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.     

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.     

Orientation perception in Williams Syndrome: Discrimination and integration

Williams Syndrome (WS) is a rare neurodevelopmental disorder, which stems from a genetic deletion on chromosome 7 and causes a profound weakness in visuospatial cognition. Our current study explores how orientation perception may contribute to the visuospatial deficits in WS. In Experiment 1, we found that WS individuals and normal 3–4 year olds had similar orientation discrimination thresholds and had similar prevalence of mirror-reversal errors for diagonal targets (±45 deg). In Experiment 2, we asked whether this immaturity in orientation discrimination would also be reflected in a task requiring integration of oriented elements. We found that sensitivities of WS individuals for detecting orientation-defined contours were higher than sensitivities of normal 3–4 year olds, and were not significantly different from sensitivities of normal adults. Together, these results suggest that orientation discrimination and orientation integration have different maturational trajectories in normal development and different susceptibilities to damage in WS. These may reflect largely separate visuospatial mechanisms.     

Artifacts and natural kinds: children's judgments about whether objects are owned

People's behavior in relation to objects depends on whether they are owned. But how do people judge whether objects are owned? We propose that people expect human-made objects (artifacts) to be more likely to be owned than naturally occurring objects (natural kinds), and we examine the development of these expectations in young children. Experiment 1 found that when shown pictures of familiar kinds of objects, 3-year-olds expected artifacts to be owned and inanimate natural kinds to be non-owned. In Experiments 2A and 2B, 3-6-year-olds likewise had different expectations about the ownership of unfamiliar artifacts and natural kinds. Children at all ages viewed unfamiliar natural kinds as non-owned, but children younger than 6 years of age only endorsed artifacts as owned at chance rates. In Experiment 3, children saw the same pictures but were also told whether objects were human-made. With this information provided, even 3-year-olds viewed unfamiliar artifacts as owned. Finally, in Experiment 4, 4- and 5-year-olds chose unfamiliar artifacts over natural kinds when judging which object in a pair belongs to a person, but not when judging which the person prefers. These experiments provide first evidence about how children judge whether objects are owned. In contrast to claims that children think about natural kinds as being similar to artifacts, the current findings reveal that children have differing expectations about whether they are owned.     

Effects of color heterogeneity on subitization

Small numbers of items can be enumerated rapidly and accurately via a process termedsubitizing. In two experiments, we examined the effect of target color heterogeneity on subitizing efficiency. In contrast to the findings of Puts and de Weert (1997), we found that observers were no less efficient at subitizing displays containing red and green items than they were at subitizing displays of a single color. We propose that these findings are consistent with subitization operating on items represented within a location master map that codes where objects are but not what they are. The data are discussed in relation to recent findings concerning the detection of single-feature targets and the functional architecture of early visual processing.     

Developmental profiles for multiple object tracking and spatial memory: typically developing preschoolers and people with Williams syndrome

The ability to track moving objects, a crucial skill for mature performance on everyday spatial tasks, has been hypothesized to require a specialized mechanism that may be available in infancy (i.e. indexes). Consistent with the idea of specialization, our previous work showed that object tracking was more impaired than a matched spatial memory task in individuals with Williams syndrome (WS), a genetic disorder characterized by severe visuo‐spatial impairment. We now ask whether this unusual pattern of performance is a reflection of general immaturity or of true abnormality, possibly reflecting the atypical brain development in WS. To examine these two possibilities, we tested typically developing 3‐ and 4‐year‐olds and people with WS on multiple object tracking (MOT) and memory for static spatial location. The maximum number of objects that could be correctly tracked or remembered (estimated from the k‐statistic) showed similar developmental profiles in typically developing 3‐ and 4‐year‐old children, but the WS profile differed from either age group. People with WS could track more objects than 3‐year‐olds, and the same number as 4‐year‐olds, but they could remember the locations of more static objects than both 3‐ and 4‐year‐olds. Combining these data with those from our previous studies, we found that typically developing children show increases in the number of objects they can track or remember between the ages of 3 and 6, and these increases grow in parallel across the two tasks. In contrast, object tracking in older children and adults with WS remains at the level of 4‐year‐olds, whereas the ability to remember multiple locations of static objects develops further. As a whole, the evidence suggests that MOT and memory for static location develop in tandem typically, but not in WS. Atypical development of the parietal lobe in people with WS could play a causal role in the abnormal, uneven pattern of performance in WS. This interpretation is consistent with the idea that multiple object tracking engages different mechanisms from those involved in memory for static object location, and that the former can be particularly disrupted by atypical development.     

