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.

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.

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.

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.

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 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.

The interference effect in arithmetic fact solving: An fMRI study.

Some multiplication facts share common digits with other, previously learned facts, and as a result, different problems are associated with different levels of interference. The detrimental effect of interference in arithmetic facts knowledge has been recently highlighted in behavioral studies, in children as well as in adults, both in typical and atypical development. The present study investigated the brain regions involved in the interference effect when solving multiplication problems. Twenty healthy adults carried out a multiplication task in an MRI scanner. The event-related design comprised problems whose interference level and problem size were manipulated in a 2×2 factorial design. After each trial, individuals were requested to indicate whether they solved the trial by retrieving the answer from long-term memory. This allowed us to examine which brain areas were sensitive to the interference effect and problem size effect as well as the retrieval strategy. The results highlighted two specific regions: the left angular gyrus was more activated for low interfering than for high interfering problems, and the right intraparietal sulcus was more activated for large problems than for small problems. In both regions, brain activity was not modulated by the other effect. These results suggest that the left angular gyrus is sensitive to the level of interference of the multiplication problems, whereas previously this region was thought to be more activated by small problems or by retrieval strategy. Here, in a design manipulating interference and problem size, while controlling for retrieval strategy, we showed that it rather reflects an automatic mapping between the problem and the answer stored in long-term memory. The right intraparietal sulcus was modulated by the problem size effect, which supports the idea that the problem size effect comes from the higher overlap between magnitude of the answers of large problems compared to small ones. Importantly, neither effects can be reduced to a strategy effect since they were present when analyzing only retrieval trials.

Spatial and numerical processing in children with high and low visuospatial abilities.

In the literature on numerical cognition, a strong association between numbers and space has been repeatedly demonstrated. However, only a few recent studies have been devoted to examine the consequences of low visuospatial abilities on calculation processing. In this study, we wanted to investigate whether visuospatial weakness may affect pure spatial processing as well as basic numerical reasoning. To do so, the performances of children with high and low visuospatial abilities were directly compared on different spatial tasks (the line bisection and Simon tasks) and numerical tasks (the number bisection, number-to-position, and numerical comparison tasks). Children from the low visuospatial group presented the classic Simon and SNARC (spatial numerical association of response codes) effects but showed larger deviation errors as compared with the high visuospatial group. Our results, therefore, demonstrated that low visuospatial abilities did not change the nature of the mental number line but rather led to a decrease in its accuracy.

Arithmetic facts storage deficit: the hypersensitivity-to-interference in memory hypothesis.

Dyscalculia, or mathematics learning disorders, is currently known to be heterogeneous (Wilson & Dehaene, ). While various profiles of dyscalculia coexist, a general and persistent hallmark of this math learning disability is the difficulty in memorizing arithmetic facts (Geary, Hoard & Hamson, ; Jordan & Montani, ; Slade & Russel, ). Arithmetic facts are simple arithmetic problems that are solved by direct retrieval from memory. Recently, De Visscher and Noël () showed hypersensitivity-to-interference in memory in an adult suffering from a specific deficit of arithmetic facts storage. According to the authors, arithmetic facts share many features. The overlapping of these features between arithmetic facts may provoke interference. Consequently, learners who are hypersensitive-to-interference could have considerable difficulties in storing arithmetic facts. The present study aims at testing this new hypothesis on fourth-grade children who are learning multiplication tables. Among 101 children that were assessed, 23 low arithmetic facts learners were selected because of their low score in arithmetic facts fluency (controlling for processing speed). Twenty-three control children were selected, matched for classroom, gender, and age. In addition to a subtest of global reasoning, these participants were given a multiplication production task and a memorization task of low- and high-interference associations. The results show that children with low arithmetic fluencies experience hypersensitivity-to-interference in memory compared with children with typical arithmetic fluencies.

The development of children's inhibition: does parenting matter?

