Signal clarity: an account of the variability in infant quantity discrimination tasks.

Infants have shown variable success in quantity comparison tasks, with infants of a given age sometimes successfully discriminating numerical differences at a 2:3 ratio but requiring 1:2 and even 1:4 ratios of change at other times. The current explanations for these variable results include the two-systems proposal - a theoretical framework that suggests that there are multiple systems at play and that these systems do not communicate early in infancy, leading to failure in certain numerical comparisons. An alternative proposal is that infants may be attending to continuous extent dimensions in these tasks rather than number per se. However, neither of these two main proposals is independently capable of accounting for the previously published data. Recently the Signal Clarity Hypothesis was proposed to account for and predict the variability (Cantrell & Smith, 2013). According to this hypothesis, infants' variable success may be understood from a framework of statistical learning taken together with the signal-to-noise ratio generated by control procedures in habituation tasks. Here we test specific predictions made by the Signal Clarity Hypothesis. Across four experiments assessing 9-month old discriminations of small and large sets (2 vs. 4 and 3 vs. 4), we demonstrate that infant success can be predicted by this novel approach and, further, that infants may discriminate smaller ratios of change than previously believed (3:4 numerical change and 2:3 cumulative area change).

Related papers:

title: Number bias for the discrimination of large visual sets in infancy
abstract: This brief report attempts to resolve the claim that infants preferentially attend to continuous variables over number [ (1999) 408; Cognit. Psychol.44 (2002) 33] with the finding that when continuous variables are controlled, infants as young as 6-months of age discriminate large numerical values [ (2003) 396; Cognition 89 (2003) B15; Cognition 74 (2000) B1]. In two parallel experiments, we compare 6-month-old infants' ability to discriminate number and ignore continuous variables with their ability to form a representation of a cumulative surface area and ignore number. We find that infants discriminate a 2-fold change in number but fail to discriminate a 2-fold change in cumulative surface area. The results point to a more complicated relationship between discrete and continuous dimensions than implied by previous literature.

title: The relative salience of discrete and continuous quantity in young infants.
abstract: Whether human infants spontaneously represent number remains contentious. Clearfield & Mix (1999) and Feigenson, Carey & Spelke (2002) put forth evidence that when presented with small sets of 1-3 items infants may preferentially attend to continuous properties of stimuli rather than to number, and these results have been interpreted as evidence that infants may not have numerical competence. Here we present three experiments that test the hypothesis that infants prefer to represent continuous variables over number. In Experiment 1, we attempt to replicate the Clearfield & Mix study with a larger sample of infants. Although we replicated their finding that infants attend to changes in contour length, infants in our study attended to number and perimeter/area simultaneously. In Experiments 2 and 3, we pit number against continuous extent for exclusively large sets (Experiment 2) and for small and large sets combined (Experiment 3). In all three experiments, infants noticed the change in number, suggesting that representing discrete quantity is not a last resort for human infants. These results should temper the conclusion that infants find continuous properties more salient than number and instead suggest that number is spontaneously represented by young infants, even when other cues are available.

title: Large number discrimination in 6-month-old infants
abstract: Six-month-old infants discriminate between large sets of objects on the basis of numerosity when other extraneous variables are controlled, provided that the sets to be discriminated differ by a large ratio (8 vs. 16 but not 8 vs. 12). The capacities to represent approximate numerosity found in adult animals and humans evidently develop in human infants prior to language and symbolic counting.

title: Number sense in human infants.
abstract: Four experiments used a preferential looking method to investigate 6-month-old infants' capacity to represent numerosity in visual-spatial displays. Building on previous findings that such infants discriminate between arrays of eight versus 16 discs, but not eight versus 12 discs (Xu & Spelke, 2000), Experiments 1 and 2 investigated whether infants' numerosity discrimination depends on the ratio of the two set sizes with even larger numerosities. Infants successfully discriminated between arrays of 16 versus 32 discs, but not 16 versus 24 discs, providing evidence that their discrimination shows the set-size ratio signature of numerosity discrimination in human adults, children and many non-human animals. Experiments 3 and 4 addressed a controversy concerning infants' ability to discriminate large numerosities (observed under conditions that control for total filled area, array size and density, item size and correlated properties such as brightness: Brannon, 2002; Xu, 2003b; Xu & Spelke, 2000) versus small numerosities (not observed under conditions that control for total contour length: Clearfield & Mix, 1999). To investigate the sources of these differing findings, Experiment 3 tested infants' large-number discrimination with controls for contour length, and Experiment 4 tested small-number discrimination with controls for total filled area. Infants successfully discriminated the large-number displays but showed no evidence of discriminating the small-number displays. These findings provide evidence that infants have robust abilities to represent large numerosities. In contrast, infants may fail to represent small numerosities in visual-spatial arrays with continuous quantity controls, consistent with the thesis that separate systems serve to represent large versus small numerosities.

