Number bias for the discrimination of large visual sets in infancy

This brief report attempts to resolve the claim that infants preferentially attend to continuous variables over number [e.g. Psychol. Sci. 10 (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 [e.g. Psychol. Sci. 14 (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.     

Number sense and quantifier interpretation

We consider connections between number sense—the ability to judge number—and the interpretation of natural language quantifiers. In particular, we present empirical evidence concerning the neuroanatomical underpinnings of number sense and quantifier interpretation. We show, further, that impairment of number sense in patients can result in the impairment of the ability to interpret sentences containing quantifiers. This result demonstrates that number sense supports some aspects of the language faculty.

Find the picture of eight turtles: a link between children's counting and their knowledge of number word semantics

An essential part of understanding number words (e.g., eight) is understanding that all number words refer to the dimension of experience we call numerosity. Knowledge of this general principle may be separable from knowledge of individual number word meanings. That is, children may learn the meanings of at least a few individual number words before realizing that all number words refer to numerosity. Alternatively, knowledge of this general principle may form relatively early and proceed to guide and constrain the acquisition of individual number word meanings. The current article describes two experiments in which 116 children (2½- to 4-year-olds) were given a Word Extension task as well as a standard Give-N task. Results show that only children who understood the cardinality principle of counting successfully extended number words from one set to another based on numerosity—with evidence that a developing understanding of this concept emerges as children approach the cardinality principle induction. These findings support the view that children do not use a broad understanding of number words to initially connect number words to numerosity but rather make this connection around the time that they figure out the cardinality principle of counting.     

Representational change and magnitude estimation: why young children can make more accurate salary comparisons than adults

Development of estimation has been ascribed to two sources: (1) a change from logarithmic to linear representations of number and (2) development of general mathematical skills. To test the representational change hypothesis, we gave children and adults a task in which an automatic, linear representation is less adaptive than the logarithmic representation: estimating the value of salaries given in fractional notation. The representational change hypothesis generated the surprising (and accurate) prediction that when estimating the magnitude of salaries given in fractional notation, young children would outperform adults, whereas when estimating the magnitude of the same salaries given in decimal notation, adults would outperform children.     

Revisiting the relation between contingency awareness and attention: Evaluative conditioning relies on a contingency focus

Although evaluative conditioning has occasionally been demonstrated in the absence of contingency awareness, many recent studies imply that its acquisition depends on the availability of attentional resources during conditioning. In previous experiments attention has typically been manipulated in a general way rather than looking at the particular focus of attention. The present study investigated the role of a focus on the CS–US contingency. Two separate distraction tasks were designed that either diverted attention from the stimuli or directed it to the stimuli while drawing attention away from the contingency between the stimuli. Both types of distraction were shown to eliminate evaluative conditioning. Significant evaluative conditioning was observed in a third group of participants who were required to attend the contingencies. A mediation analysis showed that the observed discrepancy in evaluative conditioning effects between groups was mediated by contingency awareness. The results imply that attention in terms of a stimulus focus is not sufficient for evaluative conditioning to occur. Rather, attention to the contingencies between stimuli appears to be crucial in evaluative conditioning, because it is supposed to foster the acquisition of contingency awareness.     

Enumeration of small and large numerosities: The effect of element visibility

Precise enumeration is associated with small numerosities within the subitizing range (<4 items), while approximate enumeration is associated with large numerosities (>4 items). To date, there is still debate on whether a single continuous process or dual mutually exclusive processes mediate enumeration of small and large numerosities. Here, we evaluated a compromise between these two notions: that the precise representation of number is limited to small numerosities, but that the approximate representation of numerosity spans across both small and large numerosities. We assessed the independence of precise and approximate enumeration by looking at how luminance contrast affected enumeration of elements that differ by ones (1–8) or by tens (10–80). We found that enumeration functions of ones and tens have different characteristics, which is consistent with the presence of two number systems. Subitizing was preserved for small numerosities. However, simply decreasing element visibility changed the variability signatures of small numerosities to match those of large numerosities. Together, our results suggest that small numerosities are mediated by both precise and approximate representations of numerosity.     

On the limits of infants' quantification of small object arrays

Recent work suggests that infants rely on mechanisms of object-based attention and short-term memory to represent small numbers of objects. Such work shows that infants discriminate arrays containing 1, 2, or 3 objects, but fail with arrays greater than 3 [Feigenson, L., & Carey, S. (2003). Tracking individuals via object-files: Evidence from infants' manual search. Developmental Science, 6, 568-584; Feigenson, L., Carey, S., & Hauser, M. (2002). The representations underlying infants' choice of more: Object files versus analog magnitudes. Psychological Science, 13(2), 150-156]. However, little is known about how infants represent arrays exceeding the 3-item limit of parallel representation. We explored possible formats by which infants might represent a 4-object array. Experiment 1 used a manual search paradigm to show that infants successfully discriminated between arrays of 1 vs. 2, 2 vs. 3, and 1 vs. 3 objects. However, infants failed to discriminate 1 vs. 4 despite the highly discriminable ratio, providing the strongest evidence to date for object-file representations underlying performance in this task. Experiment 2 replicated this dramatic failure to discriminate 1 from 4 in a second paradigm, a cracker choice task. We then showed that infants in the choice task succeeded at choosing the larger quantity with 0 vs. 4 crackers and with 1 small vs. 4 large crackers. These results suggest that while infants failed to represent 4 as “exactly 4”, “approximately 4”, “3”, or as even as “a plurality”, they did represent information about the array, including the existence of a cracker or cracker-material and the size of the individual objects in the array.     

