Intentional subitizing: Exploring the role of automaticity in enumeration
Highlights
► We empirically investigate the role of automaticity in enumeration. ► We show that, contrary to current theories, subitizing is not an automatic process. ► Access to numerical information requires an explicit intention to enumerate.
Introduction
The enumeration of visual stimuli appears to be underpinned by two distinct psychological processes. Although lay understandings of numerical cognition suggest that children are explicitly taught to “count” three images on a page, psychological research dictates that counting is a process reserved for the enumeration of more than four objects. By contrast, enumeration of four or fewer objects is referred to as subitizing (Chi and Klahr, 1975, Kaufman et al., 1949, Mandler and Shebo, 1982). The distinction between subitizing and counting has been motivated by the finding that people almost instantly access the numerosity of displays containing four or fewer items, implying that the numerosity is automatically available without the need for a serial individuation of each item (Trick and Pylyshyn, 1993, Trick and Pylyshyn, 1994). Reaction times (RTs) are typically flat or reveal a shallow gradient as the number of display items increase across the subitizing range (Akin and Chase, 1978, Chi and Klahr, 1975, Jensen et al., 1950, Mandler and Shebo, 1982, Piazza et al., 2002, Sathian et al., 1999, Trick and Pylyshyn, 1994). When displays contain more than four items, enumeration is not automatic and participants must index each item individually in a step-by-step manner. RT gradients are consequently much steeper in the counting range, creating a discontinuity between the subitizing and counting ranges (Jensen et al., 1950, Mandler and Shebo, 1982, Saltzman and Garner, 1948). Interestingly, subitizing is not limited to the enumeration of visual objects by adults, but exists in auditory and tactile domains (Camos and Tillman, 2008, Plaisier et al., 2009, Riggs et al., 2006), and occurs in pre-verbal infants and animals (Davis and Perusse, 1988, Spelke, 2000, Starkey and Cooper, 1980). Some researchers argue that counting and subitizing are phenomenologically distinct processes because subitizing reflects a preattentive, automatic process that proceeds via parallel processing whereas counting is a more attentionally demanding, conscious mechanism that implicates serial processing (Trick and Pylyshyn, 1993, Trick and Pylyshyn, 1994). The current study focused on investigating the role of automaticity in subitizing.
One of the most popular explanations of enumeration – the fingers of instantiation (FINST) hypothesis – presumes that subitizing occurs, at least in part, via automatic, preattentive mechanisms (Trick and Pylyshyn, 1993, Trick and Pylyshyn, 1994). FINST is rooted in the notion that the visual system is capable of indexing up to four objects before capacity limitations ensue. According to this hypothesis, four FINSTs can be ‘attached’ to four objects, individuating the objects across space. This process is both goal driven and data driven: it is automatically driven by stimuli in the visual field, but is also influenced by the individual’s intentions and goals. In other words, aspects of subitizing (for example, the parallel attentive and token indexing stages) are automatic, yet enumeration itself is a deliberate process – people do not automatically enumerate everything that they perceive (Trick & Pylyshyn, 1994). The FINST hypothesis suggests that enumeration of small numbers is rapid because objects are tagged in parallel and the participant simply has to report the number of FINSTs that are bound at that time. Enumeration of more than four items necessitates slower shifts of spatial attention because FINSTs must be serially connected, disconnected, and re-connected until all objects have been tagged and counted. The current study was interested in exploring the nature of automatic processing within subitizing.
Although the role of automaticity in subtizing has not been previously explored, recent research has challenged the notion of subitizing as a preattentive process (Burr et al., 2010, Egeth et al., 2008, Olivers and Watson, 2008, Poises et al., 2008, Railo et al., 2008, Vetter et al., 2008, Xu and Liu, 2008). These studies have revealed that attentional demands increase with increasing numbers of to-be-enumerated stimuli, even in the subitizing range. For example, a few experiments have incorporated a subitizing task into the attention blink paradigm in order to explore the relationship between subitizing and attention (Egeth et al., 2008, Olivers and Watson, 2008, Xu and Liu, 2008). The attentional blink describes a deficit in detecting the second of two targets when the second target appears within 500 ms of the first target (Raymond, Shapiro, & Arnell, 1992). Accuracy is poor for this second target because attentional resources are unavailable (Chun and Potter, 1995, Shapiro et al., 1994). If subitizing proceeds preattentively then enumeration should be accurate even when a subitizing task is inserted into the attentional blink paradigm during periods of reduced attentional capacity. However, the empirical evidence counters this logical suggestion. Specifically, the enumeration of small numerosities was found to be significantly delayed or suffered reduced accuracy inside the attentional blink period, hence implicating attention as a critical requirement for subitizing (Egeth et al., 2008, Olivers and Watson, 2008, Xu and Liu, 2008). Given the challenges to the preattentive nature of subitizing, and considering the connection between attention and automaticity, we suggest that the assumption of automaticity within subitizing may also be problematic.
