming system of East Asian languages (Chinese, Japanese) facilitates children's numerical development. The Vietnamese number-naming system also makes the base-10 system very explicit (eleven is "mÆ°oi mot," literally "ten-one," and thirty is "ba mÆ°Æ¡i," literally "three-ten"). In contrast, Western languages (English, French) include teen words (eleven to sixteen) and ten words (twenty to ninety) that make their counting systems less transparent. The main question addressed in this paper is: To what extent does a language's number-naming system impact preschoolers' numerical development? Our study participants comprised 104 Vietnamese and 104 French-speaking Belgian children between 3½ and 5½ years of age, as well as their parents. We tested the children on eight numerical tasks (counting, advanced counting, enumeration, Give-N, number-word comparison, collection comparison, addition, and approximate addition) and some general cognitive abilities (IQ and phonological loop by letter span). The parents completed a questionnaire on the frequency with which they stimulated their child's numeracy and literacy at home. The results indicated that Vietnamese children outperformed Belgian children only in counting. However, neither group differed in other symbolic or non-symbolic abilities, although Vietnamese parents tended to stimulate their child at home slightly more than Belgian parents. We concluded that the Vietnamese number-naming system's transparency led to faster acquisition of basic counting for preschoolers but did not support other more advanced numerical skills or non-symbolic numerical abilities. In addition, we extended the evidence that both transparent number-naming system and home numeracy influence young children's counting development.

Training Inhibition and Social Cognition in the Classrooms.

Executive functions and social cognition competences are associated with many important areas of life, such as school readiness, academic success or sociability. Numerous intervention programs aiming to improve these capacities have emerged and have been shown to be effective. As inhibition in particular, is closely related with social cognition competences, we developed a training program that targets both abilities and implemented it in kindergarten and lower primary school classes for 6 months. We evaluated its effectiveness at improving inhibition and social cognition as well as its possible impact on academic performance. The results showed that tackling inhibition and social cognition in the classroom at an early age improved inhibition, visual attention and flexibility as well as Theory of Mind and social information processing skills. However, the impact on academic learning was weak; a slight effect on a mathematical task was observed.

Mathematical Profile Test: A Preliminary Evaluation of an Online Assessment for Mathematics Skills of Children in Grades 1-6.

The domain of numerical cognition still lacks an assessment tool that is theoretically driven and that covers a wide range of key numerical processes with the aim of identifying the learning profiles of children with difficulties in mathematics (MD) or dyscalculia. This paper is the first presentation of an online collectively administered tool developed to meet these goals. The Mathematical Profile Test (MathPro Test) includes 18 subtests that assess numerical skills related to the core number domain or to the visual-spatial, memory or reasoning domains. The specific aim of this paper is to present the preliminary evaluation both of the sensitivity and the psychometric characteristics of the individual measures of the MathPro Test, which was administered to 622 primary school children (grades 1-6) in Belgium. Performance on the subtests increased across all grades and varied along the level of difficulty of the items, supporting the sensitivity of the test. The MathPro Test also showed satisfactory internal consistency and significant and stable correlation with a standardized test in mathematics across all grades. In particular, the achievement in mathematics was strongly associated with the performance on the subtests assessing the reasoning and the visuospatial domains throughout all school grades, whereas associations with the core number and memory tasks were found mainly in the younger children. MD children performed significantly lower than their peers; these differences in performance on the MathPro subtests also varied according to the school grades, informing us about the developmental changes of the weaknesses of children with MD. These results suggest that the MathPro Test is a very promising tool for conducting large scale research and for clinicians to sketch out the mathematical profile of children with MD or dyscalculia.

Magnitude processing in populations with spina-bifida: The role of visuospatial and working memory processes.

People with Spina Bifida usually experience difficulties with mathematics. In a series of other developmental disorders, a magnitude processing deficit was considered to be the main source of subsequent difficulties in mathematics. The processing of magnitude could be numerical (which is the larger number) or non-numerical such as spatial (e.g., which is the longer?) or temporal (which one last longer?) for instance. However, no study yet has examined directly magnitude processes in a population with Spina Bifida. On the other hand, recent studies in people with genetic syndromes have suggested that visuospatial and working memory processes play an important role in magnitude processing, including number magnitude. Therefore, in this study we explored for the first time magnitude representation using several tasks with different visuospatial and working memory processing requirements, cognitive skills frequently impaired in Spina Bifida. Results showed children with SB presented a global magnitude processing deficit for non-numerical and numerical comparison tasks, but not in symbolic number magnitude tasks compared to controls. Importantly, visuospatial skills and working memory abilities could partially explain the differences between groups in comparison and estimation tasks. This study proposes that magnitude processing difficulties in children with SB could be due to higher cognitive factors such as visuospatial and working memory processes.