Spontaneous focusing on numerosity as a domain-specific predictor of arithmetical skills

The aim of this 2 year longitudinal study was to explore whether children’s individual differences in spontaneous focusing on numerosity (SFON) in kindergarten predict arithmetical and reading skills 2 years later in school. Moreover, we investigated whether the positive relationship between SFON and mathematical skills is explained by children’s individual differences in spontaneous focusing on a non-numerical aspect. The participants were 139 Finnish-speaking children. The results show that SFON tendency in kindergarten is a significant domain-specific predictor of arithmetical skills, but not reading skills, assessed at the end of Grade 2. In addition, the relationship between SFON and number sequence skills in kindergarten is not explained by children’s individual differences in their focusing on a non-numerical aspect that is, spatial locations.     

Speech segmentation by statistical learning depends on attention

We addressed the hypothesis that word segmentation based on statistical regularities occurs without the need of attention. Participants were presented with a stream of artificial speech in which the only cue to extract the words was the presence of statistical regularities between syllables. Half of the participants were asked to passively listen to the speech stream, while the other half were asked to perform a concurrent task. In Experiment 1, the concurrent task was performed on a separate auditory stream (noises), in Experiment 2 it was performed on a visual stream (pictures), and in Experiment 3 it was performed on pitch changes in the speech stream itself. Invariably, passive listening to the speech stream led to successful word extraction (as measured by a recognition test presented after the exposure phase), whereas diverted attention led to a dramatic impairment in word segmentation performance. These findings demonstrate that when attentional resources are depleted, word segmentation based on statistical regularities is seriously compromised.     

The development of numerosity estimation: Evidence for a linear number representation early in life

Several studies investigating the development of approximate number representations used the number-to-position task and reported evidence for a shift from a logarithmic to a linear representation of numerical magnitude with increasing age. However, this interpretation as well as the number-to-position method itself has been questioned recently. The current study tested 5- and 8-year-old children on a newly established numerosity production task to examine developmental changes in number representations and to test the idea of a representational shift. Modelling of the children's numerical estimations revealed that responses of the 8-year-old children approximate a simple positive linear relation between estimated and actual numbers. Interestingly, however, the estimations of the 5-year-old children were best described by a bilinear model reflecting a relatively accurate linear representation of small numbers and no apparent magnitude knowledge for large numbers. Taken together, our findings provide no support for a shift of mental representations from a logarithmic to a linear metric but rather suggest that the range of number words which are appropriately conceptualised and represented by linear analogue magnitude codes expands during development.     

Action-related objects influence the distribution of visuospatial attention

Previous studies have shown that attention is drawn to the location of manipulable objects and is distributed across pairs of objects that are positioned for action. Here, we investigate whether central, action-related objects can cue attention to peripheral targets. Experiment 1 compared the effect of uninformative arrow and object cues on a letter discrimination task. Arrow cues led to spatial-cueing benefits across a range of stimulus onset asynchronies (SOAs: 0 ms, 120 ms, 400 ms), but object-cueing benefits were slow to build and were only significant at the 400-ms SOA. Similar results were found in Experiment 2, in which the targets were objects that could be either congruent or incongruent with the cue (e.g., screwdriver and screw versus screwdriver and glass). Cueing benefits were not influenced by the congruence between the cue and target, suggesting that the cueing effects reflected the action implied by the central object, not the interaction between the objects. For Experiment 3 participants decided whether the cue and target objects were related. Here, the interaction between congruent (but not incongruent) targets led to significant cueing/positioning benefits at all three SOAs. Reduced cueing benefits were obtained in all three experiments when the object cue did not portray a legitimate action (e.g., a bottle pointing towards an upper location, since a bottle cannot pour upwards), suggesting that it is the perceived action that is critical, rather than the structural properties of individual objects. The data suggest that affordance for action modulates the allocation of visual attention.     

You can't stop new motion: Attentional capture despite a control set for colour

When a stationary object begins to move, visual spatial attention is reflexively deployed to the location of that object. We tested whether this capture of attention by new motion is entirely stimulus driven, or whether it is contingent on an observer's goals. Participants monitored a visual display for a colour change, inducing an attentional control set (ACS) for colour. Across the three performed experiments, irrelevant new-motion cues always captured visual spatial attention, despite the ACS for colour. This persistence of the attentional cueing effect demonstrates that ACSs, in particular an ACS for colour, cannot prevent new motion from capturing attention. Unlike other stimulus types, such as luminance changes, colour singletons, and new objects, new motion may always capture attention regardless of an observer's goals. This conclusion entails that new motion is an important determinant of when, and to where, visual spatial attention is deployed.     

