Quantity discrimination: Effect of number ratio over speed and accuracy

Authors

  • Jesica Formoso Universidad de Buenos Aires, Argentina
  • Juan Pablo Barreyro Universidad de Buenos Aires, Argentina
  • Silvia Jacubovich Universidad de Buenos Aires, Argentina
  • Marina Leiman Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina
  • Irene Injoque-Ricle Universidad de Buenos Aires, Argentina

DOI:

https://doi.org/10.24265/liberabit.2016.v22n1.02

Keywords:

Quantity discrimination, estimate, children, number ratio

Abstract

The ability to estimate and discriminate quantities is of early onset in the development and prior to the acquisition of a symbolic numerical system. The performance on tasks of discrimination is modulated by the number ratio that differentiates the sets, so that smaller reasons result in slower and less effective comparisons. The objective of the present study is to analyze the precision and speed by which 4 and 6 year old children discriminate between two quantities based on the number ratio that distinguishes them. Method: a discrimination task of non-symbolic quantities (ad hoc) was given to 60 children from 4 and 6 years old in the city of Buenos Aires, Argentina. A mixed ANOVA design was carried out to analyze the amount of hits and reaction times (RT) according to age, and the number ratio that differentiates the groups. The Bonferroni contrast test was used to detect the differences in hits and RT between each reasoning. Results: (a) children age 6 showed smaller RT and more hits than children age 4. This suggests that discrimination on the basis of quantities is undergoing a process of evolutionary development. (b) The greater the number ratio in the differentiation of the sets, the more effective the discrimination. This suggests that reason modulates performance regardless of the age of the subject.

DOI: https://doi.org/10.24265/liberabit.2016.v22n1.02

Downloads

Download data is not yet available.

References

Barth, H., Beckmann, L., & Spelke, E. S. (2008). Nonsymbolic, approximate arithmetic in children: abstract addition prior to instruction. Developmental Psychology, 44(5), 1466-1477. doi: 10.1037/a0013046

Cañizares, D. C. & Reigosa-Crespo, V. (2011). Calibrando la línea numérica mental: evidencias desde el desarrollo típico y atípico. Revista Neuropsicología, Neuropsiquiatría y Neurociencias, 11(1), 17-31.

Cantlon, J. F. & Brannon, E. M. (2006). Shared system for ordering small and large numbers in monkeys and humans. Psychological Science, 17(5), 401-406. doi: 10.1111/ j.1467-9280.2006.01719.x

Dehaene, S. (2001). Precis of the number sense. Mind & Language, 16, 16-36. doi: 10.1111/1468-0017.00154

Dehaene, S. (2003). The neural basis for the Weber-Fechner law: a logarithmic mental number line. Trends in Cognitive Sciences, 7(4), 145-147. doi: 10.1016/s1364-6613(03)00055-x

Duncan, G., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., … Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428-1446. doi: 10.1037/0012-1649.44.1.217

Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8(7), 307-314. doi: 10.1016/j.tics.2004.05.002

Geary, D. C., Bailey, D. H., Littlefield, A., Wood, P., Hoard, M. K., & Nugent, L. (2009). First-grade predictors of mathematical learning disability: A latent class trajectory analysis. Cognitive Development, 24(4), 411-429. doi: 10.1016/j.cogdev.2009.10.001

Guillaume, M., Nys, J., Mussolin, C., & Content, A. (2013). Differences in the acuity of the approximal number system in adults: the effect of mathematical ability. Acta Psychologica, 144(3), 506-512. doi: 10.1016/j.actpsy.2013.09.001

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), 1457-1465. doi: 10.1037/ a0012682

Halberda, J., Ly, R., Wilmer, J. B., Naiman, D. Q., & Germine, L. (2012). Number sense across the lifespan as revealed by a massive Internet-based sample. Proceedings of the National Academy of Sciences, 109(28), 11116-11120. doi: 10.1073/ pnas.1200196109

Halberda, J., Mazzoco, M. M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlates with maths achievement. Nature, 455, 665-668 doi: 10.1038/ nature07246

Holloway, I. D. & Ansari, D. (2009). Mapping numerical magnitudes onto symbols: the numerical distance effect and individual differences in children’s mathematics achievement. Journal of Experimental Child Psychology, 103(1), 17-29. doi: 10.1016/j.jecp.2008.04.001

Inglis, M., Attridge, N., Batchelor, S., & Gilmore, C. (2011). Non-Verbal number acuity correlates with symbolic mathematics achievemente: But only children. Pshyconomic Bulletin & Review, 18(6), 1222-1229. doi: 10.3758/s13423011-0154-1

Jordan, K. E. & Brannon, E. M. (2006). Weber’s Law influences numerical representations in rhesus macaques (Macaca mulatta). Animal Cognition, 9(3), 159-172. doi: 10.1007/ s10071-006-0017-8

Laski, E. V. & Siegler, R. S. (2007). Is 27 a big number? Correlational and causal connections among numerical categorization, number line estimation, and numerical magnitude comparison. Child Development, 78(6), 17231743. doi: 10.1111/j.1467-8624.2007.01087.x

Libertus, M. E., Feigenson, L., & Halberda, J. (2013). Is approximate number precision a stable predictor of math ability? Learning and Individual Differences, 1(25), 126-133. doi: 10.1016/j.lindif.2013.02.001

Libertus, M. E., Odic, D., & Halberda, J. (2012). Intuitive sense of number correlates with math scores on collage-entrance examination. Acta Psychologica, 141(3), 373-379. doi: 10.1016/j.actpsy.2012.09.009

Lindskog, M., Winman, A., Juslin, P., & Poom, L. (2013). Measuring acuity of the approximate number system reliably and validly: the evaluation of an adaptive test procedure. Frontiers in Psychology, 4, 510. doi: 10.3389/ fpsyg.2013.00510

