•Math anxiety indirectly affects math achievement through working memory in young children.•The relationship between math anxiety and math achievement in young children is not mediated through number ...sense.•There is generally no direct path from math anxiety to math achievement in young children.
Math anxiety is considered a predictor of math achievement, although the cognitive mechanism whereby math anxiety impairs math achievement is unclear. The paper presents the results of cross-sectional (N = 241) and longitudinal (N = 369) studies conducted among early school-aged children on the cognitive mechanism whereby math anxiety impairs math achievement. The following hypotheses were tested: (1) math anxiety directly affects math achievement; (2) in accordance with processing efficiency and attentional cognitive theories, math anxiety indirectly affects math achievement through working memory; (3) in accordance with the cognitive deficit model, math anxiety indirectly affects math achievement through number sense. The results mostly confirm the mediating role of working memory and undermine the mediating role of number sense and the direct path in the relationship between math anxiety and math achievement. Because previous studies undertaken in adults show the direct path from math anxiety to math achievement and the role of symbolic number processing in explaining the relationship between the two, the methodological and developmental aspects of the obtained results are discussed in the paper.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Number sense and arithmetic fluency are fundamental to early mathematical development. However, these capacities generally fail to predict mathematical achievement in older adolescents and adults. We ...propose that later mathematical development is driven by coming to understand the higher-order principles that bring structure to mathematics.
To evaluate this proposal, we tested whether college students (n = 134) apply arithmetic principles – inverse, associativity, and commutativity – to efficiently verify arithmetic sentences mixing multiplication and division operations such as 18 × 7 ÷ 3 = 42.
This was the case. People were more accurate and faster when verifying arithmetic sentences that could be simplified by the application of arithmetic principles compared to control problems. People found problems that required the associativity principle to be more difficult (i.e., they made more errors and took longer) than those that required the inverse principle, and problems that additionally required the commutativity principle to be more difficult still. Converging evidence for the use of these principles came from their strategy self-reports. Critically, individual differences in applying these principles predicted mathematical achievement even after controlling for number sense, arithmetic fluency, and verbal achievement.
These findings have implications for theories of mathematical development and may point the way to future interventions for increasing the mathematical achievement of younger children.
•Mathematics is given structure by higher-order principles.•This study investigated understanding of inverse, associativity, and commutativity.•College students could apply these principles when solving arithmetic problems.•Individual differences in their application predicted mathematical achievement.•This was true even after controlling for number sense and arithmetic fluency.
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Penelitian ini bertujuan untuk melihat efektivitas metode pembelajaran tutor sebaya dalam meningkatkan kemampuan number sense siswa di kelas VII A SMP Negeri 1 Duripoku. Penelitian ini merupakan ...penelitian pra-eksperimental dengan one group pre test-post design. Untuk melihat apakah terdapat perbedaan rata-rata kemampuan number sense sebelum dan sesudah diterapkan metode tutor sebaya, maka dilakukan uji paired sample t-test, sementara untuk melihat efektivitasnya dilakukan analisis gain ternomalisasi (N-Gain). Dari hasil analisis data pada taraf signifikansi 5%, ditemui nilai t = 7.721 dengan signifikansi 0,00 (< 0.05) yang berarti terdapat perbedaan nilai rata-rata kemampuan number sense pada pre test dan post test, untuk hasil analisis N-Gain diperoleh bahwa efektivitas metode tutor sebaya dalam meningkatkan kemampuan number sense berada pada kategori rendah.
Humans are thought to use the approximate number system (ANS) to make quick approximations based on quantity even before learning to count. However, there has long been controversy regarding the ...salience of number versus other stimulus dimensions throughout development, including a recent proposal that number sense is derived from a sense of general magnitude. Here, we used a regression approach to disentangle numerical acuity from sensitivity to total surface area in both 5-year-old children and adults. We found that both children and adults displayed higher acuity when making numerosity judgments than total surface area judgments. Adults were largely able to ignore irrelevant stimulus features when making numerosity or total area judgments. Children were more biased by numerosity when making total area judgments than by total area when making numerosity judgments. These results provide evidence that number is more salient than total surface area even before the start of formal education and are inconsistent with the Sense of Magnitude proposal.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Visual perception has been found to be a critical factor for reading comprehension and arithmetic computation in separate lines of research with different measures of visual form perception. The ...current study of 1099 Chinese elementary school students investigated whether the same visual form perception (assessed by a geometric figure matching task) underlies both reading comprehension and arithmetic computation. The results showed that visual form perception had close relations with both reading comprehension and arithmetic computation, even after controlling for age, gender, and cognitive factors such as processing speed, attention, working memory, visuo-spatial processing, and general intelligence. Results also showed that numerosity comparison's relations with reading comprehension and arithmetic computation were fully accounted for by visual form perception. These results suggest that reading comprehension and arithmetic computation might share a similar visual form processing mechanism.
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•The nonsymbolic numerosity comparison can be processed directly and via the estimation of visual cues.•The congruency effect reflects the bias in nonsymbolic comparison due to estimation visual ...cues.•The congruency effect varied in different formats of stimulus presentation and visual cues.•The congruency effect for convex hull was smaller than that for cumulative area.