Automaticity evades a precise theoretical definition. Numerous descriptions of automatic processing have been suggested, including processing that occurs without conscious control, intention or awareness (Logan, 1988, Schneider and Shiffrin, 1977, Shiffrin and Schneider, 1977). In addition, formal definitions of automaticity have been provided by a number of authors (Gibson, 1969, LaBerge, 1973, Logan, 1992, Treisman et al., 1992). Automaticity can be contrasted with processing that is conscious, effortful, intended and controlled. Automatic processing is frequently equated with preattentive processing, and empirical evidence for interactions between the two mechanisms suggest that they are related mechanisms at minimum, and ‘different sides of the same coin’ at maximum (Logan, Taylor, & Etherton, 1999). Further, Bargh and Chartrand (1999) suggest that preattentive processing is one of the ‘major strains’ of automaticity. However, while preattentive and automatic processes are related (primarily because they can both occur in the absence of attention), the processes are not identical. For example, the way in which automatic and preattentive processes become independent of attention differs (Treisman et al., 1992). The recent challenge to subitizing as a preattentive process, and the link between preattentive processing and automaticity, suggests that it is prudent to explicitly examine the status of subitizing as an automatic process. Given the similarities between preattention and automaticity, it may be the case that subitizing is not automatic because it is not preattentive. Conversely, the dissociability between these processes means that aspects of subitizing may proceed automatically, but not preattentively.
It is important to note that the current study does not seek to explore whether enumeration proceeds automatically – irrespective of context. It would be unwise to assume that people constantly and persistently enumerate every visual object that they encounter. Similarly, the FINST hypothesis does not suggest that subitizing (or enumeration more generally) is absolutely automatic. While FINST argues that up to four items can be indexed automatically, the mapping of numerosity to number names is not presumed to be automatic but requires a controlled, conscious intention. The current study therefore asked whether the numerical value of a group of dots would be automatically accessed when participants performed a number detection task but were not asked to name the number of dots. In other words, we asked whether numerical value would be accessed when the contextual conditions were highly conducive to such numerical access.
This study required participants to search a circular visual search array and detect whether the Arabic digit “3” or “7” was present. In this manner, “3” and “7” served as targets. The task was designed so as to include one target from the subitizing range and one from the counting range. Distractor stimuli were presented in the centre of the search array and consisted of either two, three, six or seven dots. Distractors were located at fixation in order to ensure that they were positioned within participants’ visual fields. If subitizing proceeds automatically, presentation of the three-dot distractor should influence responding by speeding RTs on congruent target-3 trials and slowing RTs on target-7 trials (Henik and Tzelgov, 1982, Rubinsten et al., 2002, Soltesz et al., 2010, Soltesz et al., 2011, Szűcs et al., 2007). According to our assumptions, enumeration of numerosities in the counting range should not proceed automatically. Therefore, we did not expect to see interference from seven-dot distractors. The neutral two-dot and six-dot distractors were employed in order to prevent participants from anticipating the three or seven dot distractors (the two-dot and six-dot distractors were neutral because ‘2’ and ‘6’ were not target stimuli). Two and six dots were also chosen because they are each very close to the target digits, and fall within the subitizing and counting ranges respectively. Inclusion of the neutral distractors saw that we were able to calculate a gradient for the subitizing range distractors (the gradient between two-dot and three-dot distractor trials) and for the counting range distractors (the gradient between six-dot and seven-dot distractor trials).
We also manipulated attentional load in this study (see Vetter et al., 2008). On high load trials, the target digit was presented amongst numerous different visual-search stimuli whereas the target appeared amongst a single repeated stimulus on low load trials. The perceptual load theory predicts that interference should only occur on low load trials, where attentional resources are available, and not on high load trials where attentional resources are taxed (Lavie, 1995, Lavie and Tsal, 1994). However, if subitizing is preattentive then interference should occur across both high and low loads. Because recent research suggests that subitizing is not preattentive but requires attentional resources, we predicted that interference would be restricted to low load trials, where attentional resources are available to process the distractor dots. In sum, the current experimental design allowed us to investigate three main issues: whether subitizing proceeds automatically, whether subitizing is preattentive, and whether the subitizing and counting gradients are statistically distinct.
