{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T12:24:37Z","timestamp":1790857477471,"version":"4.1.0"},"reference-count":102,"publisher":"SAGE Publications","issue":"12","license":[{"start":{"date-parts":[[2020,7,22]],"date-time":"2020-07-22T00:00:00Z","timestamp":1595376000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"DOI":"10.13039\/501100010115","name":"R\u00e9gion Auvergne Rh\u00f4ne Alpes","doi-asserted-by":"crossref","award":["Pack Ambition Recherche Dyscog"],"award-info":[{"award-number":["Pack Ambition Recherche Dyscog"]}],"id":[{"id":"10.13039\/501100010115","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Quarterly Journal of Experimental Psychology"],"published-print":{"date-parts":[[2020,12]]},"abstract":"<jats:p>It has been hypothesised that the human neurocognitive architecture may include a perceptual ratio processing system (RPS) that supports symbolic fraction understanding. In the present study, we aimed to provide further evidence for the existence of the RPS by exploring whether individuals with a range of math skills are indeed perceptually sensitive to non-symbolic ratio magnitudes. We also aimed to test to what extent the RPS may underlie symbolic fraction processing in those individuals. In a match-to-sample task, typical adults, elementary school children, and adults with dyscalculia were asked to match a non-symbolic ratio (i.e., target) to one of two non-symbolic ratios (i.e., the match and distractor). We found that all groups of participants were sensitive to the ratio between the match and the distractor, suggesting a common reliance on the RPS. This ratio sensitivity was also observed in another group of typical adults who had to choose which of two symbolic fractions match a non-symbolic ratio, indicating that the RPS may also contribute to symbolic fraction understanding. However, no ratio dependence was observed when participants had to choose which of two symbolic fractions match another symbolic fraction, suggesting that reliance on the RPS in symbolic fraction processing is limited and may not support exact fraction processing.<\/jats:p>","DOI":"10.1177\/1747021820940631","type":"journal-article","created":{"date-parts":[[2020,6,22]],"date-time":"2020-06-22T08:26:02Z","timestamp":1592814362000},"page":"2158-2176","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":16,"title":["The ratio processing system and its role in fraction understanding: Evidence from a match-to-sample task in children and adults with and without dyscalculia"],"prefix":"10.1177","volume":"73","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5147-6277","authenticated-orcid":false,"given":"Parnika","family":"Bhatia","sequence":"first","affiliation":[{"name":"Lyon Neuroscience Research Center (CRNL), Experiential Neuroscience and Mental Training Team, INSERM U1028\u2212CNRS UMR5292, University of Lyon, Lyon, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ma\u00ebl","family":"Delem","sequence":"additional","affiliation":[{"name":"Lyon Neuroscience Research Center (CRNL), Experiential Neuroscience and Mental Training Team, INSERM U1028\u2212CNRS UMR5292, University of Lyon, Lyon, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jessica","family":"L\u00e9one","sequence":"additional","affiliation":[{"name":"Lyon Neuroscience Research Center (CRNL), Experiential Neuroscience and Mental Training Team, INSERM U1028\u2212CNRS UMR5292, University of Lyon, Lyon, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Esther","family":"Boisin","sequence":"additional","affiliation":[{"name":"Lyon Neuroscience Research Center (CRNL), Experiential Neuroscience and Mental Training Team, INSERM U1028\u2212CNRS UMR5292, University of Lyon, Lyon, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anne","family":"Cheylus","sequence":"additional","affiliation":[{"name":"Lyon Neuroscience Research Center (CRNL), Experiential Neuroscience and Mental Training Team, INSERM U1028\u2212CNRS UMR5292, University of Lyon, Lyon, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marie-Line","family":"Gardes","sequence":"additional","affiliation":[{"name":"Lyon Neuroscience Research Center (CRNL), Experiential Neuroscience and Mental Training Team, INSERM U1028\u2212CNRS UMR5292, University of Lyon, Lyon, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J\u00e9r\u00f4me","family":"Prado","sequence":"additional","affiliation":[{"name":"Lyon Neuroscience Research Center (CRNL), Experiential Neuroscience and Mental Training Team, INSERM U1028\u2212CNRS UMR5292, University of