Subitizing is attention demanding:
A hemineglect case study
Valérie Camos1, Eric Sieroff2, Aude Mariller3, & Maryline Couette2
1
2
Université de Bourgogne
Université René Descartes – Paris V
3
Hôpital National de Saint-Maurice
Running Head : Subitizing in a hemineglect case
WORDS = 3617
Corresponding author :
Valérie Camos
Université de Bourgogne
LEAD-CNRS
Pôle AAFE – Esplanade Erasme
B.P. 26513
21065 Dijon Cedex
France
Email: valérie.camos@u-bourgogne.fr
Subitizing is attention demanding:
A hemineglect case study
Abstract :
In the literature, a debate persists concerning the exact nature of subitizing. The different
models proposed to account for subitizing mainly differ in terms of whether or not attention is
thought to be necessary for the processing of the objects to be enumerated. The present paper
reports the performance of a left hemineglect patient who is unable to subitize dots in the
contralesional left hemifield whereas the subitizing ability in the ipsilesional hemifield is
preserved. Moreover, the addition of a distracter in the ipsilesional hemifield (i.e. extinction
condition) impairs his subitizing performance in the neglected hemifield, whereas no change
occurs in the preserved hemifield. These results support models, which assert that subitizing
requires attention.
Keywords:
Subitizing, Attention, Hemineglect
1
1. Introduction
Object enumeration is one of the first numerical skills thought to emerge from infants'
protonumeric capacities. This skill has been extensively studied ever since the end of the
nineteenth century, and a distinction has been made between two processes involved in
enumeration (Jevons, 1871; Wundt, 1896). Indeed, during object enumeration, response times
(RTs) do not increase linearly with the number of objects. Instead, the RTs remain relatively flat
up to three or four objects whereas they increase linearly beyond this number. Similarly, when
objects are presented only briefly, the error rate is extremely low for arrays up to three or four,
and then increases linearly. It has thus been argued that subitizing is responsible for the former
aspect of performance and counting for the latter (Chi and Klahr, 1975; Dehaene and Cohen,
1994; Kaufman, et al., 1949; Mandler and Shebo, 1982).
Although subitizing is well documented, a debate persists concerning its exact nature. The
various models proposed to account for subitizing differ in terms of the involvement of attention.
On the one hand, some models, such as Trick and Pylyshyn’s (1993; 1994) FINSTs theory and
Dehaene and Changeux’s (1993) accumulator model, assume that subitizing is primarily based on
a preattentive process. According to the FINSTs theory, a limited number of fingers of
instantiation (tags) are attributed to objects in a preattentive stage of the visual analysis of the
display. The number of tags used gives the number of objects. For Dehaene and Changeux
(1993), subitizing is based on a parallel estimation process which produces a sufficiently precise
response for small numerosities. On the other hand, several models predict that attention has to be
allocated in order to subitize objects. For example, Gallistel and Gelman (1991, 1992) suppose
that subitizing is simply a fast nonverbal counting. Mandler and Shebo (1982), and Peterson and
Simon (2000), assume that the number of presented objects is identified by means of pattern
recognition. Although these authors account for subitizing in terms of different mechanisms, both
2
counting and recognition are attentional processes. This controversy is further exacerbated by the
inconsistent results from brain imagery studies (Piazza et al., 2001, 2003; Sathian et al., 1999).
The aim of the present study was to distinguish between these two classes of model. To
this end, we tested the subitizing ability of a left hemineglect patient. Hemineglect syndrome is
characterized by impairment in orienting attention and is frequently observed following a lesion
in the right parietal lobe (Bartolomeo and Chokron, 2001; Mesulam, 1985). Patients experience
difficulties in responding to stimuli occurring in the contralesional hemifield, and this difficulty is
increased when a stimulus is simultaneously presented in the ipsilesional hemifield (extinction
phenomenon: Bisiach, 1991; Driver and Vuilleumier, 2001).
The rationale of the present study was to compare the enumeration performance obtained
in each hemifield by a left hemineglect patient. First, if counting and subitizing are based on two
distinct processes, whatever the attentional nature of these processes, then we would expect the
classic curve to be observed in each hemifield Second, because counting is attentionally
demanding even in adults (Camos and Barrouillet, in press), the patient's counting performance
should be worse for the contralesional hemifield than for the ipsilesional hemifield. Third, if
subitizing requires attention, the patient's performance should differ for the two hemifields, with
lower performance for the left and a preserved ability for the right hemifield. This attentional
hypothesis would be strengthened if subitizing performance is strongly affected by the presence
of a distracter in the right hemifield (extinction). On the contrary, if subitizing is based on a
preattentive process, the patient's subitizing ability should be preserved in both hemifields, and
should not be affected by the extinction phenomenon.