title: Origins of Number Sense
abstract: Four experiments investigated infants' sensitivity to large, approximate numerosities in auditory sequences. Prior studies provided evidence that 6-month-old infants discriminate large numerosities that differ by a ratio of 2.0, but not 1.5, when presented with arrays of visual forms in which many continuous variables are controlled. The present studies used a head-turn preference procedure to test for infants' numerosity discrimination with auditory sequences designed to control for element duration, sequence duration, interelement interval, and amount of acoustic energy. Six-month-old infants discriminated 16 from 8 sounds but failed to discriminate 12 from 8 sounds, providing evidence that the same 2.0 ratio limits numerosity discrimination in auditory-temporal sequences and visual-spatial arrays. Nine-month-old infants, in contrast, successfully discriminated 12 from 8 sounds, but not 10 from 8 sounds, providing evidence that numerosity discrimination increases in precision over development, prior to the emergence of language or symbolic counting.

title: Infants¿ enumeration of dynamic displays
abstract: This study examined infants’ enumeration of puppet jumping tasks. In Experiment 1, 5–7-month-old infants were familiarized to a puppet jumping two or three times, and tested with both numbers of jumps. Infants looked significantly longer at the new number, replicating Wynn 1996) 164]. To probe further the stability of infants’ ability to enumerate, Experiment 2 varied the rate of the jumps during habituation and controlled for rate across test trials. At test, infants showed no preference for either event, suggesting that rate changes can overpower infants’ responses to number. Experiment 3 explored an alternative explanation to infants’ enumeration, namely discrimination based on the amount of time the puppet spent jumping. Infants were familiarized to two or three jumps, then tested with alternating displays of either a familiar number of jumps with a novel jump time, or a novel number of jumps with the familiar jump time. Infants dishabituated to the display that changed in jump time, but not to the display that changed in number. Results suggest that infants’ looking in event sequences is based on amount of motion, not enumeration. This finding is consistent with studies finding perceptual processes behind infants’ supposed precocious numerical abilities.

title: Infants' enumeration of actions: numerical discrimination and its signature limits.
abstract: Are abstract representations of number - representations that are independent of the particular type of entities that are enumerated - a product of human language or culture, or do they trace back to human infancy? To address this question, four experiments investigated whether human infants discriminate between sequences of actions (jumps of a puppet) on the basis of numerosity. At 6 months, infants successfully discriminated four- versus eight-jump sequences, when the continuous variables of sequence duration, jump duration, jump rate, jump interval and duration, and extent of motion were controlled, and rhythm was eliminated. In contrast, infants failed to discriminate two- versus four-jump sequences, suggesting that infants fail to form cardinal number representations of small numbers of actions. Infants also failed to discriminate between sequences of four versus six jumps at 6 months, and succeeded at 9 months, suggesting that infants' number representations are imprecise and increase in precision with age. All of these findings agree with those of studies using visual-spatial arrays and auditory sequences, providing evidence that a single, abstract system of number representation is present and functional in infancy.

title: Number discrimination in 10-month-old infants
abstract: Two experiments investigated developmental changes in large number discrimination with visual-spatial arrays. Previous studies found that 6-month-old infants were able to discriminate arrays that differ by a ratio of 1:2 but not 2:3. We found that by 10 months, infants were able to reliably discriminate 8 from 12 elements (2:3) but not 8 from 10 elements (4:5). Thus, number discrimination improves in precision during the first year, and these findings converge with studies using auditory stimuli.

title: Attention Is Spontaneously Biased Toward Regularities
abstract: Knowledge about regularities in the environment can be used to facilitate perception, memory, and language acquisition. Given this usefulness, we hypothesized that statistically structured sources of information receive attentional priority over noisier sources, independent of their intrinsic salience or goal relevance. We report three experiments that support this hypothesis. Experiment 1 shows that regularities bias spatial attention: Visual search was facilitated at a location containing temporal regularities, even though these regularities did not predict target location, timing, or identity. Experiments 2 and 3 show that regularities bias feature attention: Attentional capture doubled in magnitude when singletons appeared, respectively, in a color or dimension with temporal regularities among task-irrelevant stimuli. Prioritization of the locations and features of regularities is not easily accounted for in the conventional dichotomy between stimulus-driven and goal-directed attention. This prioritization may in turn promote further statistical learning, helping the mind to acquire knowledge about stable aspects of the environment.

