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Journal articles on the topic 'Symbolic magnitude'

Author: Grafiati

Published: 4 June 2021

Last updated: 16 February 2022

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1

Cañizares, Danilka Castro, Vivian Reigosa Crespo, and Eduardo González Alemañy. "Symbolic and Non-Symbolic Number Magnitude Processing in Children with Developmental Dyscalculia." Spanish journal of psychology 15, no. 3 (2012): 952–66. http://dx.doi.org/10.5209/rev_sjop.2012.v15.n3.39387.

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The aim of this study was to evaluate if children with Developmental Dyscalculia (DD) exhibit a general deficit in magnitude representations or a specific deficit in the connection of symbolic representations with the corresponding analogous magnitudes. DD was diagnosed using a timed arithmetic task. The experimental magnitude comparison tasks were presented in non-symbolic and symbolic formats. DD and typically developing (TD) children showed similar numerical distance and size congruity effects. However, DD children performed significantly slower in the symbolic task. These results are consi

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2

Ebersbach, Mirjam, and Petra Erz. "Symbolic versus non-symbolic magnitude estimations among children and adults." Journal of Experimental Child Psychology 128 (December 2014): 52–68. http://dx.doi.org/10.1016/j.jecp.2014.06.005.

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3

Binda, Paola, M. Concetta Morrone, and Frank Bremmer. "Saccadic Compression of Symbolic Numerical Magnitude." PLoS ONE 7, no. 11 (2012): e49587. http://dx.doi.org/10.1371/journal.pone.0049587.

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4

Čech, Claude G., and Edward J. Shoben. "Context effects in symbolic magnitude comparisons." Journal of Experimental Psychology: Learning, Memory, and Cognition 11, no. 2 (1985): 299–315. http://dx.doi.org/10.1037/0278-7393.11.2.299.

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5

Sasanguie, Delphine, Bert De Smedt, and Bert Reynvoet. "Evidence for distinct magnitude systems for symbolic and non-symbolic number." Psychological Research 81, no. 1 (2015): 231–42. http://dx.doi.org/10.1007/s00426-015-0734-1.

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6

Fias, Wim, Jan Lammertyn, Bert Reynvoet, Patrick Dupont, and Guy A. Orban. "Parietal Representation of Symbolic and Nonsymbolic Magnitude." Journal of Cognitive Neuroscience 15, no. 1 (2003): 47–56. http://dx.doi.org/10.1162/089892903321107819.

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The close behavioral parallels between the processing of quantitative information conveyed by symbolic and non-symbolic stimuli led to the hypothesis that there exists a common cerebral representation of quantity (Dehaene, Dehaene-Lambertz, & Cohen, 1998). The neural basis underlying the encoding of number magnitude has been localized to regions in and around the intraparietal sulcus (IPS) by brain-imaging studies. However, it has never been demonstrated that these same regions are also involved in the quantitative processing of nonsymbolic stimuli. Using functional brain imaging, we expli

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7

Scalise, Nicole R., Emily N. Daubert, and Geetha B. Ramani. "Narrowing the early mathematics gap: A play-based intervention to promote low-income preschoolers’ number skills." Journal of Numerical Cognition 3, no. 3 (2018): 559–81. http://dx.doi.org/10.5964/jnc.v3i3.72.

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Preschoolers from low-income households lag behind preschoolers from middle-income households on numerical skills that underlie later mathematics achievement. However, it is unknown whether these gaps exist on parallel measures of symbolic and non-symbolic numerical skills. Experiment 1 indicated preschoolers from low-income backgrounds were less accurate than peers from middle-income backgrounds on a measure of symbolic magnitude comparison, but they performed equivalently on a measure of non-symbolic magnitude comparison. This suggests activities linking non-symbolic and symbolic number repr

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8

Opfer, John E., Dan Kim, Lisa K. Fazio, Xinlin Zhou, and Robert S. Siegler. "Cognitive mediators of US—China differences in early symbolic arithmetic." PLOS ONE 16, no. 8 (2021): e0255283. http://dx.doi.org/10.1371/journal.pone.0255283.