2. Method
2.1. Patient
3
GD is a right-handed 63 year-old man with a left hemineglect resulting from a right
fronto-parietal ischemic lesion. He also suffers from a left hemiparesis. The diagnosis of
unilateral neglect was made a few weeks after the ictus, using the GEREN test (2002). We tested
him 8 months later. Although we were not allowed to report detailed results from the clinical
examination, they indicated that GD still suffered from a left hemineglect at the time of the study.
2.2 Material and procedure
Before the experiment itself, the patient underwent a sight test that we designed ourselves.
In both the sight test and the experiment, the stimuli were presented on an Apple Powerbook G3
computer using Psyscope software (Cohen et al., 1993).
In the sight test, the stimuli were black dots of 1 cm diameter presented on a white screen.
The dots were presented one at a time in two invisible 10 x 10 cm squares the closest side of
which was situated 2 cm to the left or right of a fixation item. In consequence, the dots appeared
at an angle of 2° to 12° for the patient, who was seated 60 cm from the screen. Within each
square, the dots could appear in one of eleven different positions (Figure 1). Each position was
tested 10 times. Thus, 220 trials (2 squares x 11 positions x 10 times) were randomly presented to
the patient. Each trial began with a 1000 ms warning signal in the center of the screen (fixation
item). Next, a single dot was displayed for 200 ms in each trial. The patient was asked to say
whether or not he saw the dot. When ready, the patient clicked on the mouse. Four practice trials
were presented prior to the test.
The experiment was similar to the sight test: each trial began with a 1000 ms warning
signal in the center of the screen, followed by an array of one to six dots presented for 200 ms.
Black dots of 1 cm diameter appeared in one of the two squares. Ten different arrays were built
for each size. The positions of the dots within the arrays were randomly chosen using a matrix.
Half of the arrays were presented in the right hemifield, and the other half in the left hemifield.
4
Thus, the patient saw 120 trials (6 sizes x 10 arrays x 2 sides) in this unilateral condition. The 120
trials used in the extinction condition were identical, except that the contralateral square was
made apparent by coloring it in gray (distracter). The presence of such a distracter should induce
the extinction phenomenon. Indeed, it has recently been shown that when patients cannot predict
the hemifield in which the stimuli will occur, as in the present study, the simple presence of a
distracter is sufficient to elicit extinction (Sieroff and Urbanski, 2002).
The experimental trials were presented in two sessions separated by a 2-hour break: the
unilateral block preceded the extinction block in session 1, and the block order was reversed in
session 2. The order of presentation of each trial was randomized. The patient’s task was to say
aloud the number of dots, with a voice key stopping the timer. The patient clicked on the mouse
to trigger the next trial. Twelve practice trials (3 trials x 2 sides x 2 conditions) were presented
before each session.
3. Results
The sight test showed that GD had a left inferior quadranopsia (Figure 1). Such a visual
deficit can have an obvious impact on enumeration processes. As a consequence, before
analyzing GD’s counting and subitizing performance, we determined the number of dots that GD
could see in each trial (at over 70% visibility). This procedure resulted in a change in the overall
number of trials analyzed for each size in the left hemifield. Fifteen trials with one dot (Size 1) in
the non-damaged part of the left hemifield occurred in each condition. Similarly, Size 2 occurred
18 times, Size 3 11 times, Size 4 8 times, Size 5 2 times, and Size 6 never occurred. Because Size
6 only occurred in the right hemifield, this size was discarded from the analyses.
We analyzed the number of incorrect responses including the no-responses, and the
response times when GD did give an answer. In some trials (29 out of 208), GD did not respond.
5
An absence of response was found more frequently with left (7 and 21) than with right (1 and 0)
hemifield stimuli, 2 (1) = 4.39, p < .05 and 2 (1) = 24.36, p < .0005 in unilateral and extinction
conditions respectively. Moreover, because GD produced a large number of errors, it was not
possible to perform response time analyses for correct responses.
