More than superstition: differential effects of featural heterogeneity and change on subitizing and counting

This study investigates the effects of item heterogeneity (differences in color and shape) and moment-to-moment feature change as it relates to the issue of whether subitizing and counting involve different processes. Participants enumerated displays of up to eight items that were either homogeneous or heterogeneous. In situations where the heterogeneous displays always had approximately half of the items of one type and half of the other, heterogeneity significantly sped enumeration in the counting range (6-8 items) and significantly slowed enumeration in the subitizing range (1-3 items), a dissociation that suggests that subitizing and counting involve different operations. Moment-to-moment feature change had no effect on subitizing. However, feature change slowed counting, but only when participants were enumerating heterogeneous items that were half of one type and half of the other, as might be expected if participants were using differences in features to select items by type.     

Enumerating by pointing to locations: a new method for measuring the numerosity of visual object representations

The fast and accurate enumeration of a small set of objects, called subitizing, is thought to involve a different mechanism from other numerosity judgments, such as those based on estimation. In this report, we examine the subitizing limit using a novel enumeration task that obtained the perceived locations of enumerated objects. Observers were shown brief masked displays (50, 200, and 350 ms) of 2-9 small black discs randomly placed on a gray screen and then asked to place a marker where each disc had been located. The number of these markers provided an estimate of the number of items processed. This "pointing" methodology enabled observers to accurately "enumerate" displays containing up to six items in contrast with the four-item limit typically found when using standard reporting methods (and replicated here in Experiment 2). These results suggest a different account of the limits found in most subitizing and enumeration studies.     

感数——它能告诉我们什么?

研究者在列举任务中发现,被试对3个以内项目的报告既快又准确（一般称之为“感数”）,而对3个以上项目的报告既慢又容易出错误（“计数”）,由此他们提出感数和计数属于两种不同性质的加工过程,一系列行为数据的反应时和正确率指标支持了这一假设。此外,最近的脑成像、电生理研究还发现,感数和计数在对注意的需求上同样存在着分离——感数无需注意,只有计数过程才需注意的参与。在此基础上,研究者从不同角度提出了一些解释感数现象的理论     

Subitizing and similarity: Toward a pattern-matching theory of enumeration

Pattern-matching theories of subitizing claim that subjects enumerate displays with small numerosities by retrieving numerical responses associated with similar displays experienced in the past. Such retrieval implies that displays with small numerosities are similar to other displays of the same numerosity and dissimilar to other displays of different numerosities. These hypotheses were tested by having subjects rate the similarities of displays of dot patterns with numerosities in the range of 1-10. One group of subjects rated patterns of the same numerosity. Their ratings were higher for patterns in the subitizing range (numerosities of 1-3) than for patterns beyond the subitizing range (numerosities of 4-10). Another group rated patterns of different numerosities. Their ratings were lower in the subitizing range than beyond the subitizing range. An analysis based on multidimensional scaling suggested that numerosity could be retrieved accurately for displays of 1-3 dots, but not for displays of 4-10 dots.     

Some primitive mechanisms of spatial attention

Our approach to studying the architecture of mind has been to look for certain extremely simple mechanisms which we have good reason to suspect must exist, and to confirm these empirically. We have been concerned primarily with certain low-level mechanisms in vision which allow the visual system to simultaneously index items at multiple spatial locations, and have developed a provisional model (called the FINST model) of these mechanisms. Among the studies we have carried out to support these ideas are ones showing that subjects can track multiple independent moving targets in a field of identical distractors, and that their ability to track these targets and detect changes occuring on them does not generalize to non-targets or to items lying inside the convex polygon that they form (so that a zoom lens of attention does not fit the data). We have used a visual search paradigm to show that (serial or parallel) search can be confined to a subset of indexed items and the layout of these items is of little importance. We have also carried out a large number of studies on the phenomenon known as subitizing and have shown that subitizing occurs only when items can be preattentively individuated and in those cases location precuing has little effect, compared with when counting occurs, which suggests that subitizing may be carried out by counting active indexes rather than items in the visual field. And finally we have run studies showing that a certain motion effect which is sensitive to attention can occur at multiple precued loci. We believe that taken as a whole the evidence is most parsimoniously accounted for in terms of the hypothesis that there is an early preattentive stage in vision where a small number of salient items in the visual field are indexed and thereby made readily accessible for a variety of visual tasks.     

