Numerosities and space; indeed a cognitive illusion! A reply to de Hevia and Spelke (2009)

de Hevia and Spelke (de Hevia and Spelke (2009). Spontaneous mapping of number and space in adults and young children, Cognition, 110, 198–207) investigated the mapping of number onto space. To this end, they introduced a non-symbolic flanker task. Here subjects have to bisect a line that is flanked by a 2-dot and a 9-dot array. Similar to the symbolic line bisection task, a bias towards the larger numerosity was observed. We re-investigated these results both by creating new flanker stimuli that controlled for different (non-numerical) stimulus properties and by developing a new measurement tool. We demonstrate that the bisection bias was caused by the larger area subtended by the 9-dot array compared to the 2-dot array and not numerosity. Our study puts constraints on the results of the study by de Hevia and Spelke. The role of visual cues in numerosity processing in general is discussed.     

An association between understanding cardinality and analog magnitude representations in preschoolers

The preschool years are a time of great advances in children’s numerical thinking, most notably as they master verbal counting. The present research assessed the relation between analog magnitude representations and cardinal number knowledge in preschool-aged children to ask two questions: (1) Is there a relationship between acuity in the analog magnitude system and cardinality proficiency? (2) Can evidence of the analog magnitude system be found within mappings of number words children have not successfully mastered? To address the first question, Study 1 asked three- to five-year-old children to discriminate side-by-side dot arrays with varying differences in numerical ratio, as well as to complete an assessment of cardinality. Consistent with the analog magnitude system, children became less accurate at discriminating dot arrays as the ratio between the two numbers approached one. Further, contrary to prior work with preschoolers, a significant correlation was found between cardinal number knowledge and non-symbolic numerical discrimination. Study 2 aimed to look for evidence of the analog magnitude system in mappings to the words in preschoolers’ verbal counting list. Based on a modified give-a-number task ( [Wynn, 1990] and [Wynn, 1992] ), three- to five-year-old children were asked to give quantities between 1 and 10 as many times as possible in order to assess analog magnitude variability within their developing cardinality understanding. In this task, even children who have not yet induced the cardinality principle showed signs of analog representations in their understanding of the verbal count list. Implications for the contribution of analog magnitude representations towards mastery of the verbal count list are discussed in light of the present work.     

How lexical is the lexicon? Evidence for integrated auditory memory representations

Previous research has shown that lexical representations must include not only linguistic information (what word was said), but also indexical information (how it was said, and by whom). The present work demonstrates that even this expansion is not sufficient. Seemingly irrelevant information, such as an unattended background sound, is retained in memory and can facilitate subsequent speech perception. We presented participants with spoken words paired with environmental sounds (e.g., a phone ringing), and had them make an “animate/inanimate” decision for each word. Later performance identifying filtered versions of the words was impaired to a similar degree if the voice changed or if the environmental sound changed. Moreover, when quite dissimilar words were used at exposure and test, we observed the same result when we reversed the roles of the words and the environmental sounds. The experiments also demonstrated limits to these effects, with no benefit from repetition. Theoretically, our results support two alternative possibilities: (1) Lexical representations are memory representations, and are not walled off from those for other sounds. Indexical effects reflect simply one type of co-occurrence that is incorporated into such representations. (2) The existing literature on indexical effects does not actually bear on lexical representations – voice changes, like environmental sounds heard with a word, produce implicit memory effects that are not tied to the lexicon. We discuss the evidence and implications of these two theoretical alternatives.     

How numbers mean: Comparing random walk models of numerical cognition varying both encoding processes and underlying quantity representations

How do people derive meaning from numbers? Here, we instantiate the primary theories of numerical representation in computational models and compare simulated performance to human data. Specifically, we fit simulated data to the distributions for correct and incorrect responses, as well as the pattern of errors made, in a traditional “relative quantity” task. The results reveal that no current theory of numerical representation can adequately account for the data without additional assumptions. However, when we introduce repeated, error-prone sampling of the stimulus (e.g., Cohen, 2009) superior fits are achieved when the underlying representation of integers reflects linear spacing with constant variance. These results provide new insights into (i) the detailed nature of mental numerical representation, and, (ii) general perceptual processes implemented by the human visual system.     

Early lexical development of children raised in institutional care in Russia

Children abandoned to institutions display a host of developmental delays, including those involving general cognition and language. The majority of published studies focus on children over 3 years of age; little is known about whether these delays may be detected earlier when children undergo rapid lexical development. To investigate the early language development of children raised in institutional settings in the Russian Federation, we compared a group of children in institutional care (n = 36; 8–35 months) to their age-matched peers raised in biological families, who have never been institutionalized (n = 72) using the Russian version of the CDI. The results suggest that institutionalization is associated with pronounced delays in children's early language development with large and robust effect sizes. Among children with a history of institutionalization, these delays are also associated with difficulties in Daily Living skills, communication, and socialization.     

Fractions as percepts? Exploring cross-format distance effects for fractional magnitudes

This study presents evidence that humans have intuitive, perceptually based access to the abstract fraction magnitudes instantiated by nonsymbolic ratio stimuli. Moreover, it shows these perceptually accessed magnitudes can be easily compared with symbolically represented fractions. In cross-format comparisons, participants picked the larger of two ratios. Ratios were presented either symbolically as fractions or nonsymbolically as paired dot arrays or as paired circles. Response patterns were consistent with participants comparing specific analog fractional magnitudes independently of the particular formats in which they were presented. These results pose a challenge to accounts that argue human cognitive architecture is ill-suited for processing fractions. Instead, it seems that humans can process nonsymbolic ratio magnitudes via perceptual routes and without recourse to conscious symbolic algorithms, analogous to the processing of whole number magnitudes. These findings have important implications for theories regarding the nature of human number sense – they imply that fractions may in some sense be natural numbers, too.