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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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.
Are there some differences so small that we cannot detect them? Are some quantities so similar (e.g., the number of spots on two speckled hens) that they simply look the same to us? Although modern ...psychophysical theories such as Signal Detection Theory would predict that, with enough trials, even minute differences would be perceptible at an above-chance rate, this prediction has rarely been empirically tested for any psychological dimension, and never for the domain of number perception. In an experiment with over 400 adults, we find that observers can distinguish which of two collections has more dots from a brief glance. Impressively, observers performed above chance on every numerical comparison tested, even when discriminating a comparison as difficult as 50 versus 51 dots. Thus, we present empirical evidence that numerical discrimination abilities, consistent with SDT, are remarkably fine-grained.
Although there is substantial evidence for an innate 'number sense' that scaffolds learning about mathematics, whether the underlying representations are based on discrete or continuous perceptual ...magnitudes has been controversial. Yet the nature of the computations supported by these representations has been neglected in this debate. While basic computation of discrete non-symbolic quantities has been reliably demonstrated in adults, infants, and non-humans, far less consideration has been given to the capacity for computation of continuous perceptual magnitudes. Here we used a novel experimental task to ask if humans can learn to add non-symbolic, continuous magnitudes in accord with the properties of an algebraic group, by feedback and without explicit instruction. Three pairs of experiments tested perceptual addition under the group properties of commutativity (Experiments 1a-b), identity and inverses (Experiments 2a-b) and associativity (Experiments 3a-b), with both line length and brightness modalities. Transfer designs were used in which participants responded on trials with feedback based on sums of magnitudes and later were tested with novel stimulus configurations. In all experiments, correlations of average responses with magnitude sums were high on trials with feedback. Responding on transfer trials was accurate and provided strong support for addition under all of the group axioms with line length, and for all except associativity with brightness. Our results confirm that adult human subjects can implicitly add continuous quantities in a manner consistent with symbolic addition over the integers, and that an 'artificial algebra' task can be used to study implicit computation.
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Number sense has been systematically measured using dot comparison tasks. However, recent studies have reported that performance on dot comparison might be influenced inhibitory control and visual ...properties of dot arrays. In the present study, we analysed the influence of continuous magnitude, inhibitory control, and numerical ratio on the dot comparison performance of preschool children.
Participants were 517 preschool children from 13 different schools in Chile. Children completed a dot comparison and two inhibitory control tasks. Gebuis and Reynvoet method was used to create well-controlled dot arrays for use in the dot comparison task. A logistic mixed effects model was conducted to predict participants' dot comparison accuracy. Continuous magnitude and ratio were entered as level-1 predictors and inhibitory control as level-2 predictors.
The results showed that all predictors made a significant contribution to dot comparison accuracy. Furthermore, a significant double interaction (inhibitory control x continuous magnitude) and a triple interaction (inhibitory control x continuous magnitude x ratio) showed that the contribution of inhibitory control skills in dot comparison accuracy depends on the continuous properties of dot arrays and ratio.
These findings suggest that preschool children rely more on continuous magnitudes than numerosity in dot comparison tasks. They also indicate that the greater children's inhibitory control, the more able they are to respond based on numerosity in fully incongruent trials, particularly when ratio is low (easiest items). Taken together, the above findings support the competing processes account provided that both ANS and inhibitory control skills influence performance on dot comparison tasks.
An emergentist perspective on the origin of number sense Zorzi, Marco; Testolin, Alberto
Philosophical transactions of the Royal Society of London. Series B. Biological sciences,
02/2018, Volume:
373, Issue:
1740
Journal Article
Peer reviewed
Open access
The finding that human infants and many other animal species are sensitive to numerical quantity has been widely interpreted as evidence for evolved, biologically determined numerical capacities ...across unrelated species, thereby supporting a ‘nativist’ stance on the origin of number sense. Here, we tackle this issue within the ‘emergentist’ perspective provided by artificial neural network models, and we build on computer simulations to discuss two different approaches to think about the innateness of number sense. The first, illustrated by artificial life simulations, shows that numerical abilities can be supported by domain-specific representations emerging from evolutionary pressure. The second assumes that numerical representations need not be genetically pre-determined but can emerge from the interplay between innate architectural constraints and domain-general learning mechanisms, instantiated in deep learning simulations. We show that deep neural networks endowed with basic visuospatial processing exhibit a remarkable performance in numerosity discrimination before any experience-dependent learning, whereas unsupervised sensory experience with visual sets leads to subsequent improvement of number acuity and reduces the influence of continuous visual cues. The emergent neuronal code for numbers in the model includes both numerosity-sensitive (summation coding) and numerosity-selective response profiles, closely mirroring those found in monkey intraparietal neurons. We conclude that a form of innatism based on architectural and learning biases is a fruitful approach to understanding the origin and development of number sense.
This article is part of a discussion meeting issue ‘The origins of numerical abilities'.
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•Proportion-based number line strategies were linked with math ability at age 6–8.•Bias in number line placements was also linked with children’s math ability.•Approximate Number System (ANS) acuity ...also explained variance in math ability.•Number line estimation and ANS task performance appear to be independent.
Various laboratory-based numerical cognition measures are often found to be linked with standardized math scores, yet the exact nature of these links over development remains in question. In this study, we investigated how 0–100 number line estimation performance and dot numerosity discrimination explained variance in 6- to 8-year-olds’ standardized math ability scores, and we assessed links between tasks. Our primary goal was to assess the link between estimation performance and math ability from a theoretical perspective that models number line estimation as an instance of proportion estimation. As age increased, children’s proportion-based strategies for number line estimation became more sophisticated and estimation bias decreased. Children who spontaneously inferred and used a central reference point to guide their proportion estimates scored higher on the math ability measure (TEMA-3), demonstrating a relation between more advanced proportion estimation strategies and higher math abilities. Individual differences in estimation bias also made a lesser contribution to explaining variance in children’s math ability. Dot discrimination accuracy uniquely contributed to children’s math ability. Number line estimation performance and dot discrimination accuracy were not associated, consistent with prior research suggesting that number line estimation does not directly map onto mental numerical magnitude representations. Educational implications and future directions are discussed.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
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