Lyon, Lyon, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2020,7,22]]},"reference":[{"key":"bibr1-1747021820940631","doi-asserted-by":"crossref","unstructured":"Alibali M. W., Sidney P. G. (2015). Variability in the natural number bias: Who, when, how, and why. Learning and Instruction, 37, 56\u201361. https:\/\/doi.org\/10.1016\/j.learninstruc.2015.01.003","DOI":"10.1016\/j.learninstruc.2015.01.003"},{"key":"bibr2-1747021820940631","doi-asserted-by":"crossref","unstructured":"Bailey D. H., Hoard M. K., Nugent L., Geary D. C. (2012). Competence with fractions predicts gains in mathematics achievement. Journal of Experimental Child Psychology, 113(3), 447\u2013455. https:\/\/doi.org\/10.1016\/j.jecp.2012.06.004","DOI":"10.1016\/j.jecp.2012.06.004"},{"key":"bibr3-1747021820940631","doi-asserted-by":"crossref","unstructured":"Bailey D. H., Zhou X., Zhang Y., Cui J., Fuchs L. S., Jordan N. C.Siegler R. S. et al. (2015). Development of fraction concepts and procedures in U.S. and Chinese children. Journal of Experimental Child Psychology, 129, 68\u201383. https:\/\/doi.org\/10.1016\/j.jecp.2014.08.006","DOI":"10.1016\/j.jecp.2014.08.006"},{"key":"bibr4-1747021820940631","doi-asserted-by":"crossref","unstructured":"Bonato M., Fabbri S., Umilt\u00e0 C., Zorzi M. (2007). The mental representation of numerical fractions: Real or integer? Journal of Experimental Psychology: Human Perception and Performance, 33(6), 1410\u20131419. https:\/\/doi.org\/10.1037\/0096-1523.33.6.1410","DOI":"10.1037\/0096-1523.33.6.1410"},{"key":"bibr5-1747021820940631","doi-asserted-by":"crossref","unstructured":"Booth J. L., Newton K. J. (2012). Fractions: Could they really be the gatekeeper\u2019s doorman? Contemporary Educational Psychology, 37(4), 247\u2013253. https:\/\/doi.org\/10.1016\/j.cedpsych.2012.07.001","DOI":"10.1016\/j.cedpsych.2012.07.001"},{"key":"bibr6-1747021820940631","doi-asserted-by":"crossref","unstructured":"Boyer T. W., Levine S. C., Huttenlocher J. (2008). Development of proportional reasoning: Where young children go wrong. Developmental Psychology, 44(5), 1478\u20131490. https:\/\/doi.org\/10.1037\/a0013110","DOI":"10.1037\/a0013110"},{"key":"bibr7-1747021820940631","doi-asserted-by":"crossref","unstructured":"Braithwaite D. W., Siegler R. S. (2017). Developmental changes in the whole number bias. Developmental Science, 21(2), Article e12541. https:\/\/doi.org\/10.1111\/desc.12541","DOI":"10.1111\/desc.12541"},{"key":"bibr8-1747021820940631","doi-asserted-by":"crossref","unstructured":"Brysbaert M. (2019). How many participants do we have to include in properly powered experiments? A tutorial of power analysis with reference tables. Journal of Cognition, 2(1), 16. https:\/\/doi.org\/10.5334\/joc.72","DOI":"10.5334\/joc.72"},{"key":"bibr9-1747021820940631","first-page":"455","volume-title":"Handbook of mathematical cognition","author":"Butterworth B.","year":"2005"},{"key":"bibr10-1747021820940631","doi-asserted-by":"crossref","unstructured":"Butterworth B. (2011). Foundational numerical capacities and the origins of dyscalculia. In Dehaene S., Brannon E. (Eds.), Space, time and number in the brain (pp. 249\u2013265). Elsevier. https:\/\/doi.org\/10.1016\/B978-0-12-385948-8.00016-5","DOI":"10.1016\/B978-0-12-385948-8.00016-5"},{"key":"bibr11-1747021820940631","doi-asserted-by":"crossref","unstructured":"Carpenter T. P., Kepner H., Corbitt M. K., Lindquist M. M., Reys R. E. (1980). Results and implications of the second NAEP mathematics assessments: Elementary school. The Arithmetic Teacher, 27(8), 10\u201312, 44\u201347. http:\/\/www.jstor.org\/stable\/41191725","DOI":"10.5951\/AT.27.8.0010"},{"key":"bibr12-1747021820940631","doi-asserted-by":"crossref","unstructured":"Cavalli E., Col\u00e9 P., Leloup G., Poracchia-George F., Sprenger-Charolles L., El Ahmadi A. (2018). Screening for dyslexia in French-speaking university students: An evaluation of the detection accuracy of the Alouette test. Journal of Learning Disabilities, 51(3), 268\u2013282. https:\/\/doi.org\/10.1177\/0022219417704637","DOI":"10.1177\/0022219417704637"},{"key":"bibr13-1747021820940631","doi-asserted-by":"crossref","unstructured":"Chan W.H., Leu Y.C., Chen C.M. (2007). Exploring group-wise conceptual deficiencies of fractions for fifth and sixth graders in Taiwan. The Journal of Experimental Education, 76(1), 26\u201357. https:\/\/doi.org\/10.3200\/JEXE.76.1.26-58","DOI":"10.3200\/JEXE.76.1.26-58"},{"key":"bibr14-1747021820940631","doi-asserted-by":"crossref","unstructured":"Clarke D. M., Roche A. (2009). Students\u2019 fraction