Small subitizing range in people with Williams syndrome

Recent evidence suggests that the rapid apprehension of small numbers of objects—often called subitizing—engages a system which allows representation of up to 4 objects but is distinct from other aspects of numerical processing. We examined subitizing by studying people with Williams syndrome (WS), a genetic deficit characterized by severe visuospatial impairments, and normally developing children (4–6.5 years old). In Experiment 1, participants first explicitly counted displays of 1 to 8 squares that appeared for 5 s and reported “how many”. They then reported “how many” for the same displays shown for 250 ms, a duration too brief to allow explicit counting, but sufficient for subitizing. All groups were highly accurate up to 8 objects when they explicitly counted. With the brief duration, people with WS showed almost perfect accuracy up to a limit of 3 objects, comparable to 4-year-olds but fewer than either 5- or 6.5-year-old children. In Experiment 2, participants were asked to report “how many” for displays that were presented for an unlimited duration, as rapidly as possible while remaining accurate. Individuals with WS responded as rapidly as 6.5-year-olds, and more rapidly than 4-year-olds. However, their accuracy was as in Experiment 1, comparable to 4-year-olds and lower than older children. These results are consistent with previous findings, indicating that people with WS can simultaneously represent multiple objects, but that they have a smaller capacity than older children, on par with 4-year-olds. This pattern is discussed in the context of normal and abnormal development of visuospatial skills, in particular those linked to the representation of numerosity.     

What dot clusters and bar graphs reveal: subitizing is fast counting and subtraction

In two studies, we found that dot enumeration tasks resulted in shallow-sloped response time (RT) functions for displays of 1-4 dots and steep-sloped functions for displays of 5-8 dots, replicating results implicating subitizing and counting processes for low and high ranges of dots, respectively. Extracting number from a specific type of bar graph within the same numerical range produced a shallow-sloped but scallop-shaped RT function. Factor analysis confirmed two independent subranges for dots, but all bar graph values defined a unitary factor. Significantly, factor scores and asymmetries both showed correlations of bar graph recognition to dot subitizing but not to dot counting, strongly suggesting that subitizing was used in both enumeration of low numbers of dots and bar graph recognition. According to these results, subitizing appears to be a nonverbal process operating flexibly in either additive or subtractive fashion on analog quantities having spatial extent, a conclusion consistent with a fast-counting model of subitizing but not with other models of the subitizing process.     

Evidence for a shared mechanism used in multiple-object tracking and subitizing

It has been proposed that the mechanism that supports the ability to keep track of multiple moving objects also supports subitizing--the ability to quickly and accurately enumerate a small set of objects. To test this hypothesis, we investigated the effects on subitizing when human observers were required to perform a multiple object tracking task and an enumeration task simultaneously. In three experiments, participants (Exp. 1, N = 24; Exp. 2, N = 11; Exp. 3, N = 37) enumerated sets of zero to nine squares that were flashed while they tracked zero, two, or four moving discs. The results indicated that the number of items participants could subitize decreased by one for each item they tracked. No such pattern was seen when the enumeration task was paired with an equally difficult, but nonvisual, working memory task. These results suggest that a shared visual mechanism supports multiple object tracking and subitizing.     

Cross-modal attention modulates tactile subitizing but not tactile numerosity estimation

Debate remains about whether the same attentional mechanism subserves subitizing (with number of items less than or equal to 4) and numerosity estimation (with number of items equal to or larger than 5), and evidence is scarce from the tactile modality. Here, we examined tactile numerosity perception. Using tactile Braille displays, participants completed the following three main tasks: (1) Unisensory task with focused attention: Participants reported the number (1~12) of the tactile pins. (2) Unisensory task with divided attention: Participants compared the numbers of pins across the upper and lower area of their left index fingers, in addition to reporting the number of tactile pins on their right index fingers. (3) Cross-modal task with divided attention: Participants reported the number of tactile pins and compared the numbers of visual dots across the upper and lower part of a (illusory) rectangle that overlaid the tactile stimuli. We found that performance of subitizing rather than estimation was interfered with in dual tasks, regardless of whether distractor events were from the same modality (tactile modality) or from a different modality (visual modality). Moreover, a further test of visual/tactile working memory capacity revealed that the precision of tactile subitizing, in the presence of a visual distractor, was correlated with the capacity of visual working memory, not of tactile working memory. Overall, our study revealed that tactile numerosity perception is accounted for by amodal attentional modulation yet by differential attentional mechanisms in terms of subitizing and estimation.     

Haptic subitizing across the fingers

Numerosity judgments of small sets of items (≤ 3) are generally fast and error free, while response times and error rates increase rapidly for larger numbers of items. We investigated an efficient process used for judging small numbers of items (known as subitizing) in active touch. We hypothesized that this efficient process for numerosity judgment might be related to stimulus properties that allow for efficient (parallel) search. Our results showed that subitizing was not possible for raised lines among flat surfaces, whereas this type of stimulus could be detected in parallel over the fingers. However, subitizing was possible when the number of fingers touching a surface had to be judged while the other fingers were lowered in mid-air. In the latter case, the lack of tactile input is essential, since subitizing was not enabled by differences in proprioceptive information from the fingers. Our results show that subitizing using haptic information from the fingers is possible only when some fingers receive tactile information while other fingers do not.     