Whereas a large body of research has investigated the maturation of inhibition in relation to the prefrontal cortex, far less research has been devoted to environmental factors that could contribute to inhibition improvement. The aim of the current study was to test whether and to what extent parenting matters for inhibition development from 2 to 8years of age. Data were collected from 421 families, with 348 mother-child dyads and 342 father-child dyads participating. Children's inhibition capacities and parenting behaviors were assessed in a three-wave longitudinal data collection. The main analyses examined the impact of parenting on the development of children's inhibition capacities. They were conducted using a multilevel modeling (MLM) framework. The results lead to the conclusion that both mothers and fathers contribute through their child-rearing behavior to their children's executive functioning, even when controlling for age-related improvement (maturation) and important covariates such as gender, verbal IQ, and place of enrollment. More significant relations between children's inhibition development and parenting were displayed for mothers than for fathers. More precisely, parenting behaviors that involve higher monitoring, lower discipline, inconsistency and negative controlling, and a positive parenting style are associated with good development of inhibition capacities in children.

One first? Acquisition of the cardinal and ordinal uses of numbers in preschoolers.

We studied the acquisition of the ordinal meaning of number words and examined its development relative to the acquisition of the cardinal meaning. Three groups of 3-, 4-, and 5-year-old children were tested in two tasks requiring the use of number words in both cardinal and ordinal contexts. Understanding of the counting principles was also measured by asking the children to assess the correctness of a cartoon character's counting in both contexts. In general, the children performed cardinal tasks significantly better than ordinal ones. Tasks requiring the production of the number for a given quantity or position were solved more accurately than those testing the ability to select a set of n objects or the object in the nth position. Different profiles were obtained for the principles; those principles shared by the two contexts were mastered earlier in the cardinal context. Regarding order (ir)relevance, older children adhered to rigid ways of counting, producing better results in the ordinal context and incorrect rejections in the cardinal trials. Altogether, our data indicate that the acquisitions of cardinal and ordinal meanings of numbers are related, and cardinality precedes the development of ordinality.

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.

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.

Neural correlates of symbolic number comparison in developmental dyscalculia.

Developmental dyscalculia (DD) is a deficit in number processing and arithmetic that affects 3-6% of schoolchildren. The goal of the present study was to analyze cerebral bases of DD related to symbolic number processing. Children with DD aged 9-11 years and matched children with no learning disability history were investigated using fMRI. The two groups of children were controlled for general cognitive factors, such as working memory, reading abilities, or IQ. Brain activations were measured during a number comparison task on pairs of Arabic numerals and a color comparison task on pairs of nonnumerical symbols. In each task, pairs of stimuli that were close or far on the relevant dimension were constituted. Brain activation in bilateral intraparietal sulcus (IPS) was modulated by numerical distance in controls but not in children with DD. Moreover, although the right IPS responded to numerical distance only, the left IPS was influenced by both numerical and color distances in control children. Our findings suggest that dyscalculia is associated with impairment in areas involved in number magnitude processing and, to a lesser extent, in areas dedicated to domain-general magnitude processing.

Comparing the magnitude of two fractions with common components: which representations are used by 10- and 12-year-olds?

This study tested whether 10- and 12-year-olds who can correctly compare the magnitudes of fractions with common components access the magnitudes of the whole fractions rather than only compare the magnitudes of their components. Time for comparing two fractions was predicted by the numerical distance between the whole fractions, suggesting an access to their magnitude. In addition, we tested whether the relative magnitude of the denominator interferes with the processing of the fraction magnitude and, thus, needs to be inhibited. Response times were slower for fractions with common numerators than for fractions with common denominators, indicating an interference of the magnitude of the denominators with the selection of the larger fraction. A negative priming effect was shown for the comparison of natural numbers primed by fractions with common numerators, suggesting an inhibition of the selection of the larger denominator during the comparison of fractions. In conclusion, children who can correctly compare fractions with common components can access the magnitude of the whole fractions but remain sensitive to the interference of the relative magnitude of the denominators. This study highlights the fact that beyond the interference of natural number knowledge at the conceptual level (called the "whole number bias" by Ni & Zhou, 2005), children need to manage the interference of the magnitude of the denominators (Stroop-like effect).

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.

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.