comparison strategies as a window into robust understanding and possible pointers for instruction. Educational Studies in Mathematics, 72(1), 127\u2013138. https:\/\/doi.org\/10.1007\/s10649-009-9198-9","DOI":"10.1007\/s10649-009-9198-9"},{"key":"bibr15-1747021820940631","doi-asserted-by":"crossref","unstructured":"Cowan N. (2016). Working memory maturation: Can we get at the essence of cognitive growth? Perspectives on Psychological Science, 11(2), 239\u2013264. https:\/\/doi.org\/10.1177\/1745691615621279","DOI":"10.1177\/1745691615621279"},{"key":"bibr16-1747021820940631","doi-asserted-by":"crossref","unstructured":"De Brauwer J., Verguts T., Fias W. (2006). The representation of multiplication facts: Developmental changes in the problem size, five, and tie effects. Journal of Experimental Child Psychology, 94(1), 43\u201356. https:\/\/doi.org\/10.1016\/j.jecp.2005.11.004","DOI":"10.1016\/j.jecp.2005.11.004"},{"key":"bibr17-1747021820940631","author":"Dehaene S.","year":"1997","journal-title":"Odile Jacob"},{"key":"bibr18-1747021820940631","doi-asserted-by":"crossref","unstructured":"Dehaene S., Cohen L. (2007). Cultural recycling of cortical maps. Neuron, 56(2), 384\u2013398. https:\/\/doi.org\/10.1016\/j.neuron.2007.10.004","DOI":"10.1016\/j.neuron.2007.10.004"},{"key":"bibr19-1747021820940631","doi-asserted-by":"crossref","unstructured":"Dehaene S., Dehaene-Lambertz G., Cohen L. (1998). Abstract representations of numbers in the animal and human brain. Trends in Neurosciences, 21(8), 355\u2013361. https:\/\/doi.org\/10.1016\/S0166-2236(98)01263-6","DOI":"10.1016\/S0166-2236(98)01263-6"},{"key":"bibr20-1747021820940631","doi-asserted-by":"crossref","unstructured":"De Smedt B., Gilmore C. K. (2011). Defective number module or impaired access? Numerical magnitude processing in first graders with mathematical difficulties. Journal of Experimental Child Psychology, 108(2), 278\u2013292. https:\/\/doi.org\/10.1016\/j.jecp.2010.09.003","DOI":"10.1016\/j.jecp.2010.09.003"},{"key":"bibr21-1747021820940631","doi-asserted-by":"crossref","unstructured":"De Smedt B., No\u00ebl M.P., Gilmore C., Ansari D. (2013). How do symbolic and non-symbolic numerical magnitude processing skills relate to individual differences in children\u2019s mathematical skills? A review of evidence from brain and behavior. Trends in Neuroscience and Education, 2(2), 48\u201355. https:\/\/doi.org\/10.1016\/j.tine.2013.06.001","DOI":"10.1016\/j.tine.2013.06.001"},{"key":"bibr22-1747021820940631","doi-asserted-by":"crossref","unstructured":"Faulkenberry T. J., Pierce B. H. (2011). Mental representations in fraction comparison: Holistic versus component-based strategies. Experimental Psychology, 58(6), 480\u2013489. https:\/\/doi.org\/10.1027\/1618-3169\/a000116","DOI":"10.1027\/1618-3169\/a000116"},{"key":"bibr23-1747021820940631","doi-asserted-by":"crossref","unstructured":"Fazio L. K., Bailey D. H., Thompson C. A., Siegler R. S. (2014). Relations of different types of numerical magnitude representations to each other and to mathematics achievement. Journal of Experimental Child Psychology, 123, 53\u201372. https:\/\/doi.org\/10.1016\/j.jecp.2014.01.013","DOI":"10.1016\/j.jecp.2014.01.013"},{"key":"bibr24-1747021820940631","doi-asserted-by":"crossref","unstructured":"Feigenson L., Dehaene S., Spelke E. (2004). Core systems of number. Trends in Cognitive Sciences, 8(7), 307\u2013314. https:\/\/doi.org\/10.1016\/j.tics.2004.05.002","DOI":"10.1016\/j.tics.2004.05.002"},{"key":"bibr25-1747021820940631","doi-asserted-by":"crossref","unstructured":"Geary D. C. (2011). Consequences, characteristics, and causes of mathematical learning disabilities and persistent low achievement in mathematics. Journal of Developmental & Behavioral Pediatrics, 32(3), 250\u2013263. https:\/\/doi.org\/10.1097\/DBP.0b013e318209edef","DOI":"10.1097\/DBP.0b013e318209edef"},{"key":"bibr26-1747021820940631","doi-asserted-by":"crossref","unstructured":"Gelman R., Meck E. (1983). Preschoolers\u2019 counting: Principles before skill. Cognition, 13(3), 343\u2013359. https:\/\/doi.org\/10.1016\/0010-0277(83)90014-8","DOI":"10.1016\/0010-0277(83)90014-8"},{"key":"bibr27-1747021820940631","first-page":"272","volume-title":"Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education (pp.","author":"Gonz\u00e1lez-Forte J. M.","year":"2019"},{"key":"bibr28-1747021820940631","first-page":"665","volume":"455","author":"Halberda J.","year":"2008","journal-title":"Individual differences in non-verbal number acuity correlate with maths