Neuropsychological profiles of children with vestibular loss.

BACKGROUND: The impact of vestibular loss (VL) on cognition has been previously studied in experimental animal, human and adult patient studies showing links between VL, and cognitive impairments in space orientation, working memory, mental rotation and selective attention. However, few studies have been conducted on children with VL. OBJECTIVE: We investigated for the first time, the impact of a VL on children's cognition. METHODS: 13 children with VL (10 years, 5 months) and 60 average-age matched controls performed a neuropsychological assessment consisting of visuospatial working memory, selective visual attention, mental rotation and space orientation tasks. RESULTS: Children with VL recalled smaller sequences for both forward and backward memory subtasks (mean±SD = 6.3±1.9 and 5.3±2.6) than controls (8.2±2.3 and 7.3±2.0), have less accurate mental rotation scores (25.4±6 versus 30.8±5.1) and greater additional distance travelled in the maze task (96.4±66.6 versus 60.4±66.3); all corrected p-values <0.05. Selective visual attention measures do not show significant differences. CONCLUSIONS: Children with VL show similar cognitive difficulties that adults with VL, in tasks involving dynamic cognitive processes (higher attentional load) that in tasks requiring static cognitive processes such as visual attention task.

Investigating the respective contribution of sensory modalities and spatial disposition in numerical training.

Recent studies have suggested that multisensory redundancy may improve cognitive learning. According to this view, information simultaneously available across two or more modalities is highly salient and, therefore, may be learned and remembered better than the same information presented to only one modality. In the current study, we wanted to evaluate whether training arithmetic with a multisensory intervention could induce larger learning improvements than a visual intervention alone. Moreover, because a left-to-right-oriented mental number line was for a long time considered as a core feature of numerical representation, we also wanted to compare left-to-right-organized and randomly organized arithmetic training. Therefore, five training programs were created and called (a) multisensory linear, (b) multisensory random, (c) visual linear, (d) visual random, and (e) control. A total of 85 preschoolers were randomly assigned to one of these five training conditions. Whereas children were trained to solve simple addition and subtraction operations in the first four training conditions, story understanding was the focus of the control training. Several numerical tasks (arithmetic, number-to-position, number comparison, counting, and subitizing) were used as pre- and post-test measures. Although the effect of spatial disposition was not significant, results demonstrated that the multisensory training condition led to a significantly larger performance improvement than the visual training and control conditions. This result was specific to the trained ability (arithmetic) and is discussed in light of the multisensory redundancy hypothesis.

Impact of ageing on problem size and proactive interference in arithmetic facts solving.

Arithmetic facts (AFs) are required when solving problems such as "3 × 4" and refer to calculations for which the correct answer is retrieved from memory. Currently, two important effects that modulate the performance in AFs have been highlighted: the problem size effect and the proactive interference effect. The aim of this study is to investigate possible age-related changes of the problem size effect and the proactive interference effect in AF solving. To this end, the performance of young and older adults was compared in a multiplication production task. Furthermore, an independent measure of proactive interference was assessed to further define the architecture underlying this effect in multiplication solving. The results indicate that both young and older adults were sensitive to the effects of interference and of the problem size. That is, both interference and problem size affected performance negatively: the time needed to solve a multiplication problem increases as the level of interference and the size of the problem increase. Regarding the effect of ageing, the problem size effect remains constant with age, indicating a preserved AF network in older adults. Interestingly, sensitivity to proactive interference in multiplication solving was less pronounced in older than in younger adults suggesting that part of the proactive interference has been overcome with age.

Recruitment of the occipital cortex by arithmetic processing follows computational bias in the congenitally blind.

Arithmetic reasoning activates the occipital cortex of congenitally blind people (CB). This activation of visual areas may highlight the functional flexibility of occipital regions deprived of their dominant inputs or relate to the intrinsic computational role of specific occipital regions. We contrasted these competing hypotheses by characterizing the brain activity of CB and sighted participants while performing subtraction, multiplication and a control letter task. In both groups, subtraction selectively activated a bilateral dorsal network commonly activated during spatial processing. Multiplication triggered activity in temporal regions thought to participate in memory retrieval. No between-group difference was observed for the multiplication task whereas subtraction induced enhanced activity in the right dorsal occipital cortex of the blind individuals only. As this area overlaps with regions showing selective tuning to auditory spatial processing and exhibits increased functional connectivity with a dorsal "spatial" network, our results suggest that the recruitment of occipital regions during high-level cognition in the blind actually relates to the intrinsic computational role of the activated regions.