title: Perception of numerical invariance in neonates.
abstract: 40 healthy, normal newborn infants were evaluated with reference to their ability to discriminate among visual stimulus arrays consisting of 2 versus 3 or 4 versus 6 black dots. Infants made this discrimination within a habituation/dishabituation paradigm for the small number sets (2 to 3 and 3 to 2) but not for the larger sets (4 to 6 and 6 to 4). We argue that this suggests the ability to abstract numerical invariance from small-set visual arrays and may be evidence for complex information processing during the first week of life.

title: Infants' Individuation and Enumeration of Actions
abstract: Two experiments examined 6-month-old infants' ability to individuate and enumerate physical actions—the sequential jumps of a puppet In both experiments, which employed a habituation paradigm, infants successfully discriminated two-jump from three-jump sequences The sequences of activity in the two experiments provided for an initial exploration of the cues infants use to individuate actions Results show that (a) infants can individuate and enumerate actions in a sequence, indicating that their enumeration mechanism is quite general in the kinds of entities over which it will operate, (b) actions whose temporal boundaries are characterized by a contrast between motion and absence of motion are especially easy to individuate and enumerate, but nonetheless (c) infants can individuate and enumerate actions embedded in a sequence of continuous motion, indicating that infants possess procedures for parsing an ongoing motionful scene into distinct portions of activity

title: The multisensory representation of number in infancy.
abstract: Human infants can discriminate visual and auditory stimuli solely on the basis of number, suggesting a developmental foundation for the nonverbal number representations of adult humans. Recent studies suggest that these language-independent number representations are multisensory in both adult humans and nonhuman animals. Surprisingly, however, previous studies have yielded mixed evidence concerning whether nonverbal numerical representations independent of sensory modality are present early in human development. In this article, we use a paradigm that avoids stimulus confounds present in previous studies of cross-modal numerical mapping in infants. We show that 7-month-old infants preferentially attend to visual displays of adult humans that numerically match the number of adult humans they hear speaking. These data provide evidence that by 7 months of age, infants connect numerical representations across different sensory modalities when presented with human faces and voices. Results support the possibility of a shared system between preverbal infants and nonverbal animals for representing number.

title: Intersensory redundancy accelerates preverbal numerical competence
abstract: Intersensory redundancy can facilitate animal and human behavior in areas as diverse as rhythm discrimination, signal detection, orienting responses, maternal call learning, and associative learning. In the realm of numerical development, infants show similar sensitivity to numerical differences in both the visual and auditory modalities. Using a habituation-dishabituation paradigm, we ask here, whether providing redundant, multisensory numerical information allows six-month-old infants to make more precise numerical discriminations. Results indicate that perceptually redundant information improved preverbal numerical precision to a level of discrimination previously thought attainable only after additional months of development. Multimodal stimuli may thus boost abstract cognitive abilities such as numerical competence.

title: Auditory-visual intermodal matching of small numerosities in 6-month-old infants.
abstract: Recent studies have reported that preverbal infants are able to discriminate between numerosities of sets presented within a particular modality. There is still debate, however, over whether they are able to perform intermodal numerosity matching, i.e. to relate numerosities of sets presented with different sensory modalities. The present study investigated auditory-visual intermodal matching of small numerosities in infancy by using a violation-of-expectation paradigm. After being familiarized with events of a few objects impacting a surface successively, 6-month-old infants were alternatively presented with two and three tones while the movement of each object remained hidden behind an opaque screen. The screen was then removed to reveal either two or three objects. Results showed that the infants looked significantly longer at the numerically nonequivalent events (the three-tone/two-object and the two-tone/three-object events) than at the numerically equivalent events (the two-tone/two-object and the three-tone/three-object events) irrespective of the rate or duration of auditory tones presented. These findings suggest that infants are capable of performing intermodal matching of small numerosities and that they might possess abstract representations of numerosity beyond sensory modalities.