achievement. Nature"},{"key":"bibr29-1747021820940631","doi-asserted-by":"crossref","unstructured":"Hansen N., Rinne L., Jordan N. C., Ye A., Resnick I., Rodrigues J. (2017). Co-development of fraction magnitude knowledge and mathematics achievement from fourth through sixth grade. Learning and Individual Differences, 60, 18\u201332. https:\/\/doi.org\/10.1016\/j.lindif.2017.10.005","DOI":"10.1016\/j.lindif.2017.10.005"},{"key":"bibr30-1747021820940631","doi-asserted-by":"crossref","unstructured":"Hurst M., Cordes S. (2016). Rational-number comparison across notation: Fractions, decimals, and whole numbers. Journal of Experimental Psychology: Human Perception and Performance, 42(2), 281\u2013293. https:\/\/doi.org\/10.1037\/xhp0000140","DOI":"10.1037\/xhp0000140"},{"key":"bibr31-1747021820940631","doi-asserted-by":"crossref","unstructured":"Hurst M. A., Cordes S. (2018). Attending to relations: Proportional reasoning in 3- to 6-year-old children. Developmental Psychology, 54(3), 428\u2013439. https:\/\/doi.org\/10.1037\/dev0000440","DOI":"10.1037\/dev0000440"},{"key":"bibr32-1747021820940631","doi-asserted-by":"crossref","unstructured":"Imbo I., Vandierendonck A. (2008). Effects of problem size, operation, and working-memory span on simple-arithmetic strategies: Differences between children and adults? Psychological Research, 72(3), 331\u2013346. https:\/\/doi.org\/10.1007\/s00426-007-0112-8","DOI":"10.1007\/s00426-007-0112-8"},{"key":"bibr33-1747021820940631","doi-asserted-by":"crossref","unstructured":"Ischebeck A., Schocke M., Delazer M. (2009). The processing and representation of fractions within the brain. NeuroImage, 47(1), 403\u2013413. https:\/\/doi.org\/10.1016\/j.neuroimage.2009.03.041","DOI":"10.1016\/j.neuroimage.2009.03.041"},{"key":"bibr34-1747021820940631","doi-asserted-by":"publisher","DOI":"10.1016\/bs.pbr.2016.04.024"},{"key":"bibr35-1747021820940631","doi-asserted-by":"crossref","unstructured":"Iuculano T., Tang J., Hall C. W. B., Butterworth B. (2008). Core information processing deficits in developmental dyscalculia and low numeracy. Developmental Science, 11(5), 669\u2013680. https:\/\/doi.org\/10.1111\/j.1467-7687.2008.00716.x","DOI":"10.1111\/j.1467-7687.2008.00716.x"},{"key":"bibr36-1747021820940631","doi-asserted-by":"crossref","unstructured":"Jacob S. N., Nieder A. (2009a). Notation-independent representation of fractions in the human parietal cortex. Journal of Neuroscience, 29(14), 4652\u20134657. https:\/\/doi.org\/10.1523\/JNEUROSCI.0651-09.2009","DOI":"10.1523\/JNEUROSCI.0651-09.2009"},{"key":"bibr37-1747021820940631","doi-asserted-by":"crossref","unstructured":"Jacob S. N., Nieder A. (2009b). Tuning to non-symbolic proportions in the human frontoparietal cortex: Representation of proportions in the human brain. European Journal of Neuroscience, 30(7), 1432\u20131442. https:\/\/doi.org\/10.1111\/j.1460-9568.2009.06932.x","DOI":"10.1111\/j.1460-9568.2009.06932.x"},{"key":"bibr38-1747021820940631","doi-asserted-by":"crossref","unstructured":"Jacob S. N., Vallentin D., Nieder A. (2012). Relating magnitudes: The brain\u2019s code for proportions. Trends in Cognitive Sciences, 16(3), 157\u2013166. https:\/\/doi.org\/10.1016\/j.tics.2012.02.002","DOI":"10.1016\/j.tics.2012.02.002"},{"key":"bibr39-1747021820940631","unstructured":"Jeffreys H. (1961). Theory of Probability. Oxford: Clarendon Press."},{"key":"bibr40-1747021820940631","doi-asserted-by":"crossref","unstructured":"Jeong Y., Levine S. C., Huttenlocher J. (2007). The development of proportional reasoning: Effect of continuous versus discrete quantities. Journal of Cognition and Development, 8(2), 237\u2013256. https:\/\/doi.org\/10.1080\/15248370701202471","DOI":"10.1080\/15248370701202471"},{"key":"bibr41-1747021820940631","doi-asserted-by":"crossref","unstructured":"Jordan N. C., Hansen N., Fuchs L. S., Siegler R. S., Gersten R., Micklos D. (2013). Developmental predictors of fraction concepts and procedures. Journal of Experimental Child Psychology, 116(1), 45\u201358. https:\/\/doi.org\/10.1016\/j.jecp.2013.02.001","DOI":"10.1016\/j.jecp.2013.02.001"},{"key":"bibr42-1747021820940631","doi-asserted-by":"crossref","unstructured":"Kallai A. Y., Tzelgov J. (2009). A generalized fraction: An entity smaller than one on the mental number line. Journal of Experimental Psychology: Human Perception and Performance, 35(6), 1845\u20131864. https:\/\/doi.org\/10.1037\/a0016892","DOI":"10.1037\/a0016892"},{"key":"bibr43-1747021820940631","doi-asserted-by":"crossref","unstructured":"Kallai A. Y., Tzelgov J. (2012). When meaningful components interrupt