Executive Function, Chaos and Temperament: Specificities in Preschoolers with Externalizing Behaviors.

Various factors may contribute to the emergence of externalizing behavior (EB) problems in the preschool period. At the child level, temperament and executive function (EF) seem to play an important role, as well as environmental variables such as household chaos. In this study, we examined the profiles of 49 EB preschoolers compared to 49 typically developing (TD) preschoolers matched on age and gender. To evaluate the behavioral aspect of EB, we asked teachers and parents to fill out questionnaires, but we also used an observational paradigm. We assessed executive functions using attention, inhibition, flexibility and working memory tests. Finally, we used questionnaires to assess household chaos and child temperament. Results showed that children rated by parents as presenting EB were also assessed so by teachers and exhibited more agitation in our observational paradigm. As expected, EB children also presented weaker performance than the TD children in all EF tasks, except those measuring attention, and showed a larger reaction-time variability. Parents of the EB group reported a more chaotic environment at home. Finally, we found that child temperament (i.e., emotionality) also plays a role in group belonging. This study shows that EB children already exhibit specific characteristics by the time they are of preschool age, not only in the behavioral sphere, but also in the cognitive and environmental areas. However, despite all the differences between the two groups, a discriminant analysis showed that EF capacities have a weak power for EB diagnosis.

The effect of visual arrangement on visuospatial short-term memory: Insights from children with 22q11.2 deletion syndrome.

Recent models of visuospatial (VSSP) short-term memory postulate the existence of two dissociable mechanisms depending on whether VSSP information is presented simultaneously or sequentially. However, they do not specify to what extent VSSP short-term memory is under the influence of general VSSP processing. This issue was examined in people with 22q11.2 deletion syndrome, a genetic condition involving a VSSP deficit. The configuration of VSSP information was manipulated (structured vs. unstructured) to explore the impact of arrangement on VSSP short-term memory. Two presentation modes were used to see whether the VSSP arrangement has the same impact on simultaneous and sequential short-term memory. Compared to children matched on chronological age, children with 22q11.2 deletion syndrome showed impaired performance only for structured arrangement, regardless of the presentation mode, suggesting an influence of VSSP processing on VSSP short-term memory abilities. A revised cognitive architecture for a model of VSSP short-term memory is proposed.

Developmental Dyscalculia in Adults: Beyond Numerical Magnitude Impairment.

Numerous studies have tried to identify the core deficit of developmental dyscalculia (DD), mainly by assessing a possible deficit of the mental representation of numerical magnitude. Research in healthy adults has shown that numerosity, duration, and space share a partly common system of magnitude processing and representation. However, in DD, numerosity processing has until now received much more attention than the processing of other non-numerical magnitudes. To assess whether or not the processing of non-numerical magnitudes is impaired in DD, the performance of 15 adults with DD and 15 control participants was compared in four categorization tasks using numerosities, lengths, durations, and faces (as non-magnitude-based control stimuli). Results showed that adults with DD were impaired in processing numerosity and duration, while their performance in length and face categorization did not differ from controls' performance. Our findings support the idea of a nonsymbolic magnitude deficit in DD, affecting numerosity and duration processing but not length processing.

Evidence of the impact of visuo-spatial processing on magnitude representation in 22q11.2 microdeletion syndrome.

The influence of visuo-spatial skills on numerical magnitude processing is the subject of a long-standing debate. As most of the numerical and non-numerical magnitude abilities underpinning mathematical development are visual by nature, they are often assessed in the visual modality, thereby confusing visuo-spatial and numerical processing. In order to assess the influence of visuo-spatial processing on numerical magnitude representation, we examined magnitude processing in patients with 22q11.2 deletion syndrome (22q11DS), a genetic condition characterized by a cognitive profile with a relative weakness in visuo-spatial abilities but with preserved verbal abilities. Twenty-seven participants with 22q11DS were compared to two control groups (one matched on verbal intelligence and the other on visuo-spatial abilities) on several magnitude comparison tasks each with different visuo-spatial processing requirements. Our results showed that participants with 22q11DS present a consistent pattern of impairment in magnitude comparison tasks requiring the processing of visuo-spatial dimensions: comparison of lengths and collections. In contrast, their performance did not differ from the control groups in a visual task with no spatial processing requirement (i.e. numerical comparison of flashed dot sequences) or in auditory tasks (i.e., duration comparison and numerical comparison of sound sequences). Finally, a specific deficit of enumeration processes was observed in the subitizing range. Taken together, these results show that deficits in magnitude can occur as a consequence of a visuo-spatial deficit. This highlights the influence of the nature of the tasks selected to assess magnitude representation.