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Chinese children routinely outperform American peers in standardized tests of mathematics knowledge. To examine mediators of this effect, 95 Chinese and US 5-year-olds completed a test of overall symbolic arithmetic, an IQ subtest, and three tests each of symbolic and non-symbolic numerical magnitude knowledge (magnitude comparison, approximate addition, and number-line estimation). Overall Chinese children performed better in symbolic arithmetic than US children, and all measures of IQ and number knowledge predicted overall symbolic arithmetic. Chinese children were more accurate than US peer

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9

Teichmann, Lina, Tijl Grootswagers, Thomas Carlson, and Anina N. Rich. "Decoding Digits and Dice with Magnetoencephalography: Evidence for a Shared Representation of Magnitude." Journal of Cognitive Neuroscience 30, no. 7 (2018): 999–1010. http://dx.doi.org/10.1162/jocn_a_01257.

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Numerical format describes the way magnitude is conveyed, for example, as a digit (“3”) or Roman numeral (“III”). In the field of numerical cognition, there is an ongoing debate of whether magnitude representation is independent of numerical format. Here, we examine the time course of magnitude processing when using different symbolic formats. We presented participants with a series of digits and dice patterns corresponding to the magnitudes of 1 to 6 while performing a 1-back task on magnitude. Magnetoencephalography offers an opportunity to record brain activity with high temporal resolution

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10

Castro, D., V. Reigosa, and E. González. "232. Symbolic and non-symbolic number magnitude processing in children with developmental dyscalculia." Clinical Neurophysiology 119, no. 9 (2008): e156. http://dx.doi.org/10.1016/j.clinph.2008.04.248.

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11

Paffen, Chris L. E., Sarah Plukaard, and Ryota Kanai. "Symbolic magnitude modulates perceptual strength in binocular rivalry." Cognition 119, no. 3 (2011): 468–75. http://dx.doi.org/10.1016/j.cognition.2011.01.010.

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12

Scalise, Nicole R., and Geetha B. Ramani. "Symbolic Magnitude Understanding Predicts Preschoolers’ Later Addition Skills." Journal of Cognition and Development 22, no. 2 (2021): 185–202. http://dx.doi.org/10.1080/15248372.2021.1888732.

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13

Vanbinst, Kiran, Pol Ghesquière, and Bert De Smedt. "Is the long-term association between symbolic numerical magnitude processing and arithmetic bi-directional?" Journal of Numerical Cognition 5, no. 3 (2019): 358–70. http://dx.doi.org/10.5964/jnc.v5i3.202.

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By analyzing longitudinal data from the start to the end of primary education, we aimed to investigate whether symbolic numerical magnitude processing at the start of primary education predicted arithmetic at the end, and whether arithmetic at the start of primary education predicted later symbolic numerical magnitude processing skills at the end. In the first grade (start) and sixth grade (end) of primary education, the same group of children’s symbolic numerical magnitude processing skills and arithmetic competence were assessed. We were particularly interested in exploring the direction of

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14

Orrantia, José, Sara San Romualdo, Laura Matilla, Mercedes R. Sánchez, David Múñez, and Lieven Verschaffel. "Marcadores nucleares de la competencia aritmética en preescolares." Psychology, Society, & Education 9, no. 1 (2017): 121. http://dx.doi.org/10.25115/psye.v9i1.466.

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Resumen: Las habilidades numéricas y aritméticas son predictores críticos del éxito académico. En trabajos recientes, se ha cuestionado qué habilidades numéricas básicas se relacionan con la ejecución en aritmética, si el procesamiento de magnitudes numéricas no simbólicas o el procesamiento de magnitudes simbólicas. En el presente estudio se tomó una muestra de 104 escolares del segundo curso de Educación Infantil (EI), que completaron una tarea de comparación de magnitudes numéricas no simbólicas, una de comparación de magnitudes numéricas simbólicas y una tarea de enumeración, así como un t

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15

Hurst, Michelle Ann, Marisa Massaro, and Sara Cordes. "Fraction magnitude: Mapping between symbolic and spatial representations of proportion." Journal of Numerical Cognition 6, no. 2 (2020): 204–30. http://dx.doi.org/10.5964/jnc.v6i2.285.