the processing of the whole: The case of fractions. Acta Psychologica, 139(2), 358\u2013369. https:\/\/doi.org\/10.1016\/j.actpsy.2011.11.009","DOI":"10.1016\/j.actpsy.2011.11.009"},{"key":"bibr44-1747021820940631","doi-asserted-by":"crossref","unstructured":"Kalra P. B., Binzak J. V., Matthews P. G., Hubbard E. M. (2020). Symbolic fractions elicit an analog magnitude representation in school-age children. Journal of Experimental Child Psychology, 195, Article 104844. https:\/\/doi.org\/10.1016\/j.jecp.2020.104844","DOI":"10.1016\/j.jecp.2020.104844"},{"key":"bibr45-1747021820940631","volume-title":"Five faces of mathematical knowledge building","author":"Kieren T. E.","year":"1981"},{"key":"bibr46-1747021820940631","doi-asserted-by":"crossref","unstructured":"Kloosterman P. (2010). Mathematics skills of 17-year-olds in the United States: 1978 to 2004. Journal for Research in Mathematics Education, 41(1), 20\u201351. http:\/\/www.jstor.org\/stable\/40539363","DOI":"10.5951\/jresematheduc.41.1.0020"},{"key":"bibr47-1747021820940631","doi-asserted-by":"crossref","unstructured":"Lee M. D., Wagenmakers E.J. (2013). Bayesian Cognitive Modeling: A Practical Course. Cambridge, MA: Cambridge University Press. https:\/\/doi.org\/10.1017\/CBO9781139087759","DOI":"10.1017\/CBO9781139087759"},{"key":"bibr48-1747021820940631","unstructured":"Lefavrais P. (1967). Test de l\u2019Alouette."},{"key":"bibr49-1747021820940631","doi-asserted-by":"crossref","unstructured":"Leibovich T., Katzin N., Harel M., Henik A. (2017). From \u201csense of number\u201d to \u201csense of magnitude\u201d: The role of continuous magnitudes in numerical cognition. Behavioral and Brain Sciences, 40, Article e164. https:\/\/doi.org\/10.1017\/S0140525X16000960","DOI":"10.1017\/S0140525X16000960"},{"key":"bibr50-1747021820940631","doi-asserted-by":"crossref","unstructured":"Leslie A. M., Gelman R., Gallistel C. R. (2008). The generative basis of natural number concepts. Trends in Cognitive Sciences, 12(6), 213\u2013218. https:\/\/doi.org\/10.1016\/j.tics.2008.03.004","DOI":"10.1016\/j.tics.2008.03.004"},{"key":"bibr51-1747021820940631","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-12-801871-2.00006-X"},{"key":"bibr52-1747021820940631","doi-asserted-by":"crossref","unstructured":"Mack N. K. (1990). Learning fractions with understanding: Building on informal knowledge. Journal for Research in Mathematics Education, 21(1), 16\u201332. https:\/\/doi.org\/10.2307\/749454","DOI":"10.5951\/jresematheduc.21.1.0016"},{"key":"bibr53-1747021820940631","doi-asserted-by":"crossref","unstructured":"Mack N. K. (1995). Confounding whole-number and fraction concepts when building on informal knowledge. Journal for Research in Mathematics Education, 26(5), 422. https:\/\/doi.org\/10.2307\/749431","DOI":"10.2307\/749431"},{"key":"bibr54-1747021820940631","volume-title":"Delimiting and leveraging children\u2019s natural sense of proportion","author":"Matthews P. G.","year":"2015"},{"key":"bibr55-1747021820940631","doi-asserted-by":"crossref","unstructured":"Matthews P. G., Chesney D. L. (2015). Fractions as percepts? Exploring cross-format distance effects for fractional magnitudes. Cognitive Psychology, 78, 28\u201356. https:\/\/doi.org\/10.1016\/j.cogpsych.2015.01.006","DOI":"10.1016\/j.cogpsych.2015.01.006"},{"key":"bibr56-1747021820940631","unstructured":"Matthews P. G., Chesney D. L., McNeil N. M. (2014). Are fractions natural numbers, too? https:\/\/cogsci.mindmodeling.org\/2014\/papers\/176\/paper176.pdf"},{"key":"bibr57-1747021820940631","doi-asserted-by":"crossref","unstructured":"Matthews P. G., Lewis M. R. (2017). Fractions we cannot ignore: The nonsymbolic ratio congruity effect. Cognitive Science, 41(6), 1656\u20131674. https:\/\/doi.org\/10.1111\/cogs.12419","DOI":"10.1111\/cogs.12419"},{"key":"bibr58-1747021820940631","doi-asserted-by":"crossref","unstructured":"Matthews P. G., Lewis M. R., Hubbard E. M. (2016). Individual differences in nonsymbolic ratio processing predict symbolic math performance. Psychological Science, 27(2), 191\u2013202. https:\/\/doi.org\/10.1177\/0956797615617799","DOI":"10.1177\/0956797615617799"},{"key":"bibr59-1747021820940631","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-00491-0_10"},{"key":"bibr60-1747021820940631","doi-asserted-by":"crossref","unstructured":"Mazzocco M. M. M., Devlin K. T. (2008). Parts and \u2018holes\u2019: Gaps in rational number sense among children with vs. without mathematical learning disabilities. Developmental Science, 11(5), 