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Subitizing and counting

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File:Subitizing.svg

Counting or subitizing?

For instantaneous enlightenment, see Subitism.
Main article: Numerosity perception

Subitizing, coined in 1949 by E.L. Kaufman et al.[1] refers to the rapid, accurate, and confident judgments of number performed for small numbers of items. The term is derived from the Latin adjective subitus (meaning sudden) and captures a feeling of immediately knowing how many items lie within the visual scene, when the number of items present falls within the subitizing range.[1] Number judgments for larger set-sizes were referred to either as counting or estimating, depending on the number of elements present within the display, and the time given to observers in which to respond (i.e., estimation occurs if insufficient time is available for observers to accurately count all the items present).

The accuracy, speed, and confidence with which observers make judgments of the number of items are critically dependent on the number of elements to be enumerated. Judgments made for displays composed of around one to four items are rapid[2], accurate[3] and confident.[4] However, as the number of items to be enumerated increases beyond this amount, judgments are made with decreasing accuracy and confidence.[1] In addition, response times rise in a dramatic fashion, with an extra 250 ms – 350 ms added for each additional item within the display beyond about four.[5]

While the increase in response time for each additional element within a display is relatively large outside the subitizing range (i.e., 250 ms – 350 ms per item), there is still a significant, albeit smaller, increase within the subitizing range, for each additional element within the display (i.e., 40 ms – 100 ms per item[2]). A similar pattern of reaction times is found in young children, although with steeper slopes for both the subitizing range and the enumeration range. .[6] This suggests there is no span of apprehension as such, if this is defined as the number of items which can be immediately apprehended by cognitive processes, since there is an extra cost associated with each additional item enumerated. However, the relative difference in costs associated with enumerating items within the subitizing range are small, whether measured in terms of accuracy, confidence, or speed of response. Furthermore, the values of all measures appear to differ markedly inside and outside the subitizing range.[1] So, while there may be no span of apprehension, there appear to be real differences in the ways in which a small number of elements is processed by the visual system (i.e., approximately < 4 items), compared with larger numbers of elements (i.e., approximately > 4 items). Recent findings [7] demonstrated that subitizing and counting are not restricted to visual perception, but also extend to tactile perception (when observers had to name the number of stimulated fingertips).

Enumerating afterimages[]

File:Subitising 1-10.svg

Numbers 1-10

As the derivation of the term "subitizing" suggests, the feeling associated with making a number judgment within the subitizing range is one of immediately being aware of the displayed elements.[3] When the number of objects presented exceeds the subitizing range, this feeling is lost, and observers commonly report an impression of shifting their viewpoint around the display, until all the elements presented have been counted.[1] The ability of observers to count the number of items within a display can be limited, either by the rapid presentation and subsequent masking of items,[8] or by requiring observers to respond quickly.[1] Both procedures have little, if any, effect on enumeration within the subitizing range. These techniques may restrict the ability of observers to count items by limiting the degree to which observers can shift their "zone of attention"[9] successively to different elements within the display.

Atkinson, Campbell, and Francis[10] demonstrated that visual afterimages could be employed in order to achieve similar results. Using a flashgun to illuminate a line of white disks, they were able to generate intense afterimages in dark-adapted observers. Observers were required to verbally report how many disks had been presented, both at 10 s and at 60 s after the flashgun exposure. Observers reported being able to see all the disks presented for at least 10 s, and being able to perceive at least some of the disks after 60 s. Despite a long period of time to enumerate the number of disks presented when the number of disks presented fell outside the subitizing range (i.e., 5 - 12 disks), observers made consistent enumeration errors in both the 10 s and 60 s conditions. In contrast, no errors occurred within the subitizing range (i.e., 1 – 4 disks), in either the 10 s or 60 s conditions. This result was replicated by Simon and Vaishnavi.[11]

Brain structures involved in subitizing and counting[]

The work on the enumeration of afterimages[10][11] supports the view that different cognitive processes operate for the enumeration of elements inside and outside the subitizing range, and as such raises the possibility that subitizing and counting involve different brain circuits. However, functional imaging research has been interpreted both to support different[12] and shared processes.[13]

Balint's syndrome[]

Clinical evidence supporting the view that subitizing and counting may involve functionally and anatomically distinct brain areas comes from patients with simultanagnosia, one of the key components of Balint's syndrome.[14] Patients with this disorder suffer from an inability to perceive visual scenes properly, being unable to localize objects in space, either by looking at the objects, pointing to them, or by verbally reporting their position.[14] Despite these dramatic symptoms, such patients are able to correctly recognize individual objects.[15] Crucially, people with simultanagnosia are unable to enumerate objects outside the subitizing range, either failing to count certain objects, or alternatively counting the same object several times.[16]