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Fraction notation conveys both part-whole (3/4 is 3 out of 4) and magnitude (3/4 = 0.75) information, yet evidence suggests that both children and adults find accessing magnitude information from fractions particularly difficult. Recent research suggests that using number lines to teach children about fractions can help emphasize fraction magnitude. In three experiments with adults and 9-12-year-old children, we compare the benefits of number lines and pie charts for thinking about rational numbers. In Experiment 1, we first investigate how adults spontaneously visualize symbolic fractions. Th

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16

Colomé, Àngels. "Representation of numerical magnitude in math-anxious individuals." Quarterly Journal of Experimental Psychology 72, no. 3 (2018): 424–35. http://dx.doi.org/10.1177/1747021817752094.

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Larger distance effects in high math-anxious individuals (HMA) performing comparison tasks have previously been interpreted as indicating less precise magnitude representation in this population. A recent study by Dietrich, Huber, Moeller, and Klein limited the effects of math anxiety to symbolic comparison, in which they found larger distance effects for HMA, despite equivalent size effects. However, the question of whether distance effects in symbolic comparison reflect the properties of the magnitude representation or decisional processes is currently under debate. This study was designed t

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17

Gashaj, Venera, Yoann Uehlinger, and Claudia M. Roebers. "Numerical Magnitude Skills in 6-Years-Old Children: Exploring Specific Associations with Components of Executive Function." Journal of Educational and Developmental Psychology 6, no. 1 (2016): 157. http://dx.doi.org/10.5539/jedp.v6n1p157.

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<p>Little is known about how children learn to associate numbers with their corresponding magnitude and about individual characteristics contributing to performance differences on the numerical magnitude tasks within a relatively homogenous sample of 6-year-olds. The present study investigated the relationships between components of executive function and two different numerical magnitude skills in a sample of 162 kindergartners. The Symbolic Number Line was predicted by verbal updating and switching, whereas the Symbolic Magnitude Comparison was predicted by inhibition. Both symbolic ta

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18

Rosenberg-Lee, Miriam, Jessica M. Tsang, and Vinod Menon. "Symbolic, numeric, and magnitude representations in the parietal cortex." Behavioral and Brain Sciences 32, no. 3-4 (2009): 350–51. http://dx.doi.org/10.1017/s0140525x09990860.

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AbstractWe concur with Cohen Kadosh & Walsh (CK&W) that representation of numbers in the parietal cortex is format dependent. In addition, we suggest that all formats do not automatically, and equally, access analog magnitude representation in the intraparietal sulcus (IPS). Understanding how development, learning, and context lead to differential access of analog magnitude representation is a key question for future research.

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19

Tikhomirova, Tatiana, Yulia Kuzmina, and Sergey Malykh. "Does symbolic and non-symbolic estimation ability predict mathematical achievement across primary school years?" ITM Web of Conferences 18 (2018): 04006. http://dx.doi.org/10.1051/itmconf/20181804006.

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The article presents the results of a longitudinal study of the association between number sense and success in learning mathematics in primary school. We analysed the data of 133 schoolchildren on two aspects of number sense related to the symbolic and non-symbolic magnitude estimation abilities and academic success in mathematics in third and fourth grade. The average age of schoolchildren during the first assessment was 9.82 ± 0.30; during the second assessment – 10.82 ± 0.30. For the analysis of interrelations, the cross-lagged method was used. It was shown that the reciprocal model best d

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20

Honoré, Nastasya, and Marie-Pascale Noël. "Improving Preschoolers’ Arithmetic through Number Magnitude Training: The Impact of Non-Symbolic and Symbolic Training." PLOS ONE 11, no. 11 (2016): e0166685. http://dx.doi.org/10.1371/journal.pone.0166685.