The results showed a significant difference in errors between the two hemifields with a
higher error rate in the left hemifield (57 and 72%) than in the right hemifield (18 and 16%), 2
(1) = 17.03, p < .005 and 2 (1) = 33.13, p < .005, but no difference in response times, t (94) =
1.67, p = .10 and t < 1 in the unilateral and extinction conditions respectively (Figure 2). Before
testing our specific hypotheses, we analyzed GD’s performance in the preserved field to ensure
that he was able to subitize. In the right hemifield, GD presented the classic pattern of results in
the unilateral condition. To determine GD’s subitizing range, we used successive planned
comparisons contrasting 1 to n vs. n+1 to 5, in which the subitizing range was n at the point
where the comparison became significant (Chi and Klahr, 1975). This analysis showed that 3 was
the limit of his subitizing range, because the comparison 1 to 3 vs. 4 was the first to be significant
both in terms of errors, F (1, 9) = 6.00, p = .037, and in terms of response times, F (1, 8) = 36.90,
p < .001. It should be noted that his subitizing slope (14 msec) differed greatly from his counting
slope (368 msec) as is usually found in enumeration studies. Furthermore, GD made no errors on
the numerosities 1 to 3 whereas the error rate increased beyond this range (45%), 2 (1) = 16.46,
p < .005. Similarly, the response times were lower for these small numerosities (584 msec) and
increased for the larger ones (1345 msec), t (47) = 8.49, p < .0001. These latter results confirmed
the fact that GD possessed a preserved subitizing ability on the right side.
The analyses presented below tested our 4 predictions. First, although the error rate in
subitizing (Sizes 1 to 3) and in counting (Sizes 4 and 5) did not differ in the left hemifield for
6
either condition (ps >.10), the response times were longer in counting (1443 and 1250 msec) than
in subitizing (1027 and 897 msec), t (45) = 1.79, p = .090 and t (31) = 2.34, p = .036 in unilateral
and extinction conditions respectively. Second, concerning GD’s counting performance (i.e. for
Sizes 4 and 5), the error rate was greater in the left than in the right hemifield both in the
unilateral (80% vs 45%), 2 (1) = 3.33, p < .10, and in the extinction condition (80% vs 40%), 2
(1) = 4.29, p < .005, although the times did not differ (ps > .16). These results showed that his
performance in an attentionally demanding activity such as counting were worse when the objects
were presented in the neglect field. Third, as predicted by the hypothesis that subitizing is
attentionally demanding, GD’s error rate in the subitizing range (from 1 to 3) was significantly
greater in the left (52 and 71%) than in the right hemifield (0 and 0%), 2 (1) = 22.75, p < .0001
and 2 (1) = 36.37, p < .0001 in unilateral and extinction conditions respectively. A similar effect
was observed for response times (left: 1027 and 897 msec vs right: 584 and 563 msec), t (66) =
3.11, p = .004 and t (54) = 3.31, p = .002 in unilateral and extinction conditions respectively.
Finally, the hypothesis that subitizing requires the allocation of attention was strengthened by the
observed effect of the conditions in the left hemifield. Indeed, in this hemifield, GD made more
errors in subitizing when a distracter was presented in the ipsilesional hemifield (71%) than when
it was not (52%), 2 (1) = 3.07, p < .10, without this causing any difference in RTs, p = .43. It
should also be noted that the extinction condition provoked significantly more no-responses for
left hemifield stimuli than the unilateral condition (41% vs14%), 2 (1) = 8.25, p < .005, whereas
no significant change occurred in the error rate (0% for both conditions), response times (p =.72)
or the number of no-responses (0 and 1) for right hemifield stimuli.
4. Discussion
7
This study investigated the subitizing ability of a hemineglect patient. GD exhibited
typical performance in enumerating objects when these were presented in the ipsilesional
hemifield. His counting and subitizing slope were very similar to what is classically observed in
adults who do not suffer from brain damage (Mandler and Shebo, 1982; Sliwinski, 1997; Trick
and Pylyshyn, 1993; Tuholski et al., 2001). Although GD made more errors in counting than
would normally be expected for an adult of this age (Sliwinski, 1997; Trick et al., 1996), his
overall performance in the right hemifield reflected the distinction between the two processes,
counting and subitizing. Similarly, in the left hemifield, this distinction was still apparent, with
counting taking longer than subitizing, although the number of errors was equivalent. These
results reinforce models, which account for the discontinuities in enumeration performance in
terms of the implementation of two distinct processes (Anderson, 1993; Dehaene and Cohen,
1994; Dehaene and Changeux, 1993; Mandler and Shebo, 1982; Peterson and Simon, 2000; Trick
and Pylyshyn, 1994).