Spatial updating relies on an egocentric representation of space: Effects of the number of objects

Models of spatial updating attempt to explain how representations of spatial relationships between the actor and objects in the environment change as the actor moves. In allocentric models, object locations are encoded in an external reference frame, and only the actor’s position and orientation in that reference frame need to be updated. Thus, spatial updating should be independent of the number of objects in the environment (set size). In egocentric updating models, object locations are encoded relative to the actor, so the location of each object relative to the actor must be updated as the actor moves. Thus, spatial updating efficiency should depend on set size. We examined which model better accounts for human spatial updating by having people reconstruct the locations of varying numbers of virtual objects either from the original study position or from a changed viewing position. In consistency with the egocentric updating model, object localization following a viewpoint change was affected by the number of objects in the environment.     

The detection of temporally defined objects does not require focused attention

Perceptual grouping is crucial to distinguish objects from their background. Recent studies have shown that observers can detect an object that does not have any unique qualities other than unique temporal properties. A crucial question is whether focused attention is needed for this type of grouping. In two visual search experiments, we show that searching for an object defined by temporal grouping can occur in parallel. These findings suggest that focused attention is not needed for temporal grouping to occur. It is proposed that temporal grouping may occur because the neurons representing the changing object elements adopt firing frequencies that cause the visual system to bind these elements together without the need for focused attention.     

Affective evaluations of objects are influenced by observed gaze direction and emotional expression

Gaze direction signals another person's focus of interest. Facial expressions convey information about their mental state. Appropriate responses to these signals should reflect their combined influence, yet current evidence suggests that gaze-cueing effects for objects near an observed face are not modulated by its emotional expression. Here, we extend the investigation of perceived gaze direction and emotional expression by considering their combined influence on affective judgments. While traditional response-time measures revealed equal gaze-cueing effects for happy and disgust faces, affective evaluations critically depended on the combined product of gaze and emotion. Target objects looked at with a happy expression were liked more than objects looked at with a disgust expression. Objects not looked at were rated equally for both expressions. Our results demonstrate that facial expression does modulate the way that observers utilize gaze cues: Objects attended by others are evaluated according to the valence of their facial expression.     

Semantic feature production norms for a large set of objects and events

Semantic features produced by speakers of a language when given a word corresponding to a concept have provided insight into numerous behavioral phenomena concerning semantic representation in language-impaired and -unimpaired speakers. A number of theories concerning the organization of semantic memory have used features as their starting point. Here, we provide a set of feature norms collected from approximately 280 participants for a total of 456 words (169 nouns referring to objects, 71 nouns referring to events, and 216 verbs referring to events). Whereas a number of feature norms for object concepts already exist, we provide the first set of norms for event concepts. We have used these norms (for both objects and events) in research addressing questions concerning the similarities and differences between the semantic representation of objects and events and in research concerning the interface between semantics and syntax, given that events can be expressed in language as nouns or verbs. Some of this research is summarized here. These norms may be downloaded from www.psychonomic.org/archive.     

Spatial categories and the estimation of location

Four experiments are reported in which people organize a space hierarchically when they estimate particular locations in that space. Earlier work showed that people subdivide circles into quadrants bounded at the vertical and horizontal axes, biasing their estimates towards prototypical diagonal locations within those spatial categories (Psychological Review 98 (1991) 352). In this work Huttenlocher, Hedges, and Duncan showed that the use of such spatial categories can increase the accuracy of estimation of inexactly represented locations. The stimulus locations we examined were uniformly distributed across the circle. In the present study we explore whether variation in the distribution of locations affects how the circle is categorized. Other things being equal, categories that capture high density regions in a stimulus space should contribute most to accuracy of estimation. However, precision of boundaries is also important to accuracy; with imprecise boundaries stimuli may be misclassified, leading to large errors in estimation. We found that people use the same spatial categories regardless of the distribution of the locations. We argue that this spatial organization nevertheless can maximize the accuracy of estimates because vertical and horizontal category boundaries are the most exact, minimizing misclassification of stimuli.     

Comparing Data Sets: Implicit Summaries of the Statistical Properties of Number Sets

Comparing datasets, that is, sets of numbers in context, is a critical skill in higher order cognition. Although much is known about how people compare single numbers, little is known about how number sets are represented and compared. We investigated how subjects compared datasets that varied in their statistical properties, including ratio of means, coefficient of variation, and number of observations, by measuring eye fixations, accuracy, and confidence when assessing differences between number sets. Results indicated that participants implicitly create and compare approximate summary values that include information about mean and variance, with no evidence of explicit calculation. Accuracy and confidence increased, while the number of fixations decreased as sets became more distinct (i.e., as mean ratios increase and variance decreases), demonstrating that the statistical properties of datasets were highly related to comparisons. The discussion includes a model proposing how reasoners summarize and compare datasets within the architecture for approximate number representation.