Young children distinguish the impossible from the merely improbable.

From infancy, children show heightened interest in events that are impossible or improbable, relative to likely events. Do young children represent impossible and improbable events as points on a continuum of possibility, or do they instead treat them as categorically distinct? Here, we compared 2- and 3-y-old children's learning (N = 335) following nearly identical events that were equi-probable, improbable, or impossible. We found that children learned significantly better following impossible than possible events, no matter how unlikely.

Children's representation of coincidence.

People relish thinking about coincidences-we puzzle over their meanings and delight in conveying our experiences of them to others. But whereas some research has begun to explore how coincidences are represented by adults, little is known about the early development of these representations. Here we explored factors influencing coincidence representations in both adults and children.

What aspects of counting help infants attend to numerosity?

Recent work shows that 18-month old infants understand that counting is numerically relevant-infants who see objects counted are more likely to represent the approximate number of objects in the array than infants who see the objects labeled but not counted. Which aspects of counting signal infants to attend to numerosity in this way? Here we asked whether infants rely on familiarity with the count words in their native language, or on procedures instantiated by the counting routine, independent of specific tokens. In three experiments (N = 48), we found that 18-month old infants from English-speaking households successfully distinguished four hidden objects from two when the objects were counted correctly, regardless of their familiarity with the count words (i.

"Yay! Yuck!" toddlers use others' emotional responses to reason about hidden objects.

Young children show sensitivity to others' emotions, discriminating between facial expressions and using them to help guide their behavior. Beyond providing information about how others are feeling, emotional expressions also can support inferences about the non-social world. Here, in four experiments, we investigated 18- to 28-month-old children's ability to use others' emotional responses to reason about physical objects.

Violations of expectation trigger infants to search for explanations.

Infants look longer and explore more following violations-of-expectation, but the reasons for these surprise-induced behaviors are unclear. One possibility is that expectancy violations heighten arousal generally, thereby increasing infants' post-surprise activity. Another possibility is that infants' exploration reflects the search for an explanation for the surprising event.

Online measures of looking and learning in infancy.

Infants in laboratory settings look longer at events that violate their expectations, learn better about objects that behave unexpectedly, and match utterances to the objects that likely elicited them. The paradigms revealing these behaviors have become cornerstones of research on preverbal cognition. However, little is known about whether these canonical behaviors are observed outside laboratory settings.

Neural basis of approximate number in congenital blindness.

Although humans are unique among animals in their ability to manipulate symbolic numbers, we share with other species an approximate number sense that allows us to estimate and compare the number of objects or events in a set, such as the number of apples in a tree. Our ability to discriminate the numerosity of two sets decreases as the ratio between them becomes smaller (e.g.

Stable individual differences in infants' responses to violations of intuitive physics.

Infants look longer at impossible or unlikely events than at possible events. While these responses to expectancy violations have been critical for understanding early cognition, interpreting them is challenging because infants' responses are highly variable. This variability has been treated as an unavoidable nuisance inherent to infant research.

Dynamic changes in numerical acuity in 4-month-old infants.

Preverbal infants represent the approximate numerosity of visual and auditory arrays: By 6 months old, they reliably discriminate eight dots or tones from 16 (a 1:2 ratio), but not eight from 12 (a 2:3 ratio). The precision of this approximate number sense improves gradually over childhood and into adulthood. However, less is known about numerical abilities in younger infants, and in particular, whether there is developmental change in the number sense in the first half year of life.

When Not Choosing Leads to Not Liking: Choice-Induced Preference in Infancy.

The question of how people's preferences are shaped by their choices has generated decades of research. In a classic example, work on cognitive dissonance has found that observers who must choose between two equally attractive options subsequently avoid the unchosen option, suggesting that not choosing the item led them to like it less. However, almost all of the research on such choice-induced preference focuses on adults, leaving open the question of how much experience is necessary for its emergence.

Effects of Visual Training of Approximate Number Sense on Auditory Number Sense and School Math Ability.

Research with children and adults suggests that people's math performance is predicted by individual differences in an evolutionarily ancient ability to estimate and compare numerical quantities without counting (the approximate number system or ANS). However, previous work has almost exclusively used visual stimuli to measure ANS precision, leaving open the possibility that the observed link might be driven by aspects of visuospatial competence, rather than the amodal ANS. We addressed this possibility in an ANS training study.

Emergence of the Link Between the Approximate Number System and Symbolic Math Ability.

Experimentally manipulating Approximate Number System (ANS) precision has been found to influence children's subsequent symbolic math performance. Here in three experiments (N = 160; 81 girls; 3-5 year old) we replicated this effect and examined its duration and developmental trajectory. We found that modulation of 5-year-olds' ANS precision continued to affect their symbolic math performance after a 30-min delay.

Is Empiricism Innate? Preference for Nurture Over Nature in People's Beliefs About the Origins of Human Knowledge.

