Hostname: page-component-7479d7b7d-jwnkl Total loading time: 0 Render date: 2024-07-10T23:39:03.106Z Has data issue: false hasContentIssue false
  • English
  • Français

Possible Associations between Subitizing, Estimation and Visuospatial Working Memory (VSWM) in Children

Published online by Cambridge University Press:  05 June 2017

Jesica Formoso ,
Juan Pablo Barreyro ,
Silvia Jacubovich  and
Irene Injoque-Ricle
Jesica Formoso*
Affiliation:
Universidad de Buenos Aires (Argentina)
Juan Pablo Barreyro
Affiliation:
CONICET (Argentina)
Silvia Jacubovich
Affiliation:
Universidad de Buenos Aires (Argentina)
Irene Injoque-Ricle
Affiliation:
Universidad de Buenos Aires (Argentina)
*
*Correspondence concerning this article should be addressed to Jesica Formoso. Instituto de Investigaciones - Facultad de Psicología. Universidad de Buenos Aires – CONICET. Lavalle, 2353. C1425AAM. Ciudad de Buenos Aires (Argentina). E-mail: jformoso@psi.uba.ar
Get access Rights & Permissions [Opens in a new window]

Abstract

Researchers have focused on identifying the mechanisms involved in subitizing and its differences with estimation. Some suggest that subitizing relies on a visual indexing system in charge of the simultaneous individuation of objects that is also used by visuospatial working memory (VSWM). In adults, studies found associations between subitizing and VSWM, in the absence of correlation between VSWM and estimation. The present study analyzed the performance of 120 4 and 6-year-old children in three tasks: dot enumeration to measure subitizing capacity, quantity discrimination for estimation, and Corsi Block-tapping task for VSWM. In the enumeration task RTs (F(9, 1062)=720.59, MSE=734394, p<.001, η2=.86) and errors (F(9, 1062)=42.15, MSE=.194, p<.001, η2=.26.) increased with the array, but this growth was statistically significant only from 4 dots onward. Each subject’s subitizing range was estimated by fitting RTs with a sigmoid function of number of dots and obtaining the bend point of the curve. Data fit (age 4: R2 = .88; SD = .08; age 6: R2 = .91, SD = .08) showed a mean subitizing range of 2.79 (SD = .66) for 4 year-olds and of 3.11 (SD = .64) for 6 year-olds. Subitizing ranges and average RTs showed low association with storage (r = .274; p < .05; r = –.398; p < .001) and average RTs with concurrent processing (r = –.412; p < .001) in VSWM. Subitizing range and speed showed no association with estimation speed and a poor association with accuracy (r = .234, p < .01; r = –.398, p < .001), which suggests independent systems for small and large quantities. Subitizing and estimation measures correlated with VSWM (p < .01), which suggests that both processes may require VSWM resources.