681\u2013691. https:\/\/doi.org\/10.1111\/j.1467-7687.2008.00717.x","DOI":"10.1111\/j.1467-7687.2008.00717.x"},{"key":"bibr61-1747021820940631","doi-asserted-by":"crossref","unstructured":"Mazzocco M. M. M., Feigenson L., Halberda J. (2011). Impaired acuity of the approximate number system underlies mathematical learning disability (dyscalculia): Impaired numerical acuity contributes to MLD. Child Development, 82(4), 1224\u20131237. https:\/\/doi.org\/10.1111\/j.1467-8624.2011.01608.x","DOI":"10.1111\/j.1467-8624.2011.01608.x"},{"key":"bibr62-1747021820940631","doi-asserted-by":"crossref","unstructured":"Mazzocco M. M. M., Myers G. F., Lewis K. E., Hanich L. B., Murphy M. M. (2013). Limited knowledge of fraction representations differentiates middle school students with mathematics learning disability (dyscalculia) versus low mathematics achievement. Journal of Experimental Child Psychology, 115(2), 371\u2013387. https:\/\/doi.org\/10.1016\/j.jecp.2013.01.005","DOI":"10.1016\/j.jecp.2013.01.005"},{"key":"bibr63-1747021820940631","doi-asserted-by":"crossref","unstructured":"McCrink K., Spelke E. S., Dehaene S., Pica P. (2013). Non-symbolic halving in an Amazonian indigene group. Developmental Science, 16(3), 451\u2013462. https:\/\/doi.org\/10.1111\/desc.12037","DOI":"10.1111\/desc.12037"},{"key":"bibr64-1747021820940631","doi-asserted-by":"crossref","unstructured":"McCrink K., Wynn K. (2007). Ratio abstraction by 6-month-old infants. Psychological Science, 18(8), 740\u2013745. https:\/\/doi.org\/10.1111\/j.1467-9280.2007.01969.x","DOI":"10.1111\/j.1467-9280.2007.01969.x"},{"key":"bibr65-1747021820940631","doi-asserted-by":"crossref","unstructured":"Meert G., Gr\u00e9goire J., No\u00ebl M.P. (2009). Rational numbers: Componential versus holistic representation of fractions in a magnitude comparison task. Quarterly Journal of Experimental Psychology, 62(8), 1598\u20131616. https:\/\/doi.org\/10.1080\/17470210802511162","DOI":"10.1080\/17470210802511162"},{"key":"bibr66-1747021820940631","doi-asserted-by":"crossref","unstructured":"Meert G., Gr\u00e9goire J., No\u00ebl M.P. (2010). Comparing 5\/7 and 2\/9: Adults can do it by accessing the magnitude of the whole fractions. Acta Psychologica, 135(3), 284\u2013292. https:\/\/doi.org\/10.1016\/j.actpsy.2010.07.014","DOI":"10.1016\/j.actpsy.2010.07.014"},{"key":"bibr67-1747021820940631","doi-asserted-by":"crossref","unstructured":"Meert G., Gr\u00e9goire J., Seron X., No\u00ebl M.P. (2012). The mental representation of the magnitude of symbolic and nonsymbolic ratios in adults. Quarterly Journal of Experimental Psychology, 65(4), 702\u2013724. https:\/\/doi.org\/10.1080\/17470218.2011.632485","DOI":"10.1080\/17470218.2011.632485"},{"key":"bibr68-1747021820940631","doi-asserted-by":"crossref","unstructured":"Meert G., Gr\u00e9goire J., Seron X., No\u00ebl M.P. (2013). The processing of symbolic and nonsymbolic ratios in school-age children. PLOS ONE, 8(11), Article e82002. https:\/\/doi.org\/10.1371\/journal.pone.0082002","DOI":"10.1371\/journal.pone.0082002"},{"key":"bibr69-1747021820940631","doi-asserted-by":"publisher","DOI":"10.1037\/0012-1649.35.1.164"},{"key":"bibr70-1747021820940631","doi-asserted-by":"crossref","unstructured":"Mock J., Huber S., Bloechle J., Bahnmueller J., Moeller K., Klein E. (2019). Processing symbolic and non-symbolic proportions: Domain-specific numerical and domain-general processes in intraparietal cortex. Brain Research, 1714, 133\u2013146. https:\/\/doi.org\/10.1016\/j.brainres.2019.02.029","DOI":"10.1016\/j.brainres.2019.02.029"},{"key":"bibr71-1747021820940631","doi-asserted-by":"crossref","unstructured":"Mock J., Huber S., Bloechle J., Dietrich J. F., Bahnmueller J., Rennig J., Moeller K., et al. (2018). Magnitude processing of symbolic and non-symbolic proportions: An fMRI study. Behavioral and Brain Functions, 14(1). https:\/\/doi.org\/10.1186\/s12993-018-0141-z","DOI":"10.1186\/s12993-018-0141-z"},{"key":"bibr72-1747021820940631","doi-asserted-by":"crossref","unstructured":"M\u00f6hring W., Newcombe N. S., Levine S. C., Frick A. (2016). Spatial proportional reasoning is associated with formal knowledge about fractions. Journal of Cognition and Development, 17(1), 67\u201384. https:\/\/doi.org\/10.1080\/15248372.2014.996289","DOI":"10.1080\/15248372.2014.996289"},{"key":"bibr73-1747021820940631","doi-asserted-by":"crossref","unstructured":"Morey R. D., Romeijn J. W., Rouder J. N. (2016). The philosophy of Bayes factors and the quantification of statistical evidence. Journal of Mathematical Psychology, 72, 6\u201318. https:\/\/doi.org\/10.1016\/j.jmp.2015.11.001","DOI":"10.1016\/j.jmp.2015.11.001"},{"key":"bibr74-1747021820940631","doi-asserted-by":"publisher","DOI":"10.1038\/2151519a0"},{"key":"bibr75-1747021820940631","doi-asserted-by":"crossref","unstructured":"Ni Y. (2001). Semantic domains of rational numbers and the acquisition of fraction equivalence. Contemporary Educational Psychology, 26(3), 400\u2013417. https:\/\/doi.org\/10.1006\/ceps.2000.1072","DOI":"10.1006\/ceps.2000.1072"},{"key":"bibr76-1747021820940631","doi-asserted-by":"crossref","unstructured":"Ni Y., Zhou Y.D. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist, 40(1), 27\u201352. https:\/\/doi.org\/10.1207\/s15326985ep4001_3","DOI":"10.1207\/s15326985ep4001_3"},{"key":"bibr77-1747021820940631","doi-asserted-by":"crossref","unstructured":"Obersteiner A., Van Dooren W., Van Hoof J., Verschaffel L. (2013). The natural number bias and magnitude representation in fraction comparison by expert mathematicians. Learning and Instruction, 28, 64\u201372. https:\/\/doi.org\/10.1016\/j.learninstruc.2013.05.003","DOI":"10.1016\/j.learninstruc.2013.05.003"},{"key":"bibr78-1747021820940631","doi-asserted-by":"crossref","unstructured":"Piazza M. (2010). Neurocognitive start-up tools for symbolic number representations. Trends in Cognitive Sciences, 14(12), 542\u2013551. https:\/\/doi.org\/10.1016\/j.tics.2010.09.008","DOI":"10.1016\/j.tics.2010.09.008"},{"key":"bibr79-1747021820940631","doi-asserted-by":"crossref","unstructured":"Piazza M., Facoetti A., Trussardi A. N., Berteletti I., Conte S., Lucangeli D. Zorzi M. (2010). Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition, 116(1), 33\u201341. https:\/\/doi.org\/10.1016\/j.cognition.2010.03.012","DOI":"10.1016\/j.cognition.2010.03.012"},{"key":"bibr80-1747021820940631","doi-asserted-by":"crossref","unstructured":"Pica P. (2004). Exact and approximate arithmetic in an Amazonian indigene group. Science, 306(5695), 499\u2013503. https:\/\/doi.org\/10.1126\/science.1102085","DOI":"10.1126\/science.1102085"},{"key":"bibr81-1747021820940631","doi-asserted-by":"crossref","unstructured":"Pitkethly A., Hunting R. (1996). A review of recent research in the area of initial fraction concepts. Educational Studies in Mathematics, 30(1), 5\u201338. https:\/\/doi.org\/10.1007\/BF00163751","DOI":"10.1007\/BF00163751"},{"key":"bibr82-1747021820940631","doi-asserted-by":"publisher","DOI":"10.5038\/1936-4660.6.1.2"},{"key":"bibr83-1747021820940631","doi-asserted-by":"publisher","DOI":"10.1177\/0022219419879684"},{"key":"bibr84-1747021820940631","doi-asserted-by":"crossref","unstructured":"Rousselle L., No\u00ebl M. P. (2007). Basic numerical skills in children with mathematics learning disabilities: A comparison of symbolic vs non-symbolic number magnitude processing. Cognition, 102(3), 361\u2013395. https:\/\/doi.org\/10.1016\/j.cognition.2006.01.005","DOI":"10.1016\/j.cognition.2006.01.005"},{"key":"bibr85-1747021820940631","volume-title":"The development of numerical competence: Animal and human models","author":"Rumbaugh D. M.","year":"1993"},{"key":"bibr86-1747021820940631","doi-asserted-by":"crossref","unstructured":"Schneider M., Siegler R. S. (2010). Representations of the magnitudes of fractions. Journal of Experimental Psychology: Human Perception and Performance, 36(5), 1227\u20131238. https:\/\/doi.org\/10.1037\/a0018170","DOI":"10.1037\/a0018170"},{"key":"bibr87-1747021820940631","doi-asserted-by":"crossref","unstructured":"Siegler R. S., Duncan G. J., Davis-Kean P. E., Duckworth K., Claessens A., Engel M. Chen M. (2012). Early predictors of high school mathematics achievement. Psychological Science, 23(7), 691\u2013697. https:\/\/doi.org\/10.1177\/0956797612440101","DOI":"10.1177\/0956797612440101"},{"key":"bibr88-1747021820940631","doi-asserted-by":"crossref","unstructured":"Siegler R. S., Fazio L. K., Bailey D. H., Zhou X. (2013). Fractions: The new frontier for theories of numerical development. Trends in Cognitive Sciences, 17(1), 13\u201319. https:\/\/doi.org\/10.1016\/j.tics.2012.11.004","DOI":"10.1016\/j.tics.2012.11.004"},{"key":"bibr89-1747021820940631","doi-asserted-by":"crossref","unstructured":"Siegler R. S., Pyke A. A. (2013). Developmental and individual differences in understanding of fractions. Developmental Psychology, 49(10), 1994\u20132004. https:\/\/doi.org\/10.1037\/a0031200","DOI":"10.1037\/a0031200"},{"key":"bibr90-1747021820940631","doi-asserted-by":"crossref","unstructured":"Siegler R. S., Thompson C. A., Schneider M. (2011). An integrated theory of whole number and fractions development. Cognitive