title: Crossing the divide: infants discriminate small from large numerosities.
abstract: Although young infants have repeatedly demonstrated successful numerosity discrimination across large sets when the number of items in the sets changes twofold (E. M. Brannon, S. Abbott, & D. J. Lutz, 2004;  Wood & E. S. Spelke, 2005; F. Xu & E. S. Spelke, 2000), they consistently fail to discriminate a twofold change in number when one set is large and the other is small (<4 items; F. Feigenson, S. Carey, & M. Hauser, 2002; F. Xu, 2003). It has been theorized that this failure reflects an incompatibility in representational systems for small and large sets. The authors investigated the ability of 7-month-old infants to compare small and large sets over a variety of conditions. Results reveal that infants can successfully discriminate small from large sets when given a fourfold change, but not a twofold change, in number. The implications of these results are discussed in light of current theories of number representation.

title: Discrimination of Large and Small Numerosities by Human Infants
abstract: Six experiments investigated infants' sensitivity to numerosity in auditory sequences. In prior studies (Lipton &Spelke, 2003), 6-month-old infants discriminated sequences of 8 versus 16 but not 8 versus 12 sounds, and 9-month-old infants discriminated 8 versus 12 but not 8 versus 10 sounds, when the continuous variables of rate, sound duration, and sequence duration were controlled. The current studies investigated whether infants' numerical discrimination is subject to the signature ratio limit of adults' numerosity discrimination. Four experiments at 6 and 9 months provided evidence for this signature limit, suggesting that common mechanisms underlie numerosity discrimination in infants and adults. In further experiments, infants failed to discriminate 2 versus 4 or 2 versus 3 sounds when tested under the same conditions as with large numbers. These findings accord with studies using visual-spatial arrays (e.g., Clearfield &Mix, 1999) and suggest that separate systems underlie infants' representation o...

title: Numerosity discrimination in infants: Evidence for two systems of representations
abstract: Two experiments investigated numerosity discrimination in 6-month-old infants, comparing their performance on both large numbers (4 vs. 8 elements) and small numbers (2 vs. 4 elements) with both total filled area and total contour length controlled for. These studies provide the first direct comparison between discrimination of small and large numbers in infants with the same methodology, the same type of stimuli, and the same continuous variable controls. Results showed that infants succeeded in discriminating 4 from 8 elements but failed to discriminate 2 from 4 elements, providing evidence for the existence of two systems of number representations in infancy.

title: Tracking individuals via object-files: evidence from infants' manual search
abstract: In two experiments, a manual search task explored 12- to 14-month-old infants’ representations of small sets of objects. In this paradigm, patterns of searching revealed the number of objects infants represented as hidden in an opaque box. In Experiment 1, we obtained the set-size signature of object-file representations: infants succeeded at representing precisely 1, precisely 2, and precisely 3 objects in the box, but failed at representing 4 (or even that 4 is greater than 2). In Experiment 2, we showed that infants’ expectations about the contents of the box were based on number of individual objects, and not on a continuous property such as total object volume. These findings support the hypothesis that infants maintained representations of individuals, that object-files were the underlying means of representing these individuals, and that object-file models can be compared via one-to-one correspondence to establish numerical equivalence.

title: Infants' Discrimination of Number vs. Continuous Extent
abstract: Seven studies explored the empirical basis for claims that infants represent cardinal values of small sets of objects. Many studies investigating numerical ability did not properly control for continuous stimulus properties such as surface area, volume, contour length, or dimensions that correlate with these properties. Experiment 1 extended the standard habituation/dishabituation paradigm to a 1 vs 2 comparison with three-dimensional objects and confirmed that when number and total front surface area are confounded, infants discriminate the arrays. Experiment 2 revealed that infants dishabituated to a change in front surface area but not to a change in number when the two variables were pitted against each other. Experiments 3 through 5 revealed no sensitivity to number when front surface area was controlled, and Experiments 6 and 7 extended this pattern of findings to the Wynn (1992) transformation task. Infants' lack of a response to number, combined with their demonstrated sensitivity to one or more dimensions of continuous extent, supports the hypothesis that the representations subserving object-based attention, rather than those subserving enumeration, underlie performance in the above tasks.