As expected in a deficit in the orienting of attention like hemineglect, GD’s counting was
worse in the contralesional hemifield than in the ipsilesional hemifield. In line with the
hypothesis that the subitizing process is attention demanding, GD’s subitizing performance was
poorer in the neglected than in the preserved hemifield. The direct comparison of the two
hemifields in the same individual allows us to discard any interpretation in terms of a deficit in
the retrieval of the number-words, given GD’s total success in subitizing objects in the
ipsilesional hemifield. Nevertheless, it could be argued that the decrease in subitizing
performance observed in the contralesional field is due to a visual deficit that hampers the
preattentive analysis of the displays which, according to the FINSTs theory, is the major
mechanism in subitizing. However, two arguments weaken this interpretation. First, the sight test
ensured that the dots were presented in locations where they can be detected. Second, GD's
8
performance was similar to that of hemineglect patients with an intact visual field who were
observed by Vuilleumier and Rafal (1999; 2000). Indeed, these patients exhibited a higher error
rate in the left than in the right hemifield for subitizing 1 (6-22% vs. 0-3%) and 2 (28-38% vs. 03%) objects. GD exhibited an even higher error rate in the left hemifield (1: 33% and 2: 67%),
most probably because the dots appeared in different positions on each trial in the present study,
whereas they always appeared in the same position in Vuilleumier and Rafal’s study (1999;
2000). Thus, an interpretation in terms of a lack of attention seems to provide a more convincing
account of the fall-off in subitizing performance in GD’s contralesional hemifield.
Another argument in favor of this interpretation comes from the comparison between the
extinction and the unilateral conditions. The presence of a distracter in the ipsilesional hemifield
decreased subitizing performance in the contralesional hemifield. In the literature on hemineglect,
this kind of effect is considered to be an overwhelming argument testifying to the involvement of
attention (Bisiach, 1991; Vuilleumier and Rafal, 2000). Thus, although we could not determine
the exact nature of the process (i.e., it could be based on a pattern recognition or another
mechanism), the present study provides some evidence that the mechanism underlying subitizing
requires the allocation of attention.
References
ANDERSON JR. Rules of the mind. Hillsdale : Erlbaum, 1993.
BARTOLOMEO P and CHOKRON S. Levels of impairment in unilateral neglect. In Boller F
and Grafman J (Eds) Handbook of neuropsychology, Vol. 4 . Amsterdam: Elsevier Science
Publishers, 2001, pp. 67-98.
9
BISIACH E. Extinction and neglect: same or different? In Paillard J (Ed) Brain and space.
Oxford: Oxford University Press, 1991, pp. 251-257.
CAMOS V and BARROUILLET P. Adults counting is resource demanding. British Journal of
Psychology., in press.
CHI MTH and KLAHR D. Span and rate of apprehension in children and adults. Journal of
Experimental Child Psychology, 19: 434-439, 1975.
COHEN JD, MACWHINNEY B, FLATT M, and PROVOST J. Psyscope: A new graphic
interactive environment for designing psychology experiments. Behavior Research
Methods, Instruments, & Computers, 25: 257-271, 1993.
DEHAENE S and COHEN L. Dissociable mechanisms of subitizing and counting:
Neuropsychological evidence from simultanagnosic patients. Journal of Experimental
Psychology: Human Perception and Performance, 20: 958-975, 1994.
DEHAENE S and CHANGEUX JP. Development of elementary numerical abilities: A neuronal
model. Journal of Cognitive Neuroscience, 5: 390-407, 1993.
DRIVER J and VUILLEUMIER P. Perceptual awareness and its loss in unilateral neglect and
extinction. Cognition, 79: 39-88, 2000.
GALLISTEL CR and GELMAN R. Subitizing: The preverbal counting process. In Kessen W,
Ortony A and Craik F (Eds) Memories, thoughts, and emotions: Essays in honor of
George Mandler. Hillsdale: Erlbaum, 1991, pp. 65-81.
GALLISTEL CR and GELMAN R. Preverbal and verbal counting and computation. Cognition,
44: 43-74, 1992.