Intuitive physics: the straight-down belief and its origin

This study examines the nature and origin of a common misconception about moving objects. We first show through the use of pencil-and-paper problems that many people erroneously believe that an object that is carried by another moving object (e.g., a ball carried by a walking person) will, if dropped, fall to the ground in a straight vertical line. (In fact, such an object will fall forward in a parabolic arc.) We then demonstrate that this "straight-down belief" turns up not only on pencil-and-paper problems but also on a problem presented in a concrete, dynamic fashion (Experiment 1) and in a situation in which a subject drops a ball while walking (Experiment 2). We next consider the origin of the straight-down belief and propose that the belief may stem from a perceptual illusion. Specifically, we suggest that objects dropped from a moving carrier may be perceived as falling straight down or even backward, when in fact they move forward as they fall. Experiment 3, in which subjects view computer-generated displays simulating situations in which a carried object is dropped, and Experiment 4, in which subjects view a videotape of a walking person dropping an object, provide data consistent with this "seeing is believing" hypothesis.     

Constraints on Multiple Object Tracking in Williams Syndrome: How Atypical Development Can Inform Theories of Visual Processing

The ability to track moving objects is a crucial skill for performance in everyday spatial tasks. The tracking mechanism depends on representation of moving items as coherent entities, which follow the spatiotemporal constraints of objects in the world. In the present experiment, participants tracked 1 to 4 targets in a display of 8 identical objects. Objects moved randomly and independently (moving condition), passed behind an invisible bar (occluded condition), or momentarily disappeared by shrinking (implosion condition). Scholl and Pylyshyn (1999) found that adults can track entities under the moving and occluded conditions, but not under implosion. This finding suggests that the tracking mechanism is constrained by the spatiotemporal properties of physical objects as they move in the world. In the present study, we adapt these conditions to investigate whether this constraint holds for people with severe spatial impairments associated with Williams syndrome (WS). In Experiment 1, we compare the performance of individuals with WS and typically developing (TD) adults. TD adults replicated Scholl and Pylyshyn’s findings; performance was no different between the moving and occluded conditions but was worse under implosion. People with WS had reduced tracking capacity but demonstrated the same pattern across conditions. In Experiment 2, we tested TD 4-, 5-, and 7-year-olds. People with WS performed at a level that fell between TD 4- and 5-year-olds. These results suggest that the multiple object tracking system in WS operates under the same object-based constraints that hold in typical development.     

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.     

Color-object interference: Further tests of an executive control account

Young children are slower in naming the color of a meaningful picture than in naming the color of an abstract form (Stroop-like color-object interference). The current experiments tested an executive control account of this phenomenon. First, color-object interference was observed in 6- and 8-year-olds but not in 12- and 16-year-olds (Experiment 1). Second, meaningful pictures did not interfere in 5- to 7-year-olds’ manual sorting of objects on the basis of color (Experiment 2) or in their naming the number of colored objects in the display, that is, subitizing (Experiment 3). These findings provide support for the view that color-object interference results from the children’s immature inhibition of the prepotent but irrelevant task of object naming.     