The role of short-term memory and visuo-spatial skills in numerical magnitude processing: Evidence from Turner syndrome.

Most studies on magnitude representation have focused on the visual modality with no possibility of disentangling the influence of visuo-spatial skills and short-term memory (STM) abilities on quantification processes. This study examines this issue in patients with Turner syndrome (TS), a genetic condition characterized by a specific cognitive profile frequently associating poor mathematical achievement, low spatial skills and reduced STM abilities. In order to identify the influence of visuo-spatial and STM processing on numerical magnitude abilities, twenty female participants with TS and twenty control female participants matched for verbal IQ and education level were administered a series of magnitude comparison tasks. The tasks differed on the nature of the magnitude to be processed (continuous, discrete and symbolic magnitude), on visuo-spatial processing requirement (no/high) and on STM demands (low in simultaneous presentation vs. high in sequential presentation). Our results showed a lower acuity when participants with TS compared the numerical magnitudes of stimuli presented sequentially (low visuo-spatial processing and high STM load: Dot sequence and Sound sequence) while no difference was observed in the numerical comparison of sets presented simultaneously. In addition, the group difference in sequential tasks disappeared when controlling for STM abilities. Finally, both groups demonstrated similar performance when comparing continuous or symbolic magnitude stimuli and they exhibited comparable subitizing abilities. These results highlight the importance of STM abilities in extracting numerosity through a sequential presentation and underline the importance of considering the impact of format presentation on magnitude judgments.

Improving Preschoolers' Arithmetic through Number Magnitude Training: The Impact of Non-Symbolic and Symbolic Training.

The numerical cognition literature offers two views to explain numerical and arithmetical development. The unique-representation view considers the approximate number system (ANS) to represent the magnitude of both symbolic and non-symbolic numbers and to be the basis of numerical learning. In contrast, the dual-representation view suggests that symbolic and non-symbolic skills rely on different magnitude representations and that it is the ability to build an exact representation of symbolic numbers that underlies math learning. Support for these hypotheses has come mainly from correlative studies with inconsistent results. In this study, we developed two training programs aiming at enhancing the magnitude processing of either non-symbolic numbers or symbolic numbers and compared their effects on arithmetic skills. Fifty-six preschoolers were randomly assigned to one of three 10-session-training conditions: (1) non-symbolic training (2) symbolic training and (3) control training working on story understanding. Both numerical training conditions were significantly more efficient than the control condition in improving magnitude processing. Moreover, symbolic training led to a significantly larger improvement in arithmetic than did non-symbolic training and the control condition. These results support the dual-representation view.

The role of physical digit representation and numerical magnitude representation in children's multiplication fact retrieval.

Arithmetic facts, in particular multiplication tables, are thought to be stored in long-term memory and to be interference prone. At least two representations underpinning these arithmetic facts have been suggested: a physical representation of the digits and a numerical magnitude representation. We hypothesized that both representations are possible sources of interference that could explain individual differences in multiplication fact performance and/or in strategy use. We investigated the specificity of these interferences on arithmetic fact retrieval and explored the relation between interference and performance on the different arithmetic operations and on general mathematics achievement. Participants were 79 fourth-grade children (Mage=9.6 years) who completed a products comparison and a multiplication production task with verbal strategy reports. Performances on a speeded calculation test including the four operations and on a general mathematics achievement test were also collected. Only the interference coming from physical representations was a significant predictor of the performance across multiplications. However, both the magnitude and physical representations were unique predictors of individual differences in multiplication. The frequency of the retrieval strategy across multiplication problems and across individuals was determined only by the physical representation, which therefore is suggested as being responsible for memory storage issues. Interestingly, this impact of physical representation was not observed when predicting performance on subtraction or on general mathematical achievement. In contrast, the impact of the numerical magnitude representation was more general in that it was observed across all arithmetic operations and in general mathematics achievement.

Spatial and numerical processing in children with non-verbal learning disabilities.

Consistently with the idea that numbers and space interact with each other, the present paper aimed to investigate the impact of non-verbal learning disabilities (NVLD) on spatial and numerical processing. In order to do so, 15 NVLD and 15 control children were required to perform different spatial (the line bisection and Simon tasks) and numerical tasks (the number bisection, number-to-position and numerical comparison tasks). In every task, NVLD children presented lower accuracy scores than the control group. While both groups manifested similar pseudo-neglect and Simon effects, they however differed in the numerical comparison task: while control children presented the standard SNARC effect in the uncrossed and crossed postures, no SNARC effect was observed in the NVLD group. Our results therefore suggest that NVLD affects the accuracy and the nature of the mental number line by decreasing its precision and the saliency of its left-to-right orientation.