•The interrelationship between different number knowledge skills was investigated.•The ability to link sets to numerals is the link between informal and formal skills.•Working memory and inhibition ...differently contribute to number knowledge.•Working memory predicted most components of number knowledge.
The purpose of this study was to analyze the contribution of specific executive function (EF) components to different number knowledge skills. A sample of 143 children attending the last year of preschool educational services (Mage = 65.01 months, SD = 3.57) were tested on five number knowledge tasks from the Numerical Intelligence Battery and four EF tasks assessing working memory (WM) and inhibition. First, we examined the interrelationship between different number skills; the results suggested that the relationship between basic informal skills (set comparison and number sequence) and formal skills (seriation of Arabic numerals and number comparison) was mediated by the ability to link sets to numerals. Next, we explored the contribution of WM and inhibition to different number knowledge skills. The structural equation model showed that WM and inhibition were differentially related to specific number knowledge skills. Specifically, WM predicted most components of number knowledge, including the two basic informal skills and the number comparison, whereas inhibition contributed to the seriation of Arabic numerals. The ability to link sets to numerals was predicted only by number sequence, not by EF components.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Abstract
Animals employ quantitative abilities to gauge crucial aspects of their environment, such as food or predator density in a given area or the number of eggs in a nest. These quantitative ...skills hold ecological implications and can impact an animal’s fitness. However, our comprehension of how these abilities intersect with environmental challenges remains limited. We tested for spontaneous quantity discrimination in the sleepy lizard (Tiliqua rugosa), a long-lived species known for forming life-long pair bonds in which pairs come together for the breeding season. We subjected lizards to a Y-maze experiment presenting both discrete (comparisons involving two vs. four, two vs. six, two vs. eight, four vs. six, four vs. eight, and six vs. eight pieces) and equivalent continuous combinations (single pieces differing in size) of pumpkin pieces. Our findings revealed that sleepy lizards exhibited spontaneous quantity discrimination, favoring the larger quantity in three discrete comparisons (eight vs. two, two vs. six, four vs. six) and two continuous comparisons (eight vs. two, eight vs. four). However, low accuracy may be attributable to difficulty in visual acuity exacerbated by difficulty discriminating quantities at small ratios. Furthermore, we found no evidence for a speed-accuracy trade-off in their decision-making process. Our results suggest that sleepy lizards likely employ multiple cues to estimate quantity accurately. Considering these results in the context of previous studies on various lizard species, it becomes apparent that lizards, as a group, offer a valuable model for unraveling the evolution of cognition, given their diverse ecology and sociobiology.
When observing a simple visual scene such as an array of dots, observers can easily and automatically extract their number. How does our visual system accomplish this? We investigate the role of ...specific spatial frequencies to the encoding of number through cross-adaptation. In two experiments, observers were peripherally adapted to six randomly generated sinusoidal gratings varying from relatively low-spatial frequency (M = 0.44 c/deg) to relatively high-spatial frequency (M = 5.88 c/deg). Subsequently, observers judged which side of the screen had a higher number of dots. We found a strong number-adaptation effect to low-spatial frequency gratings (i.e., participants significantly underestimated the number of dots on the adapted side) but a significantly reduced adaptation effect for high-spatial frequency gratings. Various control conditions demonstrate that these effects are not due to a generic response bias for the adapted side, nor moderated by dot size or spacing effects. In a third experiment, we observed no cross-adaptation for centrally presented gratings. Our results show that observers’ peripheral number perception can be adapted even with stimuli lacking any numeric or segmented object information and that low spatial frequencies adapt peripheral number perception more than high ones. Together, our results are consistent with recent number perception models that suggest a key role for spatial frequency in the extraction of number from the visual signal (e.g., Paul, Ackooij, Ten Cate, & Harvey,
2022
), but additionally suggest that some spatial frequencies – especially in the low range and in the periphery – may be weighted more by the visual system when estimating number. We argue that the cross-adaptation paradigm is also a useful methodology for discovering the primitives of visual number encoding.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
A system for approximate number discrimination has been shown to arise in at least two types of hierarchical neural network models—a generative Deep Belief Network (DBN) and a Hierarchical ...Convolutional Neural Network (HCNN) trained to classify natural objects. Here, we investigate whether the same two network architectures can learn to recognise exact numerosity. A clear difference in performance could be traced to the specificity of the unit responses that emerged in the last hidden layer of each network. In the DBN, the emergence of a layer of monotonic ‘summation units’ was sufficient to produce classification behaviour consistent with the behavioural signature of the approximate number system. In the HCNN, a layer of units uniquely tuned to the transition between particular numerosities effectively encoded a thermometer-like ‘numerosity code’ that ensured near-perfect classification accuracy. The results support the notion that parallel pattern-recognition mechanisms may give rise to exact and approximate number concepts, both of which may contribute to the learning of symbolic numbers and arithmetic.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
A mental number line in human newborns Di Giorgio, Elisa; Lunghi, Marco; Rugani, Rosa ...