Flexible feature-based inhibition in visual search mediates magnified impairments of selection: evidence from carry-over effects under dynamic preview-search conditions

Evidence for inhibitory processes in visual search comes from studies using preview conditions, where responses to new targets are delayed if they carry a featural attribute belonging to the old distractor items that are currently being ignored-the negative carry-over effect (Braithwaite, Humphreys, & Hodsoll, 2003). We examined whether inhibition was applied in the same manner across different types of displays or whether the inhibitory weighting applied to different features varied with their utility for the search task. To test this, we present the first empirical investigation of negative carry-over effects under the ecologically valid conditions of dynamic visual search. Experiment 1 investigated preview search using dynamic moving and static displays. Detection was very poor when new targets carried the color of the old distractors, and this negative carry-over effect was significantly exaggerated with moving, compared with static, displays. Experiments 2a and 2b demonstrated that this effect could not be attributed to an increased role of preattentive grouping between new and old items for dynamic displays. Collectively, the findings suggest that feature-based inhibition contributes strongly to preview search through dynamic displays, and this leads to an amplified attentional blindness to new targets. The data specifically indicate that inhibitory processes in search differentially weight color and location in moving and static displays, and that feature-based inhibition may underlie many instances of sustained inattentional blindness in everyday life.     

Intentional subitizing: exploring the role of automaticity in enumeration

Subitizing is traditionally described as the rapid, preattentive and automatic enumeration of up to four items. Counting, by contrast, describes the enumeration of larger sets of items and requires slower serial shifts of attention. Although recent research has called into question the preattentive nature of subitizing, whether or not numerosities in the subitizing range can be automatically accessed is yet to be empirically tested. In the current study, participants searched for two pre-defined digits in a circular visual-search array. Distractor dots of various set sizes were placed at the centre of the array. Despite the relevance of the distractor numerosities to the target detection task, the distractors did not influence target detection, thereby suggesting that their numerosities were not automatically accessed in Experiment 1. In Experiment 2, participants were explicitly instructed to enumerate the distractor dots. Here, congruent and incongruent distractor numerosities influenced the target detection task, thereby revealing that the distractor dots were capable of generating interference. Experiment 3 ensured that dots were attended by asking participants to detect the luminance of dots. Data confirmed that subitizing was not automatic. The present study also supported the alleged discontinuity between the subitizing and counting ranges because an examination of reaction time gradients in Experiment 2 found the counting gradient to be significantly steeper than the subitizing gradient. In sum, the results suggest that subitizing is a distinct but non-automatic style of enumeration.     

The role of attention in automatization: Does attention operate at encoding, or retrieval, or both?

In this research, we investigated whether attention operates in the encoding of automatized information, the retrieval of automatized information, or in both cases. Subjects searched two-word displays for members of a target category in focused-attention or divided-attention conditions that were crossed with block (training vs. transfer). To see whether subjects encoded all available items or only attended items, we compared performance for subjects in different training conditions but in the same transfer condition. Subjects encoded attended items. To see whether subjects retrieved all the items they had in memory, or only items associated with that to which they were attending at retrieval, we compared performance for subjects in the same training conditions but in different transfer conditions. Subjects retrieved attended items. Attention was found to operate at both encoding and retrieval. These findings support the instance theory of automaticity, which predicts the role of attention at encoding and retrieval     

Is subitizing a unique numerical ability?

Two models that predict the relation between mean enumeration time and numerosity in a speeded enumeration experiment are tested. The first is a bilinear two-process model, and the second is a log-linear single-process model. Previously, support for the bilinear model has provided evidence for the existence of a unique numerical ability called “subitizing.” Both models are shown to yield close approximations to the empirical data, but at the same time to consistently violate the robust shape of these data. Two fundamental discrepancies exist: (1) Enumeration of singleelement displays is unpredictably fast, both in the data reported here and elsewhere, and (2) the response-time function for multiple elements is continuously convex upward, with a significant log-quadratic component. The findings support the contention that enumeration is a capacitylimited process, but no statistically reliable change in processing character, that is, from subitizing to some other process, is evident in enumeration of displays of up to six elements.     