Lipton, J. & Spelke, E. (2004). Discrimination of large and small numerosities by human infants. Infancy, 5(3), 271-290. doi: 10.1207/s15327078in0503_2

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: 10.1016/ j.cognition.2011.07.009

Mathôt, S., Schreij, D., & Theeuwes, J. (2012). OpenSesame: An open-source, graphical experiment builder for the social sciences. Behavior Research Methods, 44(2), 314-324. doi: 10.3758/s13428-011-0168-7

Mazzocco, M., Feigenson, L., & Halberda, J. (2011a). Preschoolers’ precision of the approximate number system predicts later school mathematics performance. PLoS One, 6(9), e23749. doi: 10.1371/journal.pone.0023749

Mazzocco, M., Feigenson, L., & Halberda, J. (2011b). Impaired Acuity of the Approximate Number System Underlies Mathematical Learning Disability (Dyscalculia). Child Development, 82(4), 1224-1237. doi: 10.1111/j.14678624.2011.01608.x

McCrink, K. & Wynn, K. (2004). Large-number addition & subtraction by 9-month-old infants. Psychological Science, 15(11), 776-781. doi: j.0956-7976.2004.00755.x

Miletto, M., Agrillo, C., Izard, V., & Bisazza, A. (2015). Relative versus absolute numerical representation in fish: Can guppies represent «fourness»? Animal Cognition. doi: 10.1007/ s10071-015-0868-y

Miletto, M., Agrillo, C., Piffer, L., & Bisazza, A. (2014). Ontogeny of the capacity to compare discrete quantities in fish. Dev Psychobiol, 56(3), 529-536. doi: 10.1002/dev.21122

Moyer, R. S. & Bayer, R. H. (1976). Mental comparison and the symbolic distance effect. Cognitive Psychology, 8(2), 228-246. doi: 10.1016/0010-0285(76)90025-6

Moyer, R. S. & Landauer, T. K. (1967). Time required for judgement of numerical inequality. Nature, 215(5109), 15191520. doi: 10.1038/2151519a0

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: 10.1016/j.jecp.2009.02.003

Nieder, A. & Miller, E. K. (2003). Coding of cognitive magnitude: Compressed scaling of numerical information in the primate prefrontal cortex. Neuron, 37(1), 149-157. doi: 10.1016/ s0896-6273(02)01144-3

Niss, M. (2003). Mathematical competencies & the learning of mathematics: The Danish KOM project. Documento presentado en 3rd Mediterranean Conference on Mathematical Education, Atenas.

Odic, D., Libertus, M. E., Feigenson, L., & Halberda, J. (2013). Developmental change in the acuity of approximate number and area representations. Developmental Psychology, 49(6), 1103-1112. doi: 10.1037/a0029472

Odic, D., Pietroski, P., Hunter, T., Lidz, J., & Halberda, J. (2013). Young children’s understanding of «more» and discrimination of number and surface area. Journal of Experimental Psychology: Learning, Memory and Cognition, 39(2), 451-461. doi: 10.1037/a0028874

Park, J. & Brannon, E. M. (2013). Training the approximate number system improves math proficiency. Psychological Science, 24(10), 2013-2019. doi: 10.1177/ 0956797613482944

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), 33-41. doi: 10.1016/j.cognition.2010.03.012

Piazza, M., Izard, V., Pinel, P., Le Bihan, D., & Dehaene, S. (2004). Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron, 44(3), 547-555. doi: 10.1016/j.neuron.2004.10.014

Piffer, L., Agrillo, C., & Hyde, D. C. (2012). Small and large number discrimination in guppies. Anim Cogn, 15(2), 215-221. doi: 10.1007/s10071-011-0447-9

Sasanguie, D., Göbel, S., Moll, K., Smets, K., & Reynvoet, B. (2013). Approximate number sense, symbolic number processing, or number-space mappings: what underlies mathematics achievement? Journal of Experimental Child Psychology, 114(3), 418-431. doi: 10.1016/j.jecp.2012.10.012

Starr, A. B., Libertus, M. E., & Brannon, E. M. (2013). Infants Show Ratio-dependent Number Discrimination Regardless of Set Size. Infancy, 18(6). doi: 10.1111/infa.12008

Vallentin, D., Bongard, S., & Nieder, A. (2012). Numerical rule coding in the prefrontal, premotor, and posterior parietal cortices of macaques. The Journal of Neuroscience, 32(19), 6621-6630. doi: 10.1523/JNEUROSCI.5071-11.2012

Xu, F. (2003). Numerosity discrimination in infants: Evidence for two systems of representations. Cognition, 89(1), B15B25. doi: 10.1016/s0010-0277(03)00050-7

Xu, F. & Arriaga, R. L. (2007). Number discrimination in 10month-old infants. British Journal of Developmental Psychology, 25, 103-108. doi: 10.1348/026151005x90704

Xu, F. & Spelke, E. (2000). Large number discrimination in 6month-old infants. Cognition, 74(1), 1-11. doi: 10.1016/ s0010-0277(99)00066-9

Xu, F., Spelke, E., & Goddard, S. (2005). Number sense in human infants. Developmental Science, 8(1), 88-101. doi: 10.1111/ j.1467-7687.2005.00395.x

Published

2016-06-30

How to Cite

Quantity discrimination: Effect of number ratio over speed and accuracy. (2016). LIBERABIT. Revista Peruana De Psicología, 22(1), 21-29. https://doi.org/10.24265/liberabit.2016.v22n1.02

Similar Articles

1-10 of 194

You may also start an advanced similarity search for this article.

Most read articles by the same author(s)