Working memory impairment in people with Williams syndrome: Effects of delay, task and stimuli

Williams syndrome (WS) is a neurodevelopmental disorder associated with impaired visuospatial representations subserved by the dorsal stream and relatively strong object recognition abilities subserved by the ventral stream. There is conflicting evidence on whether this uneven pattern in WS extends to working memory (WM). The present studies provide a new perspective, testing WM for a single stimulus using a delayed recognition paradigm in individuals with WS and typically developing children matched for mental age (MA matches). In three experiments, participants judged whether a second stimulus ‘matched’ an initial sample, either in location or identity. We first examined memory for faces, houses and locations using a 5 s delay (Experiment 1) and a 2 s delay (Experiment 2). We then tested memory for human faces, houses, cat faces, and shoes with a 2 s delay using a new set of stimuli that were better controlled for expression, hairline and orientation (Experiment 3). With the 5 s delay (Experiment 1), the WS group was impaired overall compared to MA matches. While participants with WS tended to perform more poorly than MA matches with the 2 s delay, they also exhibited an uneven profile compared to MA matches. Face recognition was relatively preserved in WS with friendly faces (Experiment 2) but not when the faces had a neutral expression and were less natural looking (Experiment 3). Experiment 3 indicated that memory for object identity was relatively stronger than memory for location in WS. These findings reveal an overall WM impairment in WS that can be overcome under some conditions. Abnormalities in the parietal lobe/dorsal stream in WS may damage not only the representation of spatial location but may also impact WM for visual stimuli more generally.     

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.     

小学生和成人不同注意条件下的感数与计数加工的比较研究

采用经典的空间线索范式,以成年人和小学二、四、六年级的学生为研究对象,考察了内、外源注意对感数和计数加工过程的影响。结果表明：（1）六年级学生和成人的感数范围为1-3或4,计数范围为4或5以上,二、四年级学生的感数范围在1-3,计数范围在4以上,支持感数和计数分离的观点。（2）对感数加工,成人和六年级学生均不受两种注意条件的影响,而对计数加工,外源性注意条件下的反应比内源性注意快;二年级学生1-6的数量加工受两种注意条件的影响,四年级学生1-5的加工不受两种注意条件的影响。（3）成人和小学生在感数和计数加工上都存在线索效应。以上结果说明：二-四年级是发展的关键期,随着年龄的增加,儿童逐渐有意识地有效利用内源和外源性线索进行数量加工,其注意指向性更明确;从发展的角度为选择注意加工理论提供了发展证据。     

Global and local processing in Williams syndrome: drawing versus perceiving.

It has been hypothesized that a local processing bias underlies overall visuospatial impairments in Williams syndrome (WS). However, recent studies have challenged this hypothesis by providing evidence against a local processing bias at the perceptual level. The aim of the present study was to further examine drawing and perceptual skills in children with WS using closely matched-hierarchical stimuli. In the drawing task children with WS exhibited a local processing bias. However, no significant preferential bias was found in the perceptual task. This indicates that children with WS do not systematically present a preferential bias for local information. Taken together the findings of the present study suggest that perceptual processing deficits per se are unlikely to explain local processing biases in visuoconstructive tasks often described in people with WS.     

Object recognition in Williams syndrome: uneven ventral stream activation

Williams syndrome (WS) is a genetic disorder associated with severe visuospatial deficits, relatively strong language skills, heightened social interest, and increased attention to faces. On the basis of the visuospatial deficits, this disorder has been characterized primarily as a deficit of the dorsal stream, the occipitoparietal brain regions that subserve visuospatial processing. However, some evidence indicates that this disorder may also affect the development of the ventral stream, the occipitotemporal cortical regions that subserve face and object recognition. The present studies examined ventral stream function in WS, with the hypothesis that faces would produce a relatively more mature pattern of ventral occipitotemporal activation, relative to other objects that are also represented across these visual areas. Using functional magnetic imaging, we compared activation patterns during viewing of human faces, cat faces, houses and shoes in individuals with WS (age 14-27), typically developing 6-9-year-olds (matched approximately on mental age), and typically developing 14-26-year-olds (matched on chronological age). Typically developing individuals exhibited changes in the pattern of activation over age, consistent with previous reports. The ventral stream topography of individuals with WS differed from both control groups, however, reflecting the same level of activation to face stimuli as chronological age matches, but less activation to house stimuli than either mental age or chronological age matches. We discuss the possible causes of this unusual topography and implications for understanding the behavioral profile of people with WS.     