Encoding strategies in self-initiated visual working memory

During a typical day, visual working memory (VWM) is recruited to temporarily maintain visual information. Although individuals often memorize external visual information provided to them, on many other occasions they memorize information they have constructed themselves. The latter aspect of memory, which we term self-initiated WM, is prevalent in everyday behavior but has largely been overlooked in the research literature. In the present study we employed a modified change detection task in which participants constructed the displays they memorized, by selecting three or four abstract shapes or real-world objects and placing them at three or four locations in a circular display of eight locations. Half of the trials included identical targets that participants could select. The results demonstrated consistent strategies across participants. To enhance memory performance, participants reported selecting abstract shapes they could verbalize, but they preferred real-world objects with distinct visual features. Furthermore, participants constructed structured memory displays, most frequently based on the Gestalt organization cue of symmetry, and to a lesser extent on cues of proximity and similarity. When identical items were selected, participants mostly placed them in close proximity, demonstrating the construction of configurations based on the interaction between several Gestalt cues. The present results are consistent with recent findings in VWM, showing that memory for visual displays based on Gestalt organization cues can benefit VWM, suggesting that individuals have access to metacognitive knowledge on the benefit of structure in VWM. More generally, this study demonstrates how individuals interact with the world by actively structuring their surroundings to enhance performance.     

Do subitizing deficits in developmental dyscalculia involve pattern recognition weakness?

The abilities of children diagnosed with developmental dyscalculia (DD) were examined in two types of object enumeration: subitizing, and small estimation (5–9 dots). Subitizing is usually defined as a fast and accurate assessment of a number of small dots (range 1 to 4 dots), and estimation is an imprecise process to assess a large number of items (range 5 dots or more). Based on reaction time (RT) and accuracy analysis, our results indicated a deficit in the subitizing and small estimation range among DD participants in relation to controls. There are indications that subitizing is based on pattern recognition, thus presenting dots in a canonical shape in the estimation range should result in a subitizing‐like pattern. In line with this theory, our control group presented a subitizing‐like pattern in the small estimation range for canonically arranged dots, whereas the DD participants presented a deficit in the estimation of canonically arranged dots. The present finding indicates that pattern recognition difficulties may play a significant role in both subitizing and subitizing deficits among those with DD.     

Role of perceptual organization while attending in depth

Seven experiments were conducted in order to explore the conditions under which visual attention can be allocated in depth. In each experiment, observers were cued to the most likely target location in stereoscopic depth displays, and targets could appear in either the cued location or in another location. In Experiments 1 and 2, we show that previous failures to observe effects of cuing in depth may have depended on the specific timing characteristics of the displays. In Experiments 3, 4, and 5, we eliminated the hypothesis, suggested by Experiments 1 and 2, that in order to allocate attention in depth, attention must be allocated to a specific object token. Experiment 6 provides evidence that, in the absence of other organizing information (e.g., color), attention can be allocated in depth on the basis of the surface information available in the display. Finally, in Experiment 7, we demonstrate that, although sufficient, surface information is not necessary for the allocation of attention; color supported the allocation of attention across multiple items that failed to fall on a single coherent surface in depth. Together, these findings suggest that attention in depth, like attention in two-dimensional displays, is determined by the perceptual organization of the display.     

Consolidation of multifeature items in visual working memory: Central capacity requirements for visual consolidation

In the present study, we examined whether greater attentional resources are required for consolidating two features (e.g., color and orientation) than for consolidating one feature (e.g., color) in visual working memory (WM). We used a dual-task procedure: Subjects performed a WM task and a secondary probe task, sometimes concurrently. In the WM task, subjects decided whether two displays (containing one to four objects composed of one or two features) were the same or different. In the probe task, subjects made a speeded discrimination response to a tone. Performance in both tasks was impaired when they were performed concurrently; however, performance costs in the tone task were not greater for multi- than for single-feature conditions (when the orientation and conjunction conditions were considered). Results suggested that equivalent attentional resources were necessary for consolidation of single-orientation or multifeature items.     

Attentional involvement in subitizing: Questioning the preattentive hypothesis

Subitizing, the rapid, effortless, and accurate enumeration of small numbers of items has been said to be carried out preattentively. If so, the preattentive processing could occur entirely in primary visual cortex, in which case it would be completed within about 50 ms, or during the feedforward sweep, in which case it would be completed within about 100 ms after the onset of an enumeration display which was followed by a mask. The stimulus–mask SOAs were 50 or 83 ms in Experiment 1, and 100 or 150 ms in Experiment 2. In both experiments subjects were more accurate and more sensitive to one-target than to two-target displays. These outcomes, in conjunction with the finding that accuracy and sensitivity were higher at the longer SOA, are inconsistent with the preattentive viewpoint and point to the necessity for attentional involvement in subitizing.