However, people with simultanagnosia have no difficulty enumerating objects within the subitizing range.[17] The disorder is associated with bilateral damage to the parietal lobe, an area of the brain linked with spatial shifts of attention.[12] These neuropsychological results are consistent with the view that the process of counting, but not that of subitizing, requires active shifts of attention. However, recent research has questioned this conclusion by finding that attention also effects subitizing.[18]

Imaging enumeration[]

A further source of research upon the neural processes of subitizing compared to counting comes from positron emission tomography (PET) research upon normal observers. Such research compares the brain activity associated with enumeration processes inside (i.e., 1–4 items) for subitizing, and outside (i.e., 5–8 items) for counting.[12][13]

Such research finds that within the subitizing and counting range activation occurs bilaterally in occipital extrastriate cortex and superior parietal lobe/intraparietal sulcus bilaterally. This has been interpreted as evidence that shared processes are involved.[13] However, the existence of further activations during counting in the right inferior frontal regions, and the anterior cingulate have been interpreted as suggesting the existing of distinct processes during counting related to the activation of regions involved in the shifting of attention.[12]

References[]

  1. ↑ 1.0 1.1 1.2 1.3 1.4 1.5 Kaufman, E. L., Lord, M. W., Reese, T. W., & Volkmann, J (1949). The discrimination of visual number. American Journal of Psychology 62: 498–525.
  2. ↑ 2.0 2.1 Saltzman, I. J., & Garner, W. R (1948). Reaction time as a measure of span of attention. The Journal of Psychology 25: 227–241.
  3. ↑ 3.0 3.1 Jevons, W. S (1871). The power of numerical discrimination. Nature 3: 281–282.
  4. ↑ Taves, E. H. (1941). Two mechanisms for the perception of visual numerousness. Archives of Psychology 37: 1–47.
  5. ↑ Trick, L. M., & Pylyshyn, Z. W (1994). Why are small and large numbers enumerated differently? A limited-capacity preattentive stage in vision. Psychological Review 101 (1): 80–102.
  6. ↑ Chi, M.T.H. & Klahr, D. (1975). Span and rate of apprehension in children and adults. Journal of Experimental Child Psychology 19: 434–439.
  7. ↑ Riggs, K. J, Ferrand, L., Lancelin, D., Fryziel, L., Dumur, G., & Simpson, A. (2006). Subitizing in tactile perception. Psychological Science 17 (4): 271–272.
  8. ↑ Mandler, G., & Shebo, B. J (1982). Subitizing: An analysis of its component processes. Journal of Experimental Psychology: General 111: 1–22.
  9. ↑ LaBerge, D., Carlson, R. L., Williams, J. K., & Bunney, B. G (1997). Shifting attention in visual space: Tests of moving-spotlight models versus an activity-distribution model. Journal of Experimental Psychology: Human Perception and Performance 23: 1380–1392.
  10. ↑ 10.0 10.1 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.
  11. ↑ 11.0 11.1 Simon, T. J., & Vaishnavi, S (1996). Subitizing and counting depend on different attentional mechanisms: Evidence from visual enumeration in afterimages. Perception & Psychophysics 58 (6): 915–926.
  12. ↑ 12.0 12.1 12.2 12.3 Corbetta, M., Shulman, G. L., Miezin, F. M., & Petersen, S. E (1995). Superior parietal cortex activation during spatial attention shifts and visual feature conjunction. Science 270: 802–805.
  13. ↑ 13.0 13.1 13.2 Piazza M, Mechelli A, Butterworth B, Price CJ. (2002). Are subitizing and counting implemented as separate or functionally overlapping processes? Neuroimage. 15(2):435-46. PMID 11798277
  14. ↑ 14.0 14.1 Balint, R (1909). Seelenlahmung des 'Schauens', optische Ataxie, raumliche Storung der Aufmerksamkeit. Monatschrift für Psychiatrie und Neurologie 25: 5–81.
  15. ↑ Robertson, L., Treisman, A., Freidman-Hill, S., & Grabowecky, M. (1997). The interaction of spatial and object pathways: Evidence from Balint's Syndrome. Journal of Cognitive Neuroscience 9 (3): 295–317.
  16. ↑ Dehaene, S (1997). The number sense: How the mind creates mathematics, New York: Oxford University Press.
  17. ↑ Dehaene, S., & Cohen, L (1994). Dissociable mechanisms of subitizing and counting: neuropsychological evidence from simultanagnosic patients. Journal of Experimental Psychology: Human Perception and Performance 20 (5): 958–975.
  18. ↑ Vetter P, Butterworth B, Bahrami B. (2008). Modulating attentional load affects numerosity estimation: evidence against a pre-attentive subitizing mechanism. PLoS ONE. 3(9):e3269. PMID 18813345
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