The extent to which the approximate number sense is based on the estimation of continuous visual properties has been widely discussed. Some investigators have hypothesized that humans are able to estimate numerosity directly and independently of visual cues. Other investigators have posited that numerosity can be processed only via the estimation of non-numeric visual properties. The latter theory is confirmed by the existence of the congruency effect, that is, greater accuracy in congruent trials where visual properties were positively correlated with numerosity compared with that in incongruent trials. In this study, we tested the assumption that the congruency effect, reflecting the bias in numerosity estimation due to the estimation of visual cues, varies depending on the format of the stimulus presentation and object heterogeneity. The study involved a sample of pupils in Grades 5–9 from Kyrgyzstan (N = 764; 48% girls; mean age = 13.06 years), whereby participants performed a nonsymbolic comparison test in four formats of stimulus presentation: paired/homogeneous, paired/heterogeneous, mixed/homogeneous, and mixed/heterogeneous. Compared arrays of figures might be congruent or incongruent for one visual parameter (convex hull or cumulative area), whereas another visual parameter was held constant for two arrays. The results of generalized linear mixed-effect models demonstrated that the largest congruency effect occurred in a paired format with homogeneous figures. The congruency effect was insignificant in the mixed/heterogeneous format. The results also revealed that the effects of the convex hull and cumulative area varied in different formats of stimulus presentations.
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Many species from diverse and often distantly related animal groups (e.g. monkeys, crows, fish and bees) have a sense of number. This means that they can assess the number of items in a set - its ...'numerosity'. The brains of these phylogenetically distant species are markedly diverse. This Review examines the fundamentally different types of brains and neural mechanisms that give rise to numerical competence across the animal tree of life. Neural correlates of the number sense so far exist only for specific vertebrate species: the richest data concerning explicit and abstract number representations have been collected from the cerebral cortex of mammals, most notably human and nonhuman primates, but also from the pallium of corvid songbirds, which evolved independently of the mammalian cortex. In contrast, the neural data relating to implicit and reflexive numerical representations in amphibians and fish is limited. The neural basis of a number sense has not been explored in any protostome so far. However, promising candidate regions in the brains of insects, spiders and cephalopods - all of which are known to have number skills - are identified in this Review. A comparative neuroscientific approach will be indispensable for identifying evolutionarily stable neuronal circuits and deciphering codes that give rise to a sense of number across phylogeny.
Abstract
Posterior parietal cortex (PPC) is thought to encode and represent the number of objects in a visual scene (i.e., numerosity). Whether this representation is shared for simultaneous and ...sequential stimuli (i.e., mode independency) is debated. We tested the existence of a common neural substrate for the encoding of these modes using fMRI. While both modes elicited overlapping BOLD response in occipital areas, only simultaneous numerosities significantly activated PPC. Unique activation for sequential numerosities was found in bilateral temporal areas. Multivoxel pattern analysis revealed numerosity selectivity in PPC only for simultaneous numerosities and revealed differential encoding of presentation modes. Voxel-wise numerosity tuning functions for simultaneous numerosities in occipital and parietal ROIs revealed increasing numerosity selectivity along an occipito-to-parietal gradient. Our results suggest that the parietal cortex is involved in the extraction of spatial but not temporal numerosity and question the idea of commonly used cortical circuits for a mode-independent numerosity representation.
On a now orthodox view, humans and many other animals possess a "number sense," or approximate number system (ANS), that represents number. Recently, this orthodox view has been subject to numerous ...critiques that question whether the ANS genuinely represents number. We distinguish three lines of critique - the arguments from congruency, confounds, and imprecision - and show that none succeed. We then provide positive reasons to think that the ANS genuinely represents numbers, and not just non-numerical confounds or exotic substitutes for number, such as "numerosities" or "quanticals," as critics propose. In so doing, we raise a neglected question: numbers of what kind? Proponents of the orthodox view have been remarkably coy on this issue. But this is unsatisfactory since the predictions of the orthodox view, including the situations in which the ANS is expected to succeed or fail, turn on the kind(s) of number being represented. In response, we propose that the ANS represents not only natural numbers (e.g., 7), but also non-natural rational numbers (e.g., 3.5). It does not represent irrational numbers (e.g., √2), however, and thereby fails to represent the real numbers more generally. This distances our proposal from existing conjectures, refines our understanding of the ANS, and paves the way for future research.
There are massive developments in children’s early number skills in the ages 4- to 6-year old during which they attend preschool education and before they transition to formal school. We investigated ...to which extent these developments can be explained by children’ schooling experiences during preschool or by chronological age related maturational changes. In a secondary data-analysis of an existing longitudinal dataset, we compared children who were similar in age but different in the amount of preschool education (Old Year 2, n = 104, Mage = 62 months SDage 0.9 months vs. Young Year 3, n = 71, Mage = 65 months, SDage = 1.5 months) as well as children who were similar in the amount of preschool experience but differed in age (Young Year 3, n = 71, Mage = 65 months, SDage = 1.5 months vs. Old Year 3, n = 104, Mage = 74 months, SDage = 1.1 months). All children completed measures of numbering (verbal counting, dot enumeration, object counting), relations (number order, numeral identification, symbolic comparison, nonsymbolic comparison) and arithmetic operations (nonverbal calculation). We observed effects of preschool on object counting, numeral recognition and number order. There were also effects of chronological age on verbal counting, number order, numeral recognition and nonverbal calculation. The current data highlight which early number skills may be particularly malleable through schooling. They provide a more careful characterization of the potential factors that contribute to children’s early numerical competencies.
•Children show massive developments in their number skills before formal school.•We examined whether these can be explained by schooling experiences and/or age.•Effects of preschool were found on object counting, number order and numeral recognition.•Age effects occurred on verbal counting, number order, numeral recognition and arithmetic.•Preschool experiences and age affect early number skills before formal schooling.
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