title: Number Versus Contour Length in Infants' Discrimination of Small Visual Sets
abstract: This study examined infants' use of contour length in number discrimination tasks. We systematically varied number and contour length in a visual habituation experiment in order to separate these two variables. Sixteen 6- to 8-month-old infants were habituated to displays of either two or three black squares on a page. They were then tested with alternating displays of either a familiar number of squares with a novel contour length or a novel number of squares with a familiar contour length. Infants dishabituated to the display that changed in contour length, but not to the display that changed in number. We conclude that infants base their discriminations on contour length or some other continuous variable that correlates with it, rather than on number.

title: Multiple cues for quantification in infancy: is number one of them?
abstract: A review and synthesis of the literature on quantification in infancy and early childhood is provided. In most current conceptualizations, early quantification is assumed to be number based. However, the extant literature provides no clear-cut evidence that infants use number to perform quantitative tasks. Instead, new research suggests that quantification is initially based on nonnumerical cues, such as area and contour length, whether or not a task involves discrete items. The authors discuss the implications of these findings with respect to early quantification and its relation to later numerical development.

title: Open questions and a proposal: A critical review of the evidence on infant numerical abilities
abstract: Considerable research has investigated infants' numerical capacities. Studies in this domain have used procedures of habituation, head turn, violation of expectation, reaching, and crawling to ask what quantities infants discriminate and represent visually, auditorily as well as intermodally. The concensus view from these studies is that infants possess a numerical system that is amodal and applicable to the quantification of any kind of entity and that this system is fundamentally separate from other systems that represent continuous magnitude. Although there is much evidence consistent with this view, there are also inconsistencies in the data. This paper provides a broad review of what we know, including the evidence suggesting systematic early knowledge as well as the peculiarities and gaps in the empirical findings with respect to the concensus view. We argue, from these inconsistencies, that the concensus view cannot be entirely correct. In light of the evidence, we propose a new hypothesis, the Signal Clarity hypothesis, that posits a developmental role for dimensions of continuous quantity within the discrete quantity system and calls for a broader research agenda that considers the covariation of discrete and continuous quantities not simply as a problem for experimental control but as information that developing infants may use to build more precise and robust representations of number.

title: The development of area discrimination and its implications for number representation in infancy.
abstract: This paper investigates the ability of infants to attend to continuous stimulus variables and how this capacity relates to the representation of number. We examined the change in area needed by 6-month-old infants to detect a difference in the size of a single element (Elmo face). Infants successfully discriminated a 1:4, 1:3 and 1:2 change in the area of the Elmo face but failed to discriminate a 2:3 change. In addition, the novelty preference was linearly related to the ratio difference between the novel and familiar area. Results suggest that Weber's Law holds for area discriminations in infancy and also reveal that at 6 months of age infants are equally sensitive to number, time and area.

title: The difficulties of representing continuous extent in infancy: using number is just easier.
abstract: This study investigates the ability of 6-month-old infants to attend to the continuous properties of a set of discrete entities. Infants were habituated to dot arrays that were constant in cumulative surface area yet varied in number for small (< 4) or large (> 3) sets. Results revealed that infants detected a 4-fold (but not 3-fold) change in area, regardless of set size. These results are in marked contrast to demonstrations that infants of the same age successfully discriminate a 2- or 3-fold change in number, providing strong counterevidence to the claim that infants use solely nonnumerical, continuous extent variables when discriminating sets. These findings also shed light on the processes involved in tracking continuous variables in infants.

title: Infants make quantity discriminations for substances.
abstract: Infants can track small groups of solid objects, and infants can respond when these quantities change. But earlier work is equivocal about whether infants can track continuous substances, such as piles of sand. Experiment 1 (N = 88) used a habituation paradigm to show infants can register changes in the size of piles of sand that they see poured from a container when there is a 1-to-4 ratio. Experiment 2 (N = 82) tested whether infants could discriminate a 1-to-2 ratio. The results demonstrate that females could discriminate the difference but males could not. These findings constitute the youngest evidence of successful quantity discriminations for a noncohesive substance and begin to characterize the nature of the representation for noncohesive entities.