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21

Schneider, Michael, Kassandra Beeres, Leyla Coban, et al. "Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: a meta-analysis." Developmental Science 20, no. 3 (2016): e12372. http://dx.doi.org/10.1111/desc.12372.

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22

Polk, Thad A., Catherine L. Reed, Janice M. Keenan, Penelope Hogarth, and C. Alan Anderson. "A Dissociation between Symbolic Number Knowledge and Analogue Magnitude Information." Brain and Cognition 47, no. 3 (2001): 545–63. http://dx.doi.org/10.1006/brcg.2001.1486.

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23

曲, 静. "Specific Representation of Symbolic Magnitude and Non-Symbol Magnitude: A Study Based on the SNARC Effect." Advances in Social Sciences 10, no. 03 (2021): 748–56. http://dx.doi.org/10.12677/ass.2021.103105.

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24

Holloway, Ian D., and Daniel Ansari. "Developmental Specialization in the Right Intraparietal Sulcus for the Abstract Representation of Numerical Magnitude." Journal of Cognitive Neuroscience 22, no. 11 (2010): 2627–37. http://dx.doi.org/10.1162/jocn.2009.21399.

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Because number is an abstract quality of a set, the way in which a number is externally represented does not change its quantitative meaning. In this study, we examined the development of the brain regions that support format-independent representation of numerical magnitude. We asked children and adults to perform both symbolic (Hindu-Arabic numerals) and nonsymbolic (arrays of squares) numerical comparison tasks as well as two control tasks while their brains were scanned using fMRI. In a preliminary analysis, we calculated the conjunction between symbolic and nonsymbolic numerical compariso

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25

Kalra, Priya B., John V. Binzak, Percival G. Matthews, and Edward M. Hubbard. "Symbolic fractions elicit an analog magnitude representation in school-age children." Journal of Experimental Child Psychology 195 (July 2020): 104844. http://dx.doi.org/10.1016/j.jecp.2020.104844.

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26

Patalano, Andrea L., Alexandra Zax, Katherine Williams, Liana Mathias, Sara Cordes, and Hilary Barth. "Intuitive symbolic magnitude judgments and decision making under risk in adults." Cognitive Psychology 118 (May 2020): 101273. http://dx.doi.org/10.1016/j.cogpsych.2020.101273.

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27

Lee, Dasom, Joohyung Chun, and Soohyun Cho. "The Instructional Dependency of SNARC Effects Reveals Flexibility of the Space-Magnitude Association of Nonsymbolic and Symbolic Magnitudes." Perception 45, no. 5 (2016): 552–67. http://dx.doi.org/10.1177/0301006616629027.

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28

Rousselle, Laurence, and Marie-Pascale Noël. "Basic numerical skills in children with mathematics learning disabilities: A comparison of symbolic vs non-symbolic number magnitude processing." Cognition 102, no. 3 (2007): 361–95. http://dx.doi.org/10.1016/j.cognition.2006.01.005.

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29

Xenidou-Dervou, Iro, Dylan Molenaar, Daniel Ansari, Menno van der Schoot, and Ernest C. D. M. van Lieshout. "Nonsymbolic and symbolic magnitude comparison skills as longitudinal predictors of mathematical achievement." Learning and Instruction 50 (August 2017): 1–13. http://dx.doi.org/10.1016/j.learninstruc.2016.11.001.

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30

Schwenk, Christin, Delphine Sasanguie, Jörg-Tobias Kuhn, Sophia Kempe, Philipp Doebler, and Heinz Holling. "(Non-)symbolic magnitude processing in children with mathematical difficulties: A meta-analysis." Research in Developmental Disabilities 64 (May 2017): 152–67. http://dx.doi.org/10.1016/j.ridd.2017.03.003.