Keywords

childrenenumerationestimationsubitizingvisuospatial working memory
Type
Research Article
Information
The Spanish Journal of Psychology , Volume 20 , 2017 , E27
Copyright
Copyright © Universidad Complutense de Madrid and Colegio Oficial de Psicólogos de Madrid 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Atkinson, J., Campbell, F. W., & Francis, M. R. (1976). The magic number 4 ± 0: A new look at visual numerosity judgements. Perception, 5, 327–334. https://doi.org/10.1068/p050327 CrossRefGoogle Scholar
Baddeley, A. D., & Logie, R. H. (1999). Working memory: The multiple component model. In Shah, A. M. P. (Ed.), Models of working memory: Mechanisms of active maintenance and executive control (pp. 28–61). New York, NY: Cambridge University Press.Google Scholar
Burr, D. C., Turi, M., & Anobile, G. (2010). Subitizing but not estimation of numerosity requires attentional resources. Journal of Vision, 10, 20. https://doi.org/10.1167/10.6.20 CrossRefGoogle Scholar
Corsi, P. M. (1972). Human memory and the medial temporal region of the brain. Montreal, Canada: McGill University.Google Scholar
Cowan, N. (2001). The magical number 4 in short-term memory: A reconsideration of mental storage capacity. Behavioral and Brain Sciences, 24(1), 87–114. https://doi.org/10.1017/S0140525X01003922 CrossRefGoogle ScholarPubMed
Chi, M. T. H., & Klahr, D. (1975). Span and ratio of apprehension in children and adults. Journal of Experimental Child Psychology, 19, 434–439.CrossRefGoogle Scholar
Dehaene, S., & Changeux, J. P. (1993). Development of elementary numerical abilities: A neuronal model. Journal of Cognitive Neuroscience, 5, 390–407. https://doi.org/10.1162/jocn.1993.5.4.390 Google Scholar
Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8, 307–314. https://doi.org/10.1016/j.tics.2004.05.002 Google Scholar
Fischer, B., Gebhardt, C., & Hartnegg, K. (2008). Subitizing and visual counting in children with problems in acquiring basic arithmetic skills. Optometry & Vision Development, 39(1).Google Scholar
Gallistel, C. R., & Gelman, R. (1991). Subitizing: The preverbal counting process. In Kessen, W., Ortony, A., & Kraik, F. (Eds.), Memories, thoughts and emotions: Essays in honor of george mandler (pp. 65–81). Hillsdale, NJ: Erlbaum.Google Scholar
Green, C. S., & Bavelier, D. (2003). Action video game modifies visual selective attention. Nature, 423, 534–537. https://doi.org/10.1038/nature01647 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, 1457–1465. https://doi.org/10.1037/a0012682 CrossRefGoogle ScholarPubMed
Hannula, M. M., Räsänen, P., & Lehtinen, E. (2007). Development of counting skills: Role of spontaneous focusing on numerosity and subitizing-based enumeration. Mathematical Thinking and Learning, 9(1), 51–57. https://doi.org/10.1080/10986060709336605 CrossRefGoogle Scholar
Hyde, D. C., Winkler-Rhoades, N., Lee, S. A., Izard, V., Shapiro, K. A., & Spelke, E. S. (2011). Spatial and numerical abilities without a complete natural language. Neuropsychologia, 49, 924–936. https://doi.org/10.1016/j.neuropsychologia.2010.12.017 Google Scholar
Injoque-Ricle, I., Barreyro, J. P., Formoso, J., & Burin, D. I. (2015). Estructura de la memoria de trabajo en jóvenes adultos y su relación con “g” [Young adults’ working memory structure and it’s relation to “g”]. PSIENCIA. Revista Latinoamericana de Ciencia Psicológica, 7, 406–417. https://doi.org/10.5872/psiencia/7.3.22 Google Scholar
Jensen, A. R. (1987). Psychometric g as a focus of concerted research effort. Intelligence, 11, 193–198. https://doi.org/10.1016/0160-2896(87)90005-5 CrossRefGoogle Scholar
Jevons, W. S. (1871). The power of numerical discrimination. Nature, 3, 281–282. https://doi.org/10.1038/003281a0 CrossRefGoogle Scholar
Kaufman, E. L., Lord, M. W., Reese, T. W., & Volkmann, J. (1949). The discrimination of visual number. The American Journal of Psychology, 62, 498–525. https://doi.org/10.2307/1418556 Google Scholar
Klahr, D. (1973). A production system for counting, subitizing, and adding. In Chase, W. G. (Ed.), Visual information processing (pp. 527–546). New York, NY: Academic Press.CrossRefGoogle Scholar
Lemer, C., Dehaene, S., Spelke, E., & Cohen, L. (2003). Approximate quantities and exact number words: Dissociable systems. Neuropsychologia, 41, 1942–1958. https://doi.org/10.1016/s0028-3932(03)00123-4 Google Scholar
Lipton, J. S., & Spelke, E. S. (2004). Discrimination of large and small numerosities by human infants. Infancy, 5, 271–290. https://doi.org/10.1207/s15327078in0503_2 CrossRefGoogle Scholar
Logan, G. D., & Zbrodoff, N. J. (2003). Subitizing and similarity: Toward a pattern-matching theory of enumeration. Psychonomic Bulletin & Review, 10, 676–682. https://doi.org/10.3758/BF03196531 CrossRefGoogle Scholar
Logie, R. H. (1995). Visuo-spatial working memory. Hove, UK: Lawrence Erlbaum.Google Scholar
Logie, R. H., & Baddeley, A. D. (1987). Cognitive processes in counting. Journal of Experimental Psychology: Learning, Memory, and Cognition, 13, 310–326. https://doi.org/10.1037/0278-7393.13.2.310 Google Scholar
