No CrossRef data available.
Article contents
A rational explanation for links between the ANS and math
Published online by Cambridge University Press: 15 December 2021
Abstract
The proposal by Clarke and Beck offers a new explanation for the association between the approximate number system (ANS) and math. Previous explanations have largely relied on developmental arguments, an underspecified notion of the ANS as an “error detection mechanism,” or affective factors. The proposal that the ANS represents rational numbers suggests that it may directly support a broader range of math skills.
- Type
- Open Peer Commentary
- Information
- Copyright
- Copyright © The Author(s), 2021. Published by Cambridge University Press
References
Baer, C., & Odic, D. (2019). Certainty in numerical judgments develops independently of the approximate number system. Cognitive Development, 52, 100817.CrossRefGoogle Scholar
Bugden, S., DeWind, N. K., & Brannon, E. M. (2016). Using cognitive training studies to unravel the mechanisms by which the approximate number system supports symbolic math ability. Current Opinion in Behavioral Sciences, 10, 73–80.CrossRefGoogle ScholarPubMed
Chen, Q., & Li, J. (2014). Association between individual differences in non-symbolic number acuity and math performance: A meta-analysis. Acta Psychologica, 148, 163–172.CrossRefGoogle ScholarPubMed
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, 53–72.CrossRefGoogle ScholarPubMed
Libertus, M. E. (2019). Understanding the link between the approximate number system and math abilities. In Geary, D., Berch, D., & Mann Koepke, K. (Eds.), Cognitive foundations for improving mathematical learning (pp. 91–106). Elsevier.CrossRefGoogle Scholar
Libertus, M. E., Odic, D., Feigenson, L., & Halberda, J. (2016). The precision of mapping between number words and the approximate number system predicts children's formal math abilities. Journal of Experimental Child Psychology, 150, 207–226.CrossRefGoogle ScholarPubMed
Libertus, M. E., Odic, D., & Halberda, J. (2012). Intuitive sense of number correlates with math scores on college-entrance examination. Acta Psychologica), 141, 373–379.CrossRefGoogle ScholarPubMed
Lindskog, M., Winman, A., & Poom, L. (2017). Individual differences in nonverbal number skills predict math anxiety. Cognition, 159, 156–162.CrossRefGoogle ScholarPubMed
Lyons, I. M., & Beilock, S. L. (2011). Numerical ordering ability mediates the relation between number-sense and arithmetic competence. Cognition, 121(2), 256–261. doi: S0010-0277(11)00198-3 [pii]10.1016/j.cognition.2011.07.009.CrossRefGoogle ScholarPubMed
Lyons, I. M., Price, G. R., Vaessen, A., Blomert, L., & Ansari, D. (2014). Numerical predictors of arithmetic success in grades 1-6. Developmental Science, 17(5), 714–726.CrossRefGoogle ScholarPubMed
Maldonado Moscoso, P. A., Anobile, G., Primi, C., & Arrighi, R. (2020). Math anxiety mediates the link between number sense and math achievements in high math anxiety young adults. Frontiers in Psychology, 11, 1095.CrossRefGoogle ScholarPubMed
Maloney, E. A., Ansari, D., & Fugelsang, J. A. (2011). The effect of mathematics anxiety on the processing of numerical magnitude. Quarterly Journal of Experimental Psychology, 64(1), 10–16. doi: 930153501 [pii]10.1080/17470218.2010.533278.CrossRefGoogle ScholarPubMed
Matthews, P. G., & Chesney, D. L. (2015). Fractions as percepts? Exploring cross-format distance effects for fractional magnitudes. Cognitive Psychology, 78, 28–56.CrossRefGoogle ScholarPubMed
Mueller, S. M., & Brand, M. (2018). Approximate number processing skills contribute to decision making under objective risk: Interactions with executive functions and objective numeracy. Frontiers in Psychology, 9, 1202.CrossRefGoogle ScholarPubMed
Mueller, S. M., Schiebener, J., Delazer, M., & Brand, M. (2018). Risk approximation in decision making: Approximative numeric abilities predict advantageous decisions under objective risk. Cognitive processing, 19(3), 297–315.CrossRefGoogle ScholarPubMed