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31

Liu, Chao, Honghong Tang, Yue-Jia Luo, and Xiaoqin Mai. "Multi-Representation of Symbolic and Nonsymbolic Numerical Magnitude in Chinese Number Processing." PLoS ONE 6, no. 4 (2011): e19373. http://dx.doi.org/10.1371/journal.pone.0019373.

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32

Pinhas, Michal, and Martin H. Fischer. "Mental movements without magnitude? A study of spatial biases in symbolic arithmetic." Cognition 109, no. 3 (2008): 408–15. http://dx.doi.org/10.1016/j.cognition.2008.09.003.

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33

Reynvoet, Bert, Bert De Smedt, and Eva Van den Bussche. "Children’s representation of symbolic magnitude: The development of the priming distance effect." Journal of Experimental Child Psychology 103, no. 4 (2009): 480–89. http://dx.doi.org/10.1016/j.jecp.2009.01.007.

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34

Defever, Emmy, Delphine Sasanguie, Titia Gebuis, and Bert Reynvoet. "Children’s representation of symbolic and nonsymbolic magnitude examined with the priming paradigm." Journal of Experimental Child Psychology 109, no. 2 (2011): 174–86. http://dx.doi.org/10.1016/j.jecp.2011.01.002.

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35

Vogel, Stephan E., Alicia Remark, and Daniel Ansari. "Differential processing of symbolic numerical magnitude and order in first-grade children." Journal of Experimental Child Psychology 129 (January 2015): 26–39. http://dx.doi.org/10.1016/j.jecp.2014.07.010.

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36

Tavakoli, Hamdollah Manzari. "The relationship between accuracy of numerical magnitude comparisons and children’s arithmetic ability: A study in Iranian primary school children." Europe’s Journal of Psychology 12, no. 4 (2016): 567–83. http://dx.doi.org/10.5964/ejop.v12i4.1175.

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The relationship between children’s accuracy during numerical magnitude comparisons and arithmetic ability has been investigated by many researchers. Contradictory results have been reported from these studies due to the use of many different tasks and indices to determine the accuracy of numerical magnitude comparisons. In the light of this inconsistency among measurement techniques, the present study aimed to investigate this relationship among Iranian second grade children (n = 113) using a pre-established test (known as the Numeracy Screener) to measure numerical magnitude comparison accur

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37

Pollack, Courtney. "Same-different judgments with alphabetic characters: The case of literal symbol processing." Journal of Numerical Cognition 5, no. 2 (2019): 241–59. http://dx.doi.org/10.5964/jnc.v5i2.163.

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Learning mathematics requires fluency with symbols that convey numerical magnitude. Algebra and higher-level mathematics involve literal symbols, such as "x", that often represent numerical magnitude. Compared to other symbols, such as Arabic numerals, literal symbols may require more complex processing because they have strong pre-existing associations in literacy. The present study tested this notion using same-different tasks that produce less efficient judgments for different magnitudes that are closer together compared to farther apart (i.e., same-different distance effects). Twenty-four

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38

Zebian, Samar, and Daniel Ansari. "Differences between literates and illiterates on symbolic but not nonsymbolic numerical magnitude processing." Psychonomic Bulletin & Review 19, no. 1 (2011): 93–100. http://dx.doi.org/10.3758/s13423-011-0175-9.

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39

Vanbinst, Kiran, Eva Ceulemans, Lien Peters, Pol Ghesquière, and Bert De Smedt. "Developmental trajectories of children’s symbolic numerical magnitude processing skills and associated cognitive competencies." Journal of Experimental Child Psychology 166 (February 2018): 232–50. http://dx.doi.org/10.1016/j.jecp.2017.08.008.

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40

Meert, Gaëlle, Jacques Grégoire, Xavier Seron, and Marie-Pascale Noël. "The mental representation of the magnitude of symbolic and nonsymbolic ratios in adults." Quarterly Journal of Experimental Psychology 65, no. 4 (2012): 702–24. http://dx.doi.org/10.1080/17470218.2011.632485.