title: Attending to One of Many: When Infants are Surprisingly Poor at Discriminating an Item's Size
abstract: Despite a prevailing assumption in the developmental literature that changes in continuous quantities (i.e., surface area, duration) are easier to detect than changes in number, very little research has focused on the verity of this assumption. The few studies that have directly examined infants’ discriminations of continuous extent have revealed that infants discriminate the duration of a single event and the area of a single item with similar levels of precision (Brannon et al., 2006; vanMarle and Wynn, 2006). But what about when items are presented in arrays? Infants appear to be much worse at representing the cumulative surface area compared to the numerosity of an array (Cordes and Brannon, 2008a), however this may be due to a noisy accumulation process and not a general finding pertaining to representations of the extent within an array. The current study investigates how well infants detect changes in the size of individual elements when they are presented within an array. Our results indicate that infants are less sensitive to continuous properties of items when they are presented within a set than when presented in isolation. Specifically we demonstrate that infants required a fourfold change in item size to detect a change when items were presented within a set of homogeneous elements. Rather than providing redundant cues that aided discrimination, presenting a set of identical elements appeared to hamper an infant's ability to detect changes in a single element's size. In addition to providing some of the first evidence to suggest that the presence of multiple items may hinder extent representations, these results provide converging lines of evidence to support the claim that, contrary to popular belief, infants are better at tracking number than continuous properties of a set.

title: The categorical representation of visual pattern information by young infants
abstract: The present research studied 3- and 4-month-old infants' ability to acquire two categories simultaneously. A familiarization-novelty preference procedure and geometrical form categories were used in all experiments. In Experiments I and 3, infants were familiarized with either a single form category, two form categories, or a single form category plus a set of forms that did not define a category. The results showed that, despite increased attentional and memorial demands, presentation of an additional form category did not harm the efficiency of categorization (Experiment 1) and changed the representation of the form category information from exemplars to a prototype (Experiment 3). Contrasting form information that was not categorical in structure decreased the infant's ability to recognize new members of the single familiar category (Experiment 1) and hindered the infant's ability to form a categorical representation (Experiment 3). The categorization behavior observed in Experiment 1, as indexed by the generalization of habituation to novel forms from a familiar category, was shown not to be a consequence of the inability to discriminate between individual members from the familiar form category (Experiment 2). The implications of these results for cognitive development are discussed.

title: Development of exclusivity in perceptually based categories of young infants.
abstract: The exclusivity of perceptually defined categorical representations for natural animal categories in young infants was investigated. Previously, as well as in Experiment 1, evidence was obtained for a categorical representation for cats in 3- and 4-month-old infants that excluded dogs but included perceptually similar female lions after a number of different familiarization procedures. However, in Experiment 2 both dogs and female lions were found to be excluded when the initial familiarization with cats alone was followed by six pairings of familiar cats and novel lions intermingled with two added pairings of familiar cats. The present results indicate that a categorical representation can attain a high level of exclusivity during early infancy as a consequence of experience with exemplars of the contrasting categories that accents the perceptual similarities among members of a category and the perceptual differences among exemplars from different categories.

title: Correlated symptoms and simulated medical classification.
abstract: Category learning theories can be separated into those that expect judgments to be sensitive to configural information and those that expect judgments to be based on a weighted, additive summation of information. Predictions of these two classes of models were investigated in a simulated medical diagnosis task. Subjects learned about a fictitious disease or about two diseases from hypothetical case studies in which some symptoms were correlated with each other and others were independent. Following this initial training, subjects were presented either with pairs of new cases and asked to judge which was more likely to have the disease or with a single case and asked which disease was present. Across four experiments, subjects proved to be sensitive to configural information. When choosing between pairs of new cases, subjects tended to choose the case that preserved the correlation over the case that broke the correlation, even when the case with correlated symptoms contained fewer typical symptoms. When judging which disease was present in a single case, subjects' diagnoses were determined primarily by the correlated symptoms. Implications of these findings to process models of categorization are discussed.

title: Changes in the Ability to Detect Ordinal Numerical Relationships Between 9 and 11 Months of Age.
abstract: When are the precursors of ordinal numerical knowledge first evident in infancy? Brannon (2002) argued that by 11 months of age, infants possess the ability to appreciate the greater than and less than relations between numerical values but that this ability experiences a sudden onset between 9 and 11 months of age. Here we present 5 experiments that explore the changes that take place between 9 and 11 months of age in infants' ability to detect reversals in the ordinal direction of a sequence of arrays. In Experiment 1, we replicate the finding that 11- but not 9-month-old infants detect a numerical ordinal reversal. In Experiment 2 we rule out an alternative hypothesis that 11-month-old infants attended to changes in the absolute numerosity of the first stimulus in the sequence rather than a reversal in ordinal direction. In Experiment 3, we demonstrate that 9-month-old infants are not aided by additional exposure to each numerosity stimulus in a sequence. In Experiment 4 we find that 11-month-old but not 9-month-old infants succeed at detecting the reversal in a nonnumerical size or area-based rule, casting doubt on Brannon's prior claim that what develops between 9 and 11 months of age is a specifically numerical ability. In Experiment 5 we demonstrate that 9-month-old infants are capable of detecting a reversal in ordinal direction but only when there are multiple converging cues to ordinality. Collectively these data indicate that at 11 months of age infants can represent ordinal relations that are based on number, size, or cumulative area, whereas at 9 months of age infants are unable to use any of these dimensions in isolation but instead require a confluence of cues.

