Developmental dyscalculia is thought to be a specific impairment of mathematics ability. Currently dominant cognitive neuroscience theories of developmental dyscalculia suggest that it originates ...from the impairment of the magnitude representation of the human brain, residing in the intraparietal sulcus, or from impaired connections between number symbols and the magnitude representation. However, behavioral research offers several alternative theories for developmental dyscalculia and neuro-imaging also suggests that impairments in developmental dyscalculia may be linked to disruptions of other functions of the intraparietal sulcus than the magnitude representation. Strikingly, the magnitude representation theory has never been explicitly contrasted with a range of alternatives in a systematic fashion. Here we have filled this gap by directly contrasting five alternative theories (magnitude representation, working memory, inhibition, attention and spatial processing) of developmental dyscalculia in 9–10-year-old primary school children. Participants were selected from a pool of 1004 children and took part in 16 tests and nine experiments. The dominant features of developmental dyscalculia are visuo-spatial working memory, visuo-spatial short-term memory and inhibitory function (interference suppression) impairment. We hypothesize that inhibition impairment is related to the disruption of central executive memory function. Potential problems of visuo-spatial processing and attentional function in developmental dyscalculia probably depend on short-term memory/working memory and inhibition impairments. The magnitude representation theory of developmental dyscalculia was not supported.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
A significant body of research links individual differences in symbolic numerical abilities, such as arithmetic, to number sense, the neurobiological system used to approximate and manipulate ...quantities without language or symbols. However, recent findings from cognitive neuroscience challenge this influential theory. Our current review presents an overview of evidence for the number sense account of symbolic numerical abilities and then reviews recent studies that challenge this account, organized around the following four assertions. (1) There is no number sense as traditionally conceived. (2) Neural substrates of number sense are more widely distributed than common consensus asserts, complicating the neurobiological evidence linking number sense to numerical abilities. (3) The most common measures of number sense are confounded by other cognitive demands, which drive key correlations. (4) Number sense and symbolic number systems (Arabic digits, number words, and so on) rely on distinct neural mechanisms and follow independent developmental trajectories. The review follows each assertion with comments on future directions that may bring resolution to these issues.
Our current review presents an overview of evidence for the number sense account of symbolic numerical abilities and then reviews recent studies that challenge this account.
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BFBNIB, FZAB, GIS, IJS, IZUM, KILJ, NLZOH, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBMB, UL, UM, UPUK
Background
Evidence exists that there are two main underlying cognitive factors in mathematical difficulties: working memory and number sense. It is suggested that real math difficulties appear when ...both working memory and number sense are weak, here referred to as the double deficit (DD) hypothesis.
Aims
The aim of this study was to test the DD hypothesis within a longitudinal time span of 2 years.
Sample
A total of 670 children participated. The mean age was 4.96 years at the start of the study and 7.02 years at the end of the study.
Methods
At the end of the first year of kindergarten, both visual–spatial working memory and number sense were measured by two different tasks. At the end of first grade, mathematical performance was measured with two tasks, one for math facts and one for math problems.
Results
Multiple regressions revealed that both visual working memory and symbolic number sense are predictors of mathematical performance in first grade. Symbolic number sense appears to be the strongest predictor for both math areas (math facts and math problems). Non‐symbolic number sense only predicts performance in math problems. Multivariate analyses of variance showed that a combination of visual working memory and number sense deficits (NSDs) leads to the lowest performance on mathematics.
Conclusions
Our DD hypothesis was confirmed. Both visual working memory and symbolic number sense in kindergarten are related to mathematical performance 2 years later, and a combination of visual working memory and NSDs leads to low performance in mathematical performance.