Developmental science,
November 2019, 2019-11-00, 20191101, Volume:
22, Issue:
6
Journal Article
Open access
Humans represent numbers on a mental number line with smaller numbers on the left and larger numbers on the right side. A left‐to‐right oriented spatial–numerical association, (SNA), has been ...demonstrated in animals and infants. However, the possibility that SNA is learnt by early exposure to caregivers’ directional biases is still open. We conducted two experiments: in Experiment 1, we tested whether SNA is present at birth and in Experiment 2, we studied whether it depends on the relative rather than the absolute magnitude of numerousness. Fifty‐five‐hour‐old newborns, once habituated to a number (12), spontaneously associated a smaller number (4) with the left and a larger number (36) with the right side (Experiment 1). SNA in neonates is not absolute but relative. The same number (12) was associated with the left side rather than the right side whenever the previously experienced number was larger (36) rather than smaller (4) (Experiment 2). Control on continuous physical variables showed that the effect is specific of discrete magnitudes. These results constitute strong evidence that in our species SNA originates from pre‐linguistic and biological precursors in the brain.
Neonates, after being habituated to a certain number of dots, associated a smaller number with the left and a larger number with the right side. This evidence demonstrates that neonates spontaneously associate numbers with space.
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DOBA, FZAB, GIS, IJS, IZUM, KILJ, NLZOH, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBMB, UILJ, UKNU, UL, UM, UPUK
The learning of addition and subtraction that usually be done in sequence impact students’ tendency to separate type of the strategies employ to solve the related problems. In fact, there are a ...number of situations that can be observed and solved through both lenses. Therefore, in this study we designed a simultaneous addition and subtraction of two-digit numbers learning trajectory. The learning activities were constructed based on Realistic Mathematics Education (RME) Approach. This design study was conducted in three steps consist of preliminary study, teaching experiments, and retrospective analysis. The teaching experiments were done in two cycle, the first was done with four students and the second was done with 33 students in two classes of an elementary school located in Singaraja, Bali. The data related to number sense ability were gathered from observation and students’ written work in solving worksheet and post-test. The collected data were analyzed using constant comparative method. From the results, we found that a simultaneous learning of two-digit numbers addition and subtraction were effectively develop the students’ number sense and encourage the students to develop efficient counting strategies.
Informes tanto nacionales como internacionales (v.gr., TERCE, PISA) han revelado un bajo rendimiento en matemáticas en la población escolar panameña. Este estudio fue diseñado para evaluar la ...eficacia de una intervención de Nivel 1 del modelo de Respuesta a la Intervención (RtI) en matemáticas. La intervención fue implementada por maestros panameños para mejorar las habilidades matemáticas tempranas de los estudiantes de primer grado de primaria. Se seleccionó una muestra de 926 alumnos de primer curso de primaria (edad en meses, media= 79.3, DT= 5.4) que estaba dividida en dos grupos: un grupo experimental (N= 534, 266 varones, 268 mujeres), y un grupo control (N=392, 185 varones, 207 mujeres). Se instruyó a los maestros en la administración de los Indicadores de Progreso de Aprendizaje en Matemáticas (IPAM) que es una medida basada en el currículo compuesta por cinco medidas aisladas (comparación de magnitudes, series numéricas, operaciones de un dígito, operaciones multidígitos y comprensión del valor posicional) para ser administrada en tres momentos diferentes del curso escolar; y en la implementación de un programa de matemáticas que se implementó con una instrucción directa, estructurada y explícita para mejorar las habilidades matemáticas básicas. La intervención tuvo un impacto positivo significativo ya que se encontraron diferencias significativas entre los estudiantes del grupo experimental y de control en las pendientes de crecimiento para las medidas de comparación de magnitudes, series numéricas, operaciones multidígitos y comprensión del valor posicional, excepto en operaciones de un dígito. En conclusión, los estudiantes panameños de primer grado se beneficiaron de una intervención de Nivel 1 basada en habilidades matemáticas básicas, implementada por maestros en servicio activo.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Numbers are fundamental mathematical concepts that underlie various other mathematical principles. This research investigates the relationship between number sense and the numeracy abilities of ...fifth-grade elementary school students. A cross-sectional survey method was used, with 205 respondents voluntarily participating. The results showed a reciprocal relationship between number sense and numeracy in elementary school students. Emphasising number sense can enhance flexibility in numeracy solutions. Number sense can be developed through assigning math tasks related to the students' environment or associating it with other learning processes. The study emphasises the importance of number sense in the primary school mathematics curriculum.
This text focuses on the development of number sense, specifically addressing the challenges associated with understanding the number system, including the connections to and difficulties in early ...arithmetic learning. It provides a synthesis of the scientific literature related to this development. It concludes by proposing a hypothesis for the development of number sense, associated with the construction of dynamic and pictorial mental representations. This continuum proposes five key phases: perception of small quantities, additive thinking, multiplicative thinking and pre-place value, passage to tens and passage to hundreds and understanding place value.
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