Mandler, G., & Shebo, B. J. (1982). Subitizing: An analysis of its component processes. Journal of Experimental Psychology: General, 111, 1–22. https://doi.org/10.1037/0096-3445.111.1.1 Google Scholar
Mathôt, S., Schreij, D., & Theeuwes, J. (2012). OpenSesame: An open-source, graphical experiment builder for the social sciences. Behavior Research Methods, 44, 314–324. https://doi.org/10.3758/s13428-011-0168-7 CrossRefGoogle ScholarPubMed
Mazza, V., & Caramazza, A. (2015). Multiple object individuation and subitizing in enumeration: A view from electrophysiology. Frontiers in Human Neuroscience, 9, 162. https://doi.org/10.3389/fnhum.2015.00162 CrossRefGoogle ScholarPubMed
Miller, L. T., & Vernon, P. A. (1996). Intelligence, reaction time and working memory in 4- to 6-year-old children. Intelligence, 22, 155–190.Google Scholar
Odic, D., Libertus, M. E., Feigenson, L., & Halberda, J. (2013). Developmental change in the acuity of approximate number and area representations. Developmental Psychology, 49, 1103–1112. https://doi.org/10.1037/a0029472 CrossRefGoogle ScholarPubMed
Pagano, S., Lombardi, L., & Mazza, V. (2014). Brain dynamics of attention and working memory engagement in subitizing. Brain Research, 1543, 244–252. https://doi.org/10.1016/j.brainres.2013.11.025 Google Scholar
Piazza, M., Fumarola, A., Chinello, A., & Melcher, D. (2011). Subitizing reflects visuo-spatial object individuation capacity. Cognition, 121(1), 147–153. https://doi.org/10.1016/j.cognition.2011.05.007 CrossRefGoogle ScholarPubMed
Railo, H., Koivisto, M., Revonsuo, A., & Hannula, M. M. (2008). The role of attention in subitizing. Cognition, 107(1), 82–104. https://doi.org/10.1016/j.cognition.2007.08.004 CrossRefGoogle ScholarPubMed
Revkin, S. K., Piazza, M., Izard, V., Cohen, L., & Dehaene, S. (2008). Does subitizing reflect numerical estimation? Psychological Science, 19, 607–614. https://doi.org/10.1111/j.1467-9280.2008.02130.x Google Scholar
Sattler, J. M. (1992). Assessment of children: WISC-III and WPPSI-R supplement. San Diego, CA: Author.Google Scholar
Sebaugh, J. L., & McCray, P. D. (2003). Defining the linear portion of a sigmoid-shaped curve: Bend points. Pharmaceutical Statistics, 2, 167–174.Google Scholar
Shimomura, T., & Kumada, T. (2011). Spatial working memory load affects counting but not subitizing in enumeration. Attention, Perception, & Psychophysics, 73, 1694–1709. https://doi.org/10.3758/s13414-011-0135-5 CrossRefGoogle Scholar
Svenson, O., & Sjöberg, K. (1978). Subitizing and counting processes in young children. Scandinavian Journal of Psychology, 19, 247–250. https://doi.org/10.1111/j.1467-9450.1978.tb00327.x CrossRefGoogle Scholar
Tellegen, A., & Briggs, P. (1967). Old wine in new skins: Grouping Wechsler subtests into new scales. Journal of Consulting Psychology, 31, 499–506.Google Scholar
Trick, L. M. (2005). The role of working memory in spatial enumeration: Patterns of selective interference in subitizing and counting. Pshyconomic Bulletin & Review, 12, 675–681. https://doi.org/10.3758/bf03196757 Google Scholar
Trick, L. M. (2008). More than superstition: Differential effects of featural heterogeneity and change on subitizing and counting. Perception & Psychophysics, 70, 743–760. https://doi.org/10.3758/pp.70.5.743 CrossRefGoogle ScholarPubMed
Trick, L. M., Enns, J. T., & Brodeur, D. A. (1996). Life span changes in visual enumeration: The number discrimination task. Developmental Psychology, 32, 925–932. https://doi.org/10.1037/0012-1649.32.5.925 Google Scholar
Trick, L. M., & Pylyshyn, Z. W. (1994). Why are small and large numbers enumerates differently? A limited-capacity preattentive stage in vision. Psychological Review, 101, 80–102. https://doi.org/10.1037/0033-295x.101.1.80 CrossRefGoogle ScholarPubMed
Vetter, P., Butterworth, B., & Bahrami, B. (2008). Modulating attentional load affects numerosity estimation: Evidence against a pre-attentive subitizing mechanism. PLoS One, 3, e3269. https://doi.org/10.1371/journal.pone.0003269 CrossRefGoogle ScholarPubMed
Von Glasersfeld, E. (1982). Subitizing: The role of figural patterns in the development of numerical concepts. Archives de Pshycologie, 50, 191–218.Google Scholar
Watson, D. G., Maylor, E. A., & Bruce, L. A. M. (2005). The efficiency of feature-based subitization and counting. Journal of Experimental Psychology. Human Perception and Performance, 31, 1449–1462. https://doi.org/10.1037/0096-1523.31.6.1449 CrossRefGoogle ScholarPubMed
Wechsler, D. (1994). Test de inteligencia para niños WISC-III, Manual [Wechsler intelligence scale for children WISC-III, Manual] . Buenos Aires, Argentina: Paidós.Google Scholar
Wilhelm, O., & Oberauer, K. (2006). Why are reasoning ability and working memory capacity related to mental speed? An investigation of stimulus–response compatibility in choice reaction time tasks. European Journal of Cognitive Psychology, 18(1), 18–50.CrossRefGoogle Scholar
Xu, F., Spelke, E. S., & Goddard, S. (2005). Number sense in human infants. Developmental Science, 8, 88–101. https://doi.org/10.1111/j.1467-7687.2005.00395.x Google Scholar