The origins of human knowledge are an enduring puzzle: what parts of what we know require learning, and what depends on intrinsic structure? Although the nature-nurture debate has been a central question for millennia and has inspired much contemporary research in psychology and neuroscience, it remains unknown whether people share intuitive, prescientific theories about the answer. Here we report that people ( = 1,188) explain fundamental perceptual and cognitive abilities by appeal to learning and instruction, rather than genes or innateness, even for abilities documented in the first days of life. U.

Infants recognize counting as numerically relevant.

Children do not understand the meanings of count words like "two" and "three" until the preschool years. But even before knowing the meanings of these individual words, might they recognize that counting is "about" the dimension of number? Here in five experiments, we asked whether infants already associate counting with quantities. We measured 14- and 18-month olds' ability to remember different numbers of hidden objects that either were or were not counted by an experimenter before hiding.

Violations of Core Knowledge Shape Early Learning.

Research on cognitive development has revealed that even the youngest minds detect and respond to events that adults find surprising. These surprise responses suggest that infants have a basic set of "core" expectations about the world that are shared with adults and other species. However, little work has asked what purpose these surprise responses serve.

Numerical cognition is resilient to dramatic changes in early sensory experience.

Humans and non-human animals can approximate large visual quantities without counting. The approximate number representations underlying this ability are noisy, with the amount of noise proportional to the quantity being represented. Numerate humans also have access to a separate system for representing exact quantities using number symbols and words; it is this second, exact system that supports most of formal mathematics.

Infants use linguistic group distinctions to chunk items in memory.

Although the capacity of infants' working memory is highly constrained, infants can overcome this limit via chunking; for example, they can use spatial cues to group individual objects into sets, thereby increasing memory efficiency. Here we investigated the use of abstract social knowledge as a basis for chunking. In four experiments, we asked whether 16-month-olds can use their sensitivity to distinctions between languages to efficiently chunk an array.

Approximate number sense correlates with math performance in gifted adolescents.

Nonhuman animals, human infants, and human adults all share an Approximate Number System (ANS) that allows them to imprecisely represent number without counting. Among humans, people differ in the precision of their ANS representations, and these individual differences have been shown to correlate with symbolic mathematics performance in both children and adults. For example, children with specific math impairment (dyscalculia) have notably poor ANS precision.

Expectancy violations promote learning in young children.

Children, including infants, have expectations about the world around them, and produce reliable responses when these expectations are violated. However, little is known about how such expectancy violations affect subsequent cognition. Here we tested the hypothesis that violations of expectation enhance children's learning.

A dissociation between small and large numbers in young children's ability to "solve for x" in non-symbolic math problems.

Solving for an unknown addend in problems like 5+x=17 is challenging for children. Yet, previous work (Kibbe & Feigenson, 2015) found that even before formal math education, young children, aged 4- to 6-years, succeeded when problems were presented using non-symbolic collections of objects rather than symbolic digits. This reveals that the Approximate Number System (ANS) can support pre-algebraic intuitions.

Better together: Multiple lines of evidence for a link between approximate and exact number representations: A reply to Merkley, Matejko, and Ansari.

The results of our recent experiments suggest that temporarily modulating children's approximate number system (ANS) precision leads to a domain-specific change in their symbolic math performance (Journal of Experimental Child Psychology, 2016, Vol. 147, pp. 82-99).

Absence of visual experience modifies the neural basis of numerical thinking.

In humans, the ability to reason about mathematical quantities depends on a frontoparietal network that includes the intraparietal sulcus (IPS). How do nature and nurture give rise to the neurobiology of numerical cognition? We asked how visual experience shapes the neural basis of numerical thinking by studying numerical cognition in congenitally blind individuals. Blind (n = 17) and blindfolded sighted (n = 19) participants solved math equations that varied in difficulty (e.

The precision of mapping between number words and the approximate number system predicts children's formal math abilities.

Children can represent number in at least two ways: by using their non-verbal, intuitive approximate number system (ANS) and by using words and symbols to count and represent numbers exactly. Furthermore, by the time they are 5years old, children can map between the ANS and number words, as evidenced by their ability to verbally estimate numbers of items without counting. How does the quality of the mapping between approximate and exact numbers relate to children's math abilities? The role of the ANS-number word mapping in math competence remains controversial for at least two reasons.

Visual working memory capacity increases between ages 3 and 8 years, controlling for gains in attention, perception, and executive control.

Research in adults has aimed to characterize constraints on the capacity of Visual Working Memory (VWM), in part because of the system's broader impacts throughout cognition. However, less is known about how VWM develops in childhood. Existing work has reached conflicting conclusions as to whether VWM storage capacity increases after infancy, and if so, when and by how much.

Changing the precision of preschoolers' approximate number system representations changes their symbolic math performance.

From early in life, humans have access to an approximate number system (ANS) that supports an intuitive sense of numerical quantity. Previous work in both children and adults suggests that individual differences in the precision of ANS representations correlate with symbolic math performance. However, this work has been almost entirely correlational in nature.