Visually guided step descent in children with Williams syndrome

Individuals with Williams syndrome (WS) have impairments in visuospatial tasks and in manual visuomotor control, consistent with parietal and cerebellar abnormalities. Here we examined whether individuals with WS also have difficulties in visually controlling whole-body movements. We investigated visual control of stepping down at a change of level in children with WS (5-16-year-olds), who descended a single step while their movement was kinematically recorded. On each trial step height was set unpredictably, so that visual information was necessary to perceive the step depth and position the legs appropriately before landing. Kinematic measures established that children with WS did not use visual information to slow the leg at an appropriate point during the step. This pattern contrasts with that observed in typically developing 3- and 4-year-old children, implying severe impairment in whole-body visuomotor control in WS. For children with WS, performance was not significantly predicted by low-level visual or balance problems, but improved significantly with verbal age. The results suggest some plasticity and development in WS whole-body control. These data clearly show that visuospatial and visuomotor deficits in WS extend to the locomotor domain. Taken together with evidence for parietal and cerebellar abnormalities in WS, these results also provide new evidence for the role of these circuits in the visual control of whole-body movement.     

Piecing together numerical language: children's use of default units in early counting and quantification

When asked to ‘find three forks’, adult speakers of English use the noun ‘fork’ to identify units for counting. However, when number words (e.g. three) and quantifiers (e.g. more, every) are used with unfamiliar words (‘Give me three blickets’) noun‐specific conceptual criteria are unavailable for picking out units. This poses a problem for young children learning language, who begin to use quantifiers and number words by age 2, despite knowing a relatively small number of nouns. Without knowing how individual nouns pick out units of quantification – e.g. what counts as a blicket– how could children decide whether there are three blickets or four? Three experiments suggest that children might solve this problem by assigning ‘default units’ of quantification to number words, quantifiers, and number morphology. When shown objects that are broken into arbitrary pieces, 4‐year‐olds in Experiment 1 treated pieces as units when counting, interpreting quantifiers, and when using singular–plural morphology. Experiment 2 found that although children treat object‐hood as sufficient for quantification, it is not necessary. Also sufficient for individuation are the criteria provided by known nouns. When two nameable things were glued together (e.g. two cups), children counted the glued things as two. However, when two arbitrary pieces of an object were put together (e.g. two parts of a ball), children counted them as one, even if they had previously counted the pieces as two. Experiment 3 found that when the pieces of broken things were nameable (e.g. wheels of a bicycle), 4‐year‐olds did not include them in counts of whole objects (e.g. bicycles). We discuss the role of default units in early language acquisition, their origin in acquisition, and how children eventually acquire an adult semantics identifying units of quantification.     

Subitizing and counting in typical and atypical development

Enumeration performance in standard dot counting paradigms was investigated for different age groups with typical and atypically poor development of arithmetic skills. Experiment 1 showed a high correspondence between response times and saccadic frequencies for four age groups with typical development. Age differences were more marked for the counting than the subitizing range. In Experiment 2 we found a discontinuity between subitizing and counting for dyscalculic children; however, their subitizing slopes were steeper than those of typically developing control groups, indicating a dysfunctional subitizing mechanism. Across both experiments a number of factors could be identified that affect enumeration in the subitizing and the counting range differentially. These differential patterns further support the assumption of two qualitatively different enumeration processes.     

Global and Local processing in Williams Syndrome: Drawing versus Perceiving

It has been hypothesized that a local processing bias underlies overall visuospatial impairments in Williams syndrome (WS). However, recent studies have challenged this hypothesis by providing evidence against a local processing bias at the perceptual level. The aim of the present study was to further examine drawing and perceptual skills in children with WS using closely matched-hierarchical stimuli. In the drawing task children with WS exhibited a local processing bias. However, no significant preferential bias was found in the perceptual task. This indicates that children with WS do not systematically present a preferential bias for local information. Taken together the findings of the present study suggest that perceptual processing deficits per se are unlikely to explain local processing biases in visuoconstructive tasks often described in people with WS.