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From continuous magnitudes to symbolic numbers: The centrality of ratio

Published online by Cambridge University Press:  27 July 2017

Pooja G. Sidney
Affiliation:
Department of Psychological Sciences, Kent State University, Kent, OH 44242psidney1@kent.educthomp77@kent.edupoojasidney.comhttp://www.clarissathompson.com
Clarissa A. Thompson
Affiliation:
Department of Psychological Sciences, Kent State University, Kent, OH 44242psidney1@kent.educthomp77@kent.edupoojasidney.comhttp://www.clarissathompson.com
Percival G. Matthews
Affiliation:
Department of Educational Psychology, University of Wisconsin–Madison, Madison, WI 53706-1796pmatthews@wisc.eduemhubbard@wisc.eduhttps://website.education.wisc.edu/pmatthews/http://website.education.wisc.edu/edneurolab/
Edward M. Hubbard
Affiliation:
Department of Educational Psychology, University of Wisconsin–Madison, Madison, WI 53706-1796pmatthews@wisc.eduemhubbard@wisc.eduhttps://website.education.wisc.edu/pmatthews/http://website.education.wisc.edu/edneurolab/

Abstract

Leibovich et al.'s theory neither accounts for the deep connections between whole numbers and other classes of number nor provides a potential mechanism for mapping continuous magnitudes to symbolic numbers. We argue that focusing on non-symbolic ratio processing abilities can furnish a more expansive account of numerical cognition that remedies these shortcomings.

Type
Open Peer Commentary
Copyright
Copyright © Cambridge University Press 2017 

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References

Barth, H. C. & Paladino, A. M. (2011) The development of numerical estimation: Evidence against a representational shift. Developmental Science 14(1):125–35. doi: 10.1111/j.1467-7687.2010.00962.x.Google Scholar
DeWolf, M., Grounds, M. A., Bassok, M. & Holyoak, K. J. (2014) Magnitude comparison with different types of rational numbers. Journal of Experimental Psychology: Human Perception and Performance 40(1):7182. doi: 10.1037/a0032916.Google ScholarPubMed
Gallistel, C. R. & Gelman, R. (2000) Non-verbal numerical cognition: From reals to integers. Trends in Cognitive Sciences 4(2):5965. doi: 10.1016/S1364-6613(99)01424-2.CrossRefGoogle ScholarPubMed
Halberda, J. & Feigenson, L. (2008) Developmental change in the acuity of the “number sense”: The approximate number system in 3-, 4-, 5-, and 6-year-olds and adults. Developmental Psychology 44(5):1457–65. doi: 10.1037/a0012682.Google Scholar
Henik, A. & Tzelgov, J. (1982) Is three greater than five: The relation between physical and semantic size in comparison tasks. Memory & Cognition 10(4):389–95. doi: 10.3758/BF03202431.Google Scholar
Jacob, S. N. & Nieder, A. (2009) Tuning to non-symbolic proportions in the human frontoparietal cortex. European Journal of Neuroscience 30(7):1432–42. doi: 10.1111/j.1460-9568.2009.06932.x.CrossRefGoogle ScholarPubMed
Jacob, S. N., Vallentin, D. & Nieder, A. (2012) Relating magnitudes: The brain's code for proportions. Trends in Cognitive Sciences 16(3):157–66. doi: 10.1016/j.tics.2012.02.002.CrossRefGoogle ScholarPubMed
Leibovich, T., Kallai, A. & Itamar, S. (2016a) What do we measure when we measure magnitudes? In: Continuous issues in numerical cognition, ed. Henik, A., pp. 355–73. Elsevier. doi: 10.1016/B978-0-12-801637-4.00016-0.Google Scholar
Matthews, P. G. & Chesney, D. L. (2015) Fractions as percepts? Exploring cross-format distance effects for fractional magnitudes. Cognitive Psychology 78:2856. doi: 10.1016/j.cogpsych.2015.01.006.CrossRefGoogle ScholarPubMed
Matthews, P. G. & Lewis, M. R. (2016) Fractions we cannot ignore: The nonsymbolic ratio congruity effect. Cognitive Science. Available online. doi: 10.1111/cogs.12419.Google Scholar
Matthews, P. G., Lewis, M. R. & Hubbard, E. M. (2016) Individual differences in nonsymbolic ratio processing predict symbolic math performance. Psychological Science 27(2):191202. doi: 10.1177/0956797615617799.Google Scholar
McCrink, K. & Wynn, K. (2007) Ratio abstraction by 6-month-old infants. Psychological Science 18(8):740–45. doi: 10.1111/j.1467-9280.2007.01969.x.Google Scholar
Moyer, R. S. & Landauer, T. K. (1967) Time required for judgements of numerical inequality. Nature 215(5109):1519–20. doi: 10.1038/2151519a0.CrossRefGoogle ScholarPubMed
Piazza, M. (2010) Neurocognitive start-up tools for symbolic number representations. Trends in Cognitive Sciences 14(12):542–51. doi: 10.1016/J.Tics.2010.09.008.Google Scholar
Siegler, R. S., Thompson, C. A. & Schneider, M. (2011) An integrated theory of whole number and fractions development. Cognitive Psychology 62(4):273–96. Available at: https://doi.org/10.1016/j.cogpsych.2011.03.001.Google Scholar
Thompson, C. A. & Opfer, J. E. (2010) How 15 hundred is like 15 cherries: Effect of progressive alignment on representational changes in numerical cognition. Child Development 81(6):1768–86. doi: 10.1111/j.1467-8624.2010.01509.x.Google Scholar
Vallentin, D. & Nieder, A. (2008) Behavioral and prefrontal representation of spatial proportions in the monkey. Current Biology 18(18):1420–25. doi: 10.1016/j.cub.2008.08.042.Google Scholar