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41

Jun Zhang. "Symbolic and numerical computation on Bessel functions of complex argument and large magnitude." Journal of Computational and Applied Mathematics 75, no. 1 (1996): 99–118. http://dx.doi.org/10.1016/s0377-0427(96)00063-5.

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42

Heine, Angela, Sascha Tamm, Jacqueline Wißmann, and Arthur M. Jacobs. "Electrophysiological correlates of non-symbolic numerical magnitude processing in children: Joining the dots." Neuropsychologia 49, no. 12 (2011): 3238–46. http://dx.doi.org/10.1016/j.neuropsychologia.2011.07.028.

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43

Donlan D. V. M. Bishop G. J. Hitch, C. "Magnitude comparisons by children with specific language impairments: evidence of unimpaired symbolic processing." International Journal of Language & Communication Disorders 33, no. 2 (1998): 149–60. http://dx.doi.org/10.1080/136828298247802.

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44

Gertner, Limor, Isabel Arend, and Avishai Henik. "Effects of non-symbolic numerical information suggest the existence of magnitude–space synesthesia." Cognitive Processing 13, S1 (2012): 179–83. http://dx.doi.org/10.1007/s10339-012-0449-9.

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45

Goffin, Celia, and Daniel Ansari. "Beyond magnitude: Judging ordinality of symbolic number is unrelated to magnitude comparison and independently relates to individual differences in arithmetic." Cognition 150 (May 2016): 68–76. http://dx.doi.org/10.1016/j.cognition.2016.01.018.

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46

Mussolin, Christophe, Anne De Volder, Cécile Grandin, Xavier Schlögel, Marie-Cécile Nassogne, and Marie-Pascale Noël. "Neural Correlates of Symbolic Number Comparison in Developmental Dyscalculia." Journal of Cognitive Neuroscience 22, no. 5 (2010): 860–74. http://dx.doi.org/10.1162/jocn.2009.21237.

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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 no

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47

Matejko, Anna A., and Daniel Ansari. "Trajectories of Symbolic and Nonsymbolic Magnitude Processing in the First Year of Formal Schooling." PLOS ONE 11, no. 3 (2016): e0149863. http://dx.doi.org/10.1371/journal.pone.0149863.

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48

Chew, Cindy S., Jason D. Forte, and Robert A. Reeve. "Cognitive factors affecting children’s nonsymbolic and symbolic magnitude judgment abilities: A latent profile analysis." Journal of Experimental Child Psychology 152 (December 2016): 173–91. http://dx.doi.org/10.1016/j.jecp.2016.07.001.

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49

Obersteiner, Andreas, and Veronika Hofreiter. "Do we have a sense for irrational numbers?" Journal of Numerical Cognition 2, no. 3 (2017): 170–89. http://dx.doi.org/10.5964/jnc.v2i3.43.

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Number sense requires, at least, an ability to assess magnitude information represented by number symbols. Most educated adults are able to assess magnitude information of rational numbers fairly quickly, including whole numbers and fractions. It is to date unclear whether educated adults without training are able to assess magnitudes of irrational numbers, such as the cube root of 41. In a computerized experiment, we asked mathematically skilled adults to repeatedly choose the larger of two irrational numbers as quickly as possible. Participants were highly accurate on problems in which reaso

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50

Notebaert, Karolien, Sabine Nelis, and Bert Reynvoet. "The Magnitude Representation of Small and Large Symbolic Numbers in the Left and Right Hemisphere: An Event-related fMRI Study." Journal of Cognitive Neuroscience 23, no. 3 (2011): 622–30. http://dx.doi.org/10.1162/jocn.2010.21445.

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Numbers are known to be processed along the left and right intraparietal sulcus. The present study investigated hemispheric differences between the magnitude representation of small and large symbolic numbers. To this purpose, an fMRI adaptation paradigm was used, where the continuous presentation of a habituation number was interrupted by an occasional deviant number. The results presented a distance-dependent increase of activation: larger ratios of habituation and deviant number caused a larger recovery of activation. Similar activation patterns were observed for small and large symbolic nu

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