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.     

Magnitude comparison in preschoolers: what counts? Influence of perceptual variables

This study examined numerosity comparison in 3-year-old children. Predictions derived from the analog numerical model and the object-file model were contrasted by testing the effects of size and ratio between numerosities to be compared. Different perceptual controls were also introduced to evaluate the hypothesis that comparison by preschoolers is based on correlated perceptual variables rather than on number per se. Finally, the relation between comparison performance and verbal counting knowledge was investigated. Results showed no evidence that preschoolers use an analog number magnitude or an object-file mechanism to compare numerosities. Rather, their inability to compare sets controlled for surface area suggests that they rely on perceptual cues. Furthermore, the development of numerosity-based representations seems to be related to some understanding of the cardinality concept.     

What counts as knowing? The development of conceptual and procedural knowledge of counting from kindergarten through Grade 2

The development of conceptual and procedural knowledge about counting was explored for children in kindergarten, Grade 1, and Grade 2 (N = 255). Conceptual knowledge was assessed by asking children to make judgments about three types of counts modeled by an animated frog: standard (correct) left-to-right counts, incorrect counts, and unusual counts. On incorrect counts, the frog violated the word-object correspondence principle. On unusual counts, the frog violated a conventional but inessential feature of counting, for example, starting in the middle of the array of objects. Procedural knowledge was assessed using speed and accuracy in counting objects. The patterns of change for procedural knowledge and conceptual knowledge were different. Counting speed and accuracy (procedural knowledge) improved with grade. In contrast, there was a curvilinear relation between conceptual knowledge and grade that was further moderated by children's numeration skills (as measured by a standardized test); the most skilled children gradually increased their acceptance of unusual counts over grade, whereas the least skilled children decreased their acceptance of these counts. These results have implications for studying conceptual and procedural knowledge about mathematics.     

The development of ordinal numerical knowledge in infancy

A critical question in cognitive science concerns how numerical knowledge develops. One essential component of an adult concept of number is ordinality: the greater than and less than relationships between numbers. Here it is shown in two experiments that 11-month-old infants successfully discriminated, whereas 9-month-old infants failed to discriminate, sequences of numerosities that descended in numerical value from sequences that increased in numerical value. These results suggest 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 develops between 9 and 11 months of age. In an additional experiment 9-month-old infants succeeded at discriminating the ordinal direction of sequences that varied in the size of a single square rather than in number, suggesting that a capacity for non-numerical ordinal judgments may develop before a capacity for ordinal numerical judgments. These data raise many questions about how infants represent number and what happens between 9 and 11 months to support ordinal numerical judgments.     

Salamanders (<Emphasis Type="Italic">Plethodon cinereus</Emphasis>) go for more: rudiments of number in an amphibian

Techniques traditionally used in developmental research with infants have been widely used with nonhuman primates in the investigation of comparative cognitive abilities. Recently, researchers have shown that human infants and monkeys select the larger of two numerosities in a spontaneous forced-choice discrimination task. Here we adopt the same method to assess in a series of experiments spontaneous choice of the larger of two numerosities in a species of amphibian, red-backed salamanders (Plethodon cinereus). The findings indicate that salamanders "go for more," just like human babies and monkeys. This rudimentary capacity is a type of numerical discrimination that is spontaneously present in this amphibian. Electronic Publication     

Conscious control over the content of unconscious cognition

Visual stimuli (primes) presented too briefly to be consciously identified can nevertheless affect responses to subsequent stimuli - an instance of unconscious cognition. There is a lively debate as to whether such priming effects originate from unconscious semantic processing of the primes or from reactivation of learned motor responses that conscious stimuli afford during preceding practice. In four experiments we demonstrate that unconscious stimuli owe their impact neither to automatic semantic categorization nor to memory traces of preceding stimulus-response episodes, but to their match with pre-specified cognitive action-trigger conditions. The intentional creation of such triggers allows actors to control the way unconscious stimuli bias their behaviour.     

Number and type of toys affect joint attention of mothers and infants

Establishing joint attention with a caregiver on a physical object provides an optimal environment for language learning for infants. In the present study, we investigated whether 12-month-olds and their mothers establish higher quality joint attention interactions in the presence of fewer compared to more toys. As a secondary goal, we investigated how different types of toys affect how mother-infant dyads establish joint attention. In a five-minute free play setting, mothers and infants participated in either Five Toy (n = 48) or Twelve Toy (n = 33) groups. They were given organizational (i.e., toys that require arrangement of parts), responsive (i.e., toys that emit sounds via manipulation), and symbolic toys (i.e., toys that elicit pretend play). Results showed that compared to the Twelve Toy group, joint attention interactions in the Five Toy group were less frequent, lasted longer, were more likely to be initiated by maternal following than by maternal directing of infants’ attention, and more likely to be coordinated in which infants demonstrated awareness of the mothers’ simultaneous attentional focus by looking at their mothers, vocalizing, or turn-taking. We further found longer joint attention durations on organizational compared to symbolic toys, which were preferred to a lesser extent by the dyads. With responsive toys, mothers were more likely to initiate joint attention by following their infants’ attention. Joint attention interactions lasted longer and were more likely to be coordinated in the second half compared to the first half of the play session, suggesting that over time it became easier for the mothers and infants to settle on certain toys for more elaborate play. In sum, mothers and infants establish higher-quality joint attention with fewer toys in general and with organizational toys in particular.     

Too much to count on: impaired very small numbers in corticobasal degeneration

Patients with corticobasal degeneration (CBD) have calculation impairments. This study examined whether impaired number knowledge depends on verbal mediation. We focused particularly on knowledge of very small numbers, where there is a precise relationship between a cardinality and its number concept, but little hypothesized role for verbal mediation. We evaluated accuracy and reaction time (RT) for matching dot arrays and Arabic numerals involving smaller (2-4) and larger (5-9) cardinalities in non-aphasic patients with CBD (n=16), frontotemporal dementia (FTD; n=23), and healthy controls (n=15). CBD were less accurate and slowed at judging smaller Arabic numeral-dot array stimuli compared to FTD patients and controls. Moreover, only CBD showed longer RTs judging successively larger number-dot array pairs among the smaller cardinalities. Difficulty judging very small numbers is impaired in CBD, suggesting degraded representation of precise number knowledge that does not depend on language functioning.     

Mapping numerical magnitudes onto symbols: the numerical distance effect and individual differences in children's mathematics achievement

Although it is often assumed that abilities that reflect basic numerical understanding, such as numerical comparison, are related to children’s mathematical abilities, this relationship has not been tested rigorously. In addition, the extent to which symbolic and nonsymbolic number processing play differential roles in this relationship is not yet understood. To address these questions, we collected mathematics achievement measures from 6- to 8-year-olds as well as reaction times from a numerical comparison task. Using the reaction times, we calculated the size of the numerical distance effect exhibited by each child. In a correlational analysis, we found that the individual differences in the distance effect were related to mathematics achievement but not to reading achievement. This relationship was found to be specific to symbolic numerical comparison. Implications for the role of basic numerical competency and the role of accessing numerical magnitude information from Arabic numerals for the development of mathematical skills and their impairment are discussed.