title: Enumeration of collective entities by 5-month-old infants
abstract: Recent findings suggest that infants are capable of distinguishing between different numbers of objects, and of performing simple arithmetical operations. But there is debate over whether these abilities result from capacities dedicated to numerical cognition, or whether infants succeed in such experiments through more general, non-numerical capacities, such as sensitivity to perceptual features or mechanisms of object tracking. We report here a study showing that 5-month-olds can determine the number of collective entities -- moving groups of items -- when non-numerical perceptual factors such as contour length, area, density, and others are strictly controlled. This suggests both that infants can represent number per se, and that their grasp of number is not limited to the domain of objects.

title: Two core systems of numerical representation in infants
abstract: Two nonverbal representation systems, the analog magnitude system (AMS) and the object tracking system (OTS), have been proposed to explain how humans and nonhuman animals represent numerosities. There has long been debate about which of the two systems is responsible for representing small numerosities (<4). This review focuses on findings with human infants to inform that debate. We argue that the empirical data cannot all be explained by a single system, and in particular, infants’ failures to compare small and large numerosities – the boundary effect – undermines the claim that the AMS can account for infants’ numerical abilities in their entirety. We propose that although the two systems coexist throughout the lifespan, competition between the systems is primarily a developmental phenomenon. Potential factors that drive the engagement of each system in infancy, such as stimulus features and task demands, are discussed, and directions for future research are suggested.

title: Using Habituation of Looking Time to Assess Mental Processes in Infancy
abstract: Habituation of looking time has become the standard method for studying cognitive processes in infancy. This method has a long history and derives from the study of memory and habituation itself. Often, however, it is not clear how researchers make decisions about how to implement habituation as a tool to study processes such as categorization, object representation, and memory. This article describes the challenges for implementing this tool and describes a set of best practices for its use to study perception and cognition in infancy.

title: Infant perception of numerosity.
abstract: A multiple habituation paradigm was used to determine whether 10--12-month-old infants were able to discriminate between visual arrays which differed only in their numerosity (2 vs. 3, 3, vs. 4, or 4 vs. 5 items). 96 infants were tested in one of two conditions. In the heterogeneous condition, infants were habituated to a series of slides in which only the number of items remained invariant, while the item type (e.g., dogs, houses, etc.), size, and position varied on each slide. In the homogeneous condition, both the item type (chicks) and number remained invariant, while the size and position of the stimuli varied. Infants in both conditions were then tested with slides which contained either N + 1 or N - 1 items. The results demonstrated that, regardless of condition (homogeneous/heterogeneous), infants were able to discriminate between 2 and 3 items and unable to discriminate between 4 and 5 items. For the 3 versus 4 discrimination, a condition x sex interaction indicated that females discriminated between the items in the homogeneous condition while males were able to make the discrimination in the heterogeneous condition. Since the subjects in this study were preverbal infants, the results suggest that early counting skills are preceded by a more perceptual awareness of numerosity.

title: Visual perception of numerosity in infancy.
abstract: Numerosity was defined as an invariant property of a collection of objects specifying its numerical size. Infants looked at displays of small numerosities that changed optic structure such that size was not tied to certain static or dynamic configurational properties of the display but remained constant across patterns of optic motion. The displayed figures moved continuously and at a constant speed. The trajectories were irregular and could produce occlusion of objects. The task used involved infant-controlled habituation of visual looking time. At age 5 months, 8 months, and 13 months, 44 infants were tested for the numerosities 2, 3, and 4 in three randomly ordered sessions.