Mundy, E., & Gilmore, C. K. (2009). Children's mapping between symbolic and nonsymbolic representations of number. Journal of Experimental Child Psychology, 103(4), 490–502. doi:S0022-0965(09)00035-6 [pii] 10.1016/j.jecp.2009.02.003.CrossRefGoogle Scholar
Mussolin, C., Nys, J., Leybaert, J., & Content, A. (2016). How approximate and exact number skills are related to each other across development: A review. Developmental Review, 39, 1–15.CrossRefGoogle Scholar
O'Grady, S., & Xu, F. (2020). The development of nonsymbolic probability judgments in children. Child Development, 91(3), 784–798.CrossRefGoogle ScholarPubMed
Park, J., Bermudez, V., Roberts, R. C., & Brannon, E. M. (2016). Non-symbolic approximate arithmetic training improves math performance in preschoolers. Journal of Experimental Child Psychology, 152, 278–293.CrossRefGoogle ScholarPubMed
Pinheiro-Chagas, P., Wood, G., Knops, A., Krinzinger, H., Lonnemann, J., Starling-Alves, I., … Haase, V. G. (2014). In how many ways is the approximate number system associated with exact calculation? PLoS One, 9(11), e111155.CrossRefGoogle ScholarPubMed
Schneider, M., Beeres, K., Coban, L., Merz, S., Schmidt, S. S., Stricker, J., & De Smedt, B. (2017). Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: A meta-analysis. Developmental Science, 20(3), e12372. doi: 10.1111/desc.12372CrossRefGoogle ScholarPubMed
Vo, V. A., Li, R., Kornell, N., Pouget, A., & Cantlon, J. F. (2014). Young children bet on their numerical skills: Metacognition in the numerical domain. Psychological Science, 25(9), 1712–1721. doi: 10.1177/0956797614538458CrossRefGoogle ScholarPubMed
Wagner, J. B., & Johnson, S. C. (2011). An association between understanding cardinality and analog magnitude representations in preschoolers. Cognition, 119(1), 10–22. doi:10.1016/j.cognition.2010.11.014CrossRefGoogle ScholarPubMed
Wang, J., Odic, D., Halberda, J., & Feigenson, L. (2016). Changing the precision of preschoolers’ approximate number system representations changes their symbolic math performance. Journal of Experimental Child Psychology, 147, 82–99.CrossRefGoogle ScholarPubMed
Wong, H., & Odic, D. (2021). The intuitive number sense contributes to symbolic equation error detection abilities. Journal of Experimental Psychology: Learning, Memory, and Cognition, 47(1), 1–10.Google ScholarPubMed
Target article
The number sense represents (rational) numbers
Related commentaries (26)
A rational explanation for links between the ANS and math
Constructing rationals through conjoint measurement of numerator and denominator as approximate integer magnitudes in tradeoff relations
Contents of the approximate number system
Distinguishing the specific from the recognitional and the canonical, and the nature of ratios
Non-symbolic and symbolic number and the approximate number system
Not so rational: A more natural way to understand the ANS
Numbers in action
Numerical cognition needs more and better distinctions, not fewer
Numerical cognition: Unitary or diversified system(s)?
Numerosities are not ersatz numbers
Numerosity, area-osity, object-osity? Oh my
Perceived number is not abstract
Positing numerosities may be metaphysically extravagant; positing representation of numerosities is not
Ratio-based perceptual foundations for rational numbers, and perhaps whole numbers, too?
Real models: The limits of behavioural evidence for understanding the ANS
Representation of pure magnitudes in ANS
Second-order characteristics don't favor a number-representing ANS
Sizes, ratios, approximations: On what and how the ANS represents
The approximate number system represents magnitude and precision
The approximate number system represents rational numbers: The special case of an empty set
The number sense does not represent numbers, but cardinality comparisons
The number sense represents multitudes and magnitudes
The perception of quantity ain't number: Missing the primacy of symbolic reference
Unwarranted philosophical assumptions in research on ANS
Weighted numbers
What are we doing when we perceive numbers?
Author response
Numbers, numerosities, and new directions