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BFBNIB, DOBA, FZAB, GIS, IJS, IZUM, KILJ, NLZOH, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBMB, SIK, UILJ, UKNU, UL, UM, UPUK
Tujuan dari penelitian ini untuk mengetahui pengaruh number sense terhadap hasil belajar matematika siswa di SMP Negeri 8 Tarakan sehingga guru dapat merencanakan pembelajaran dari karakteristik ...number sense yang mereka miliki. Populasi dalam penelitian ini adalah seluruh kelas VIII di SMP N 8 Tarakan sedangkan pengambilan sampel menggunakan teknik simple random sampling. Teknik yang digunakan dalam penelitian ini adalah analisis regresi linier sederhana dimana kemampuan number sense siswa sebagai X dan hasil belajar matematika siswa sebagai Y. dari hasil penelitian diperoleh model persamaan linier regresi sederhana 14Y=4,003+0,22 X dimana jika kemampuan number sense siswa nol maka hasil belajar matematika siswa 4,003 sedangkan jika kemampuan number sense meningkat sebesar 1 satuan maka hasil belajar siswa akan naik sebesar 0,22. Sedangkan dengan menggunakan R square diperoleh nilai sebesar 0,163 artinya pengaruh number sense hanya sekitar 16,3% terhadap hasil belajar matematika, artinya salah satu hal yang mempengaruhi hasil belajar matematika siswa adalah kemampuan number sense.
Numerical cognition in children with cerebral palsy de Freitas Feldberg, Silvia Cristina; da Silva Gusmão Cardoso, Thiago; Santos, Flavia H. ...
Research in developmental disabilities,
December 2021, 2021-12-00, 20211201, Volume:
119
Journal Article
Peer reviewed
•Participant’s.•Measured by the Raven Matrices scales.•On the other hand, IQ scores were in typical levels for all groups.•van Rooijen.•Maintain that working memory and level of intelligence ...affects.•With numerical cognition.
Children with Cerebral Palsy (CP) often perform poorly in mathematics. It is not yet clear to what extent mathematics difficulties in this clinical condition are similar to those observed in developmental dyscalculia. To better elucidate this issue, we conducted an exploratory cross-sectional study with a sample of children and adolescents with congenital brain injuries and educational history of problems in Mathematics. Fifty students aged 7–15 years, of both genders (28 males) participated in the study, 31 with typical development (TD) and 19 of whom diagnosed with spastic CP. Nine had hemiplegia and ten diplegia. Assessment procedures included a neuropsychological battery covering numerical cognition (ZAREKI-R) and working memory (AWMA) skills, and a computerized task for comparing non-symbolic magnitudes as a measure of number sense. Despite average intelligence coefficient, participants with CP underperformed the TD in five of the 12 ZAREKI-R subtests, as well as in the number sense and working memory tasks. scores were lower among hemiplegic children compared to diplegic, numerical cognition was impaired in all CP group, unveiling a dyscalculia secondary to neurodevelopmental impairments. Therefore, we can consider that mathematical learning difficulties in CP as being heterogeneous and associated with the immaturity of neuropsychological functions, with consequences for the development of numerical cognition.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Preverbal infants spontaneously represent the number of objects in collections. Is this 'sense of number' (also referred to as Approximate Number System, ANS) part of the cognitive foundations of ...mathematical skills? Multiple studies reported a correlation between the ANS and mathematical achievement in children. However, some have suggested that such correlation might be mediated by general-purpose inhibitory skills. We addressed the question using a longitudinal approach: we tested the ANS of 60 12 months old infants and, when they were 4 years old (final N = 40), their symbolic math achievement as well as general intelligence and inhibitory skills. Results showed that the ANS at 12 months is a specific predictor of later maths skills independent from general intelligence or inhibitory skills. The correlation between ANS and maths persists when both abilities are measured at four years. These results confirm that the ANS has an early, specific and longstanding relation with mathematical abilities in childhood.