title: Multiple visual quantitative cues enhance discrimination of dynamic stimuli during infancy.
abstract: Infants possess basic capabilities to assess various quantitative properties such as number, size, and time. Preverbal discriminations are approximate, however, and are similarly limited across these dimensions. Here, we present the first evidence that multiple sources of quantitative unisensory information about dynamic stimuli-namely, simultaneous visual cues to changes in both number and surface area-may accelerate 6-month-olds' quantitative competence. Using a habituation-dishabituation paradigm, results from Experiment 1 demonstrate that, when provided with such visual cues to multiple quantitative properties that occur in the same direction, infants make more precise discriminations than has been shown when they receive information about either cue alone. Moreover, Experiment 2 demonstrates that infants' discrimination also benefits from simultaneous visual cues to quantitative changes that occur in opposite directions. Finally, Experiment 3 demonstrates that these findings are not driven by infants' ability to discriminate a 2:3 ratio change in surface area of a dynamic stimulus alone. Thus, we hypothesize that enhanced quantitative discrimination occurs because simultaneous visual quantitative changes may be more salient than single-source information, which could better recruit attention and result in more precise learning and remembering.

title: Set size and culture influence children's attention to number.
abstract: Much research evidences a system in adults and young children for approximately representing quantity. Here we provide evidence that the bias to attend to discrete quantity versus other dimensions may be mediated by set size and culture. Preschool-age English-speaking children in the United States and Japanese-speaking children in Japan were tested in a match-to-sample task where number was pitted against cumulative surface area in both large and small numerical set comparisons. Results showed that children from both cultures were biased to attend to the number of items for small sets. Large set responses also showed a general attention to number when ratio difficulty was easy. However, relative to the responses for small sets, attention to number decreased for both groups; moreover, both U.S. and Japanese children showed a significant bias to attend to total amount for difficult numerical ratio distances, although Japanese children shifted attention to total area at relatively smaller set sizes than U.S. children. These results add to our growing understanding of how quantity is represented and how such representation is influenced by context--both cultural and perceptual.

title: Similarity, frequency, and category representations.
abstract: This article studies the joint roles of similarity and frequency in determining graded category structure. Perceptual classification learning experiments were conducted in which presentation frequencies of individual exemplars were manipulated. The exemplars had varying degrees of similarity to members of the target and contrast categories. Classification accuracy and typicality ratings increased for exemplars presented with high frequency and for members of the target category that were similar to the high-frequency exemplars. Typicality decreased for members of the contrast category that were similar to the high-frequency exemplars. A frequency-sensitive similarity-to-exemplars model provided a good quantitative account of the classification learning and typicality data. The interactive relations among similarity, frequency, and categorization are considered in the General Discussion. Among the most well-established findings in the categorization literature is that categories have "graded structures" (Rips, Schoben, & Smith, 1973; Rosch, 1973, 1978; Rosch & Mervis, 1975; Smith & Medin, 1981). Rather than all instances of a category being "equal," it appears that certain instances are better examples than others. For example, people reliably rate a robin as a better example of the category birds

title: Infants Show Ratio-dependent Number Discrimination Regardless of Set Size.
abstract: Evidence for approximate number system (ANS) representations in infancy is robust but has typically only been found when infants are presented with arrays of four or more elements. In addition, several studies have found that infants fail to discriminate between small numbers when continuous variables such as surface area and contour length are controlled. These findings suggest that under some circumstances, infants fail to recruit either the ANS or object file representations for small sets. Here, we used a numerical change detection paradigm to assess 6-month-old infants' ability to represent small values. In Experiment 1, infants were tested with 1 versus 3, 1 versus 2, and 2 versus 3 dots. Infants successfully discriminated 1 versus 3 and 1 versus 2, but failed with 2 versus 3. In Experiment 2, we tested whether infants could compare small and large values with a 2 versus 4 condition. Across both experiments, infants' performance exhibited ratio dependence, the hallmark of the ANS. Our results indicate that infants can attend to the purely numerical attributes of small sets and that the numerical change detection paradigm accesses ANS representations in infancy regardless of set size.

title: The development of visual short-term memory capacity in infants.
abstract: Four experiments assessed visual short-term memory capacity in 4- to 13-month-old infants by comparing their looking to changing and nonchanging stimulus streams presented side by side. In each stream, 1 to 6 colored squares repeatedly appeared and disappeared. In changing streams, the color of a different randomly chosen square changed each time the display reappeared; the colors remained the same in nonchanging streams. Infants should look longer at changing streams, but only if they can remember the colors of the squares. The youngest infants preferred changing streams only when the displays contained one object, whereas older infants preferred changing streams when the displays contained up to 4 objects. Thus, visual short-term memory capacity increases significantly across the first year of life.