Psychology, 62(4), 273\u2013296. https:\/\/doi.org\/10.1016\/j.cogpsych.2011.03.001","DOI":"10.1016\/j.cogpsych.2011.03.001"},{"key":"bibr91-1747021820940631","doi-asserted-by":"crossref","unstructured":"Sophian C. (2000). Perceptions of proportionality in young children: Matching spatial ratios. Cognition, 75(2), 145\u2013170. https:\/\/doi.org\/10.1016\/S0010-0277(00)00062-7","DOI":"10.1016\/S0010-0277(00)00062-7"},{"key":"bibr92-1747021820940631","doi-asserted-by":"crossref","unstructured":"Stafylidou S., Vosniadou S. (2004). The development of students\u2019 understanding of the numerical value of fractions. Learning and Instruction, 14(5), 503\u2013518. https:\/\/doi.org\/10.1016\/j.learninstruc.2004.06.015","DOI":"10.1016\/j.learninstruc.2004.06.015"},{"key":"bibr93-1747021820940631","doi-asserted-by":"crossref","unstructured":"Steffe L. P., Olive J. (2010). Children\u2019s fractional knowledge. Springer US. https:\/\/doi.org\/10.1007\/978-1-4419-0591-8","DOI":"10.1007\/978-1-4419-0591-8"},{"key":"bibr94-1747021820940631","unstructured":"Stigler J. W., Givvin K. B., Thompson B. J. (2010). What community college developmental mathematics students understand about mathematics. MathAMATYC Educator, 1(3), 4\u201316."},{"key":"bibr95-1747021820940631","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-3168-1"},{"key":"bibr96-1747021820940631","doi-asserted-by":"crossref","unstructured":"Vallentin D., Nieder A. (2010). Representations of visual proportions in the primate posterior parietal and prefrontal cortices: Proportion processing in the monkey brain. European Journal of Neuroscience, 32(8), 1380\u20131387. https:\/\/doi.org\/10.1111\/j.1460-9568.2010.07427.x","DOI":"10.1111\/j.1460-9568.2010.07427.x"},{"key":"bibr97-1747021820940631","doi-asserted-by":"crossref","unstructured":"Vamvakoussi X., Vosniadou S. (2010). How many decimals are there between two fractions ? Aspects of secondary school students\u2019 understanding of rational numbers and their notation. Cognition and Instruction, 28(2), 181\u2013209. https:\/\/doi.org\/10.1080\/07370001003676603","DOI":"10.1080\/07370001003676603"},{"key":"bibr98-1747021820940631","doi-asserted-by":"crossref","unstructured":"Van Hoof J., Lijnen T., Verschaffel L., Van Dooren W. (2013). Are secondary school students still hampered by the natural number bias? A reaction time study on fraction comparison tasks. Research in Mathematics Education, 15(2), 154\u2013164. https:\/\/doi.org\/10.1080\/14794802.2013.797747","DOI":"10.1080\/14794802.2013.797747"},{"key":"bibr99-1747021820940631","doi-asserted-by":"crossref","unstructured":"Wechsler D. (2008). Wechsler adult intelligence scale\u2013Fourth Edition (WAIS\u2013IV), 22(498), 1. San Antonio, TX: NCS Pearson.","DOI":"10.1037\/t15169-000"},{"key":"bibr100-1747021820940631","unstructured":"Woodcock R. W., Mather N., McGrew K. S., Wendling B. J. (2001). Woodcock-Johnson III tests of cognitive abilities. Itasca, IL: Riverside Publishing Company."},{"key":"bibr101-1747021820940631","doi-asserted-by":"crossref","unstructured":"Yoshida H., Sawano K. (2002). Overcoming cognitive obstacles in learning fractions: Equal-partitioning and equal-whole. Japanese Psychological Research, 44(4), 183\u2013195. https:\/\/doi.org\/10.1111\/1468-5884.00021","DOI":"10.1111\/1468-5884.00021"},{"key":"bibr102-1747021820940631","doi-asserted-by":"crossref","unstructured":"Zhang L., Fang Q., Gabriel F. C., Szucs D. (2014). The componential processing of fractions in adults and children: Effects of stimuli variability and contextual interference. Frontiers in Psychology, 5, Article 981. https:\/\/doi.org\/10.3389\/fpsyg.2014.00981","DOI":"10.3389\/fpsyg.2014.00981"}],"container-title":["Quarterly Journal of Experimental Psychology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1747021820940631","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/1747021820940631","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1747021820940631","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T07:05:35Z","timestamp":1777705535000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/1747021820940631"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,22]]},"references-count":102,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2020,12]]}},"alternative-id":["10.1177\/1747021820940631"],"URL":"https:\/\/doi.org\/10.1177\/1747021820940631","relation":{},"ISSN":["1747-0218","1747-0226"],"issn-type":[{"value":"1747-0218","type":"print"},{"value":"1747-0226","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,7,22]]}}}