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FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SBCE, SBMB, UL, UM, UPUK
Mapping number to space is natural and spontaneous but often nonveridical, showing a clear compressive nonlinearity that is thought to reflect intrinsic logarithmic encoding of numerical values. We ...asked 78 adult participants to map dot arrays onto a number line across nine trials. Combining participant data, we confirmed that on the first trial, mapping was heavily compressed along the number line, but it became more linear across trials. Responses were well described by logarithmic compression but also by a parameter-free Bayesian model of central tendency, which quantitatively predicted the relationship between nonlinearity and number acuity. To experimentally test the Bayesian hypothesis, we asked 90 new participants to complete a color-line task in which they mapped noise-perturbed color patches to a “color line.” When there was more noise at the high end of the color line, the mapping was logarithmic, but it became exponential with noise at the low end. We conclude that the nonlinearity of both number and color mapping reflects contextual Bayesian inference processes rather than intrinsic logarithmic encoding.
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NUK, OILJ, SAZU, UKNU, UL, UM, UPUK
One important factor that hampers children's learning of mathematics is math anxiety (MA). Still, the mechanisms by which MA affects performance remain debated. The current study investigated the ...relationship between MA, basic number processing abilities (i.e., cardinality and ordinality processing), and executive functions in school children enrolled in grades 4-7 (
= 127). Children were divided into a high math anxiety group (
29) and a low math anxiety group (
= 31) based on the lowest quartile and the highest quartile. Using a series of analyses of variances, we find that highly math-anxious students do not perform worse on cardinality processing tasks (i.e., digit comparison and non-symbolic number sense), but that they perform worse on numerical and non-numerical ordinality processing tasks. We demonstrate that children with high MA show poorer performance on a specific aspect of executive functions-shifting ability. Our models indicate that shifting ability is tied to performance on both the numerical and non-numerical ordinality processing tasks. A central factor seems to be the involvement of executive processes during ordinality judgements, and executive functions may constitute the driving force behind these delays in numerical competence in math-anxious children.
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NUK, OILJ, SAZU, UKNU, UL, UM, UPUK
Francis Galton first reported that humans mentally organize numbers from left to right on a mental number line (1880). This spatial-numerical association was long considered to result from writing ...and reading habits. More recently though, newborns and animals showed a left-to-right oriented spatial numerical association challenging the primary role assigned to culture in determining the link between number and space. Despite growing evidence supporting the intrinsic association between number and space in different species, its adaptive value is still largely unknown.
Here we tested for an advantage in identification of left versus right target positions in 3- to 6-year-old children. Children watched as a toy was hidden under one of 10 linearly arranged identical cups and were then asked to help a stuffed animal retrieve the toy. On each trial, the toy was hidden in the 2nd, 3rd, or 4th cup, from the left or right. To prevent children from staring at the target cup, they were asked to pick up the stuffed animal from under their chair after witnessing the hiding of the toy and then to help the stuffed animal find the toy. Older children were more accurate than younger children. Children exhibited a serial position effect, with performance higher for more exterior targets. Remarkably, children also showed a left bias: they remembered the left targets better than the right targets. Only the youngest children were dramatically influenced by the location of the experimenter during search. Additional analyses support the hypothesis that children used a left-to-right oriented searching strategy in this spatial/ordinal task.
•Children show a left bias.•Children remember the left targets better than the right targets.•Children use a left-to-right searching strategy in performing an ordinal task.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
In a longitudinal study, we investigated the direct and indirect contributions of two aspects of executive functioning - attentional and behavioral control - to the development of early literacy and ...numeracy in kindergarten and first grade. Ninety children (mean age = 6.0 years at Time 1) were assessed on multiple direct measures of executive functioning, as well as phonological awareness and number sense in kindergarten, and word reading and mathematics in first grade. Structural equation models showed that both attentional and behavioral control predicted phonological awareness and number sense. Attentional control had an indirect (via phonological awareness) effect on word reading only, while behavioral control had a direct effect on mathematics and an indirect effect (via phonological awareness) on word reading. Since attentional and behavioral control differentially relate to the emergence of literacy and numeracy, it is concluded that executive functioning has domain-specific effects on children's development.
•Attentional and behavioral control are two components of executive functioning.•These components relate differentially to early literacy and numeracy development.•Attentional and behavioral control predict phonological awareness and number sense.•Attentional control predicts word reading via phonological awareness.•Behavioral control directly predicts mathematics.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
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