Section snippets
Experiment 1
Experiment 1 was primarily designed to investigate whether the numerosity of dots in the subitizing range can be automatically accessed, and cause interference on a numerical target detection task. If activation of the numerosity is automatic, it should interfere with target detection due to congruent and incongruent relationships between the target and distractor numerosities. As discussed in Section 1, this experiment did not ask about the automaticity of enumeration in general (under any
Experiment 2
Experiment 2 reacted to the finding that the distractor dots did not interfere with the target detection task in Experiment 1. We therefore questioned whether distractor dots are ever able to influence RTs in this paradigm. To that end, this experiment was identical to Experiment 1 with one exception; participants were requested to verbally enumerate the distractor dots after they responded to the target detection task. If the distractor dots successfully generate interference in this task, the
Experiment 3
Experiments 1 and 2 collectively suggest that participants accessed the distractor dots’ numerical values only when there was an explicit intention for enumeration. However, it is important to rule out alternative interpretations of these findings. For example, although we argue that attention was directed towards the distractor dots in Experiment 1 (given their location at fixation – see Section 1), we cannot guarantee that the distractors were attended in that experiment. It is therefore
General discussion
The current study examined the role of automaticity in subitizing by presenting distractor dots within a numerical target detection task. The results suggested that accessing numerical information in the subitizing range is not automatic because the numerosity of the distractor dots was only accessed when participants were explicitly asked to enumerate those stimuli. Our study also contributed to the ongoing controversy concerning whether or not subitizing and counting are distinct phenomena.
Acknowledgements
This research was funded by a Grant to DS from the Medical Research Council (G0900643), and a Gates Cambridge studentship to HP. The authors would like to thank Alison Nobes for her assistance in collecting data for these experiments.
References (57)
- et al.
Discontinuity in the enumeration of sequentially presented auditory and visual stimuli
Cognition
(2008) - et al.
Span and rate of apprehension in children and adults
Journal of Experimental Psychology
(1975) Central capacity limits in consistent mapping, visual search tasks: Four channels or more?
Cognitive Psychology
(1984)- et al.
Counting in everyday life: Discrimination and enumeration
Neuropsychologia
(2006) - et al.
Are subitizing and counting implemented as separate or functionally overlapping processes?
NeuroImage
(2002) - et al.
One, two, three, many – Subitizing in active touch
Acta Psychologica
(2009) - et al.
The role of attention in subitizing
Cognition
(2008) - et al.
The development of internal representations of magnitude and their association with Arabic numerals
Journal of Experimental Child Psychology
(2002) - et al.
Can subitizing survive the attentional blink? An ERP study
Neuroscience Letters
(2008) - et al.
Quantification of three-dimensional structures
Journal of Experimental Psychology: Human Perception and Performance
(1978)
Is subitizing a unique numerical ability?
Perception and Psychophysics
Subitizing: Magical numbers of mere superstition?
Psychological Research
The unbearable automaticity of being
American Psychologist
Look here but ignore what you see: Effects of distractors at fixation
Journal of Experimental Psychology: Human Perception and Performance
Subitizing but not estimation of numerosity requires attentional resources
Journal of Vision
A two-stage model for multiple target detection in rapid serial visual presentation
Journal of Experimental Psychology: Human Perception and Performance
Numerical competence in animals: Definitional issues, current evidence, and a new research agenda
Behavioural and Brain Scieneces
Dissociable mechanisms of subitizing and counting: Neuropsychologial evidence from simultagnosic patients
Journal of Experimental Psychology: Human Perception and Performance
Neuropsychological evidence for a dissociation in counting and subitizing
Neurocase
The role of attention in subitizing: Is the magical number 1?
Visual Cognition
Involuntary covert orienting is contingent on attentional control settings
Journal of Experimental Psychology: Human Perception and Performance
Failures to ignore entirely irrelevant distractors: The role of load
Journal of Experimental Psychology: Applied
Principles of perceptual learning and development
Enumerating by poitning to locations: a new method for measuring the numerosity of visual object representations
Attention Perception and Psychophysics
Is three greater than five: The relation between physical and semantic size in comparison tasks
Memory and Cognition
The subitizing and coutning of visually presented fields of dots
Journal of Psychology
The discrimination of visual number
American Journal of Psychology
Attention and the measurement of perceptual learning
Memory and Cognition
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