GEREN / French collaborative study group on assessment of unilateral neglect. Sensitivity of
clinical and behavioural tests of spatial neglect after right hemisphere stroke. Journal of
Neurology, Neurosurgery, and Psychiatry, 73: 160-166, 2002.
10
JEVONS WS. The power of numerical discrimination. Nature, 3: 281-282, 1871.
KAUFMAN EL, LORD MW, REESE TW, and VOLKMANN J. The discrimination of visual
number. American Journal of Psychology, 62: 498-525, 1949.
MANDLER G and SHEBO BJ. Subitizing: An analysis of its component processes. Journal of
Experimental Psychology: General, 111: 1-22, 1982.
MESULAM MM. Attention, confusional states and neglect. In Mesulam MM (Ed) Principles of
behavioral neurology. Philadelphia: Davis, 1985, pp. 125-168.
PIAZZA M, GIACOMINI E, LE BIHAN D, and DEHAENE S. Single-trial classification of
parallel preattentive and serial attentive processes using fMRI, submitted, Proceeding of the
Royal Society Biological Sciences, 270: 1237-1245, 2003.
PIAZZA M, MECHELLI A, BUTTERWORTH B, and PRICE CJ. Are subitizing and counting
implemented as separate or functionally overlapping processes? NeuroImage, 15: 435-446,
2001.
PETERSON SA and SIMON TJ. Computational evidence for the subitizing phenomenon as an
emergent property of the human cognitive architecture. Cognitive Science, 24: 93-122,
2000.
SATHIAN K, SIMON TJ, PETERSON S, PATEL GA, HOFFMAN JM, and GRAFTON ST.
Neural evidence linking visual object enumeration and attention. Journal of Cognitive
Neuroscience, 11: 36-51, 1999.
SIEROFF E and URBANSKI M. Conditions of visual verbal extinction: Does the ipsilesional
stimulus have to be identified? Brain and Cognition, 48: 563-569, 2002.
SLIWINSKI M. Aging and counting speed: Evidence for process-specific slowing, Psychology
and Aging, 12: 38-49, 1997.
11
TRICK LM, ENNS JT, and BRODEUR DA. Life span changes in visual enumeration: The
number discrimination task. Developmental Psychology, 32: 925-932, 1996.
TRICK LM and PYLYSHYN ZW. What enumeration studies can show us about spatial
attention: Evidence for limited capacity preattentive processing. Journal of Experimental
Psychology: Human Perception and Performance, 19: 331-351, 1993.
TRICK LM and PYLYSHYN ZW. Why are small and large numbers enumerated differently? A
limited capacity preattentive stage in vision. Psychological Review, 101: 80-102, 1994.
TUHOLSKI SW, ENGLE RW, and BAYLIS GC. Individual differences in working memory
capacity and enumeration. Memory and Cognition, 29: 484-492, 2001.
VUILLEUMIER PO and RAFAL RD. “Both” means more than ‘two”: localizing and counting in
patients with visuospatial neglect. Nature Neuroscience, 2: 783-784, 1999.
VUILLEUMIER PO and RAFAL RD. A systematic study of visual extinction: Between- and
within-filed deficits of attention in hemispace neglect. Brain, 123: 163-1279, 2000.
WUNDT W. Grundriss der psychologie. Leipzig: Engelmann, 1896.
12
Acknowledgments
We would like to thank GD for his kind participation, as well as Professors Bussel and Azouvi,
Mrs Agard, and the Service de Rééducation Neurologique at Hôpital Raymond-Poincaré for their
help. Finally, we are grateful to Patrik Vuilleumier for providing us the results of his patients.
Figure Captions
Figure 1
The 11 different positions used in each square to test the vision and the associate percentage of
correct detection by G.D. when dots were presented in the left side. The line delimited the
visually damaged part in the left side.
Figure 2
Mean percentages of errors (bars) and mean response times in ms (lines) as a function of the side,
the size of the arrays, and the conditions.
13
Figure 1
90
80
90
90
10
0
80
50
70
10
90
14
Figure 2
100
2100
unilateral
extin ctio n
unilateral
extin ctio n
90
1800
80
Percenta ge of errors
60
1200
50
900
40
30
Response times
1500
70
600
20
300
10
0
0
1
2
3
left
4
5
1
2
3
4
5
right
15