Symbolic arithmetic is fundamental to science, technology and economics, but its acquisition by children typically requires years of effort, instruction and drill1,2. When adults perform mental arithmetic, they activate nonsymbolic, approximate number representations3,4, and their performance suffers if this nonsymbolic system is impaired5. Nonsymbolic number representations also allow adults, children, and even infants to add or subtract pairs of dot arrays and to compare the resulting sum or difference to a third array, provided that only approximate accuracy is required6–10. Here (...) we report that young children, who have mastered verbal counting and are on the threshold of arithmetic instruction, can build on their nonsymbolic number system to perform symbolic addition and subtraction11–15. Children across a broad socio-economic spectrum solved symbolic problems involving approximate addition or subtraction of large numbers, both in a laboratory test and in a school setting. Aspects of symbolic arithmetic therefore lie within the reach of children who have learned no algorithms for manipulating numerical symbols. Our findings help to delimit the sources of children’s difficulties learning symbolic arithmetic, and they suggest ways to enhance children’s engagement with formal mathematics. We presented children with approximate symbolic arithmetic problems in a format that parallels previous tests of non-symbolic arithmetic in preschool children8,9. In the first experiment, five- to six-year-old children were given problems such as ‘‘If you had twenty-four stickers and I gave you twenty-seven more, would you have more or less than thirty-five stickers?’’. Children performed well above chance (65.0%, t1952.77, P 5 0.012) without resorting to guessing or comparison strategies that could serve as alternatives to arithmetic. Children who have been taught no symbolic arithmetic therefore have some ability to perform symbolic addition problems. The children’s performance nevertheless fell short of performance on non-symbolic arithmetic tasks using equivalent addition problems with numbers presented as arrays of dots and with the addition operation conveyed by successive motions of the dots into a box (71.3% correct, F1,345 4.26, P 5 0.047)8.. (shrink)

This chapter argues that human and animal minds indeed depend on a collection of domain-specific, task-specific, and encapsulated cognitive systems: on a set of cognitive ‘modules’ in Fodor's sense. It also argues that human and animal minds are endowed with domain-general, central systems that orchestrate the information delivered by core knowledge systems. The chapter begins by reviewing the literature on spatial reorientation in animals and in young children, arguing that spatial reorientation bears the hallmarks of core knowledge and of modularity. (...) It then considers studies of older children and adults, arguing that human spatial representations change qualitatively over development and show capacities not found in any other species. Finally, it presents two new experiments that investigate the role of emerging spatial language in uniquely human navigation performance. (shrink)

Geometry defines entities that can be physically realized in space, and our knowledge of abstract geometry may therefore stem from our representations of the physical world. Here, we focus on Euclidean geometry, the geometry historically regarded as “natural”. We examine whether humans possess representations describing visual forms in the same way as Euclidean geometry – i.e., in terms of their shape and size. One hundred and twelve participants from the U.S. (age 3–34 years), and 25 participants from the Amazon (age (...) 5–67 years) were asked to locate geometric deviants in panels of 6 forms of variable orientation. Participants of all ages and from both cultures detected deviant forms defined in terms of shape or size, while only U.S. adults drew distinctions between mirror images (i.e. forms differing in “sense”). Moreover, irrelevant variations of sense did not disrupt the detection of a shape or size deviant, while irrelevant variations of shape or size did. At all ages and in both cultures, participants thus retained the same properties as Euclidean geometry in their analysis of visual forms, even in the absence of formal instruction in geometry. These findings show that representations of planar visual forms provide core intuitions on which humans’ knowledge in Euclidean geometry could possibly be grounded. (shrink)

Under many circumstances, children and adult rats reorient themselves through a process which operates only on information about the shape of the environment (e.g., Cheng, 1986; Hermer & Spelke, 1996). In contrast, human adults relocate themselves more flexibly, by conjoining geometric and nongeometric information to specify their position (Hermer & Spelke, 1994). The present experiments used a dual-task method to investigate the processes that underlie the flexible conjunction of information. In Experiment 1, subjects reoriented themselves flexibly when they (...) performed no secondary task, but they reoriented themselves like children and adult rats when they engaged in verbal shadowing of continuous speech. In Experiment 2, subjects who engaged in nonverbal shadowing of a continuous rhythm reoriented like nonshadowing subjects, suggesting that the interference effect in Experiment 1 did not stem from general limits on working memory or attention but from processes more specific to language. In further experiments, verbally shadowing subjects detected and remembered both nongeometric information (Experiment 3) and geometric information (Experiments 1, 2, and 4), but they failed to conjoin the two types of information to specify the positions of objects (Experiment 4). Together. (shrink)

Adults and infants display a robust ability to perceive the unity of a center-occluded object when the visible ends of the object undergo common motion (e.g. Kellman, P.J., Spelke, E.S., 1983. Perception of partly occluded objects in infancy. Cognitive Psychology 15, 483±524). Ecologically oriented accounts of this ability focus on the primacy of motion in the perception of segregated objects, but Gestalt theory suggests a broader possibility: observers may perceive object unity by detecting patterns of synchronous change, of which (...) common motion is a special case. We investigated this possibility with observations of adults and 4-month-old infants. Participants viewed a center-occluded object whose visible surfaces were either misaligned or aligned, stationary or moving, and unchanging or synchronously changing in color or bright- ness in various temporal patterns (e.g. ¯ashing). Both alignment and common motion con- tributed to adults' perception of object unity, but synchronous color changes did not. For infants, motion was an important determinant of object unity, but other synchronous changes and edge alignment were not. When a stationary object with aligned edges underwent syn- chronous changes in color or brightness, infants showed high levels of attention to the object, but their perception of its unity appeared to be indeterminate. An inherent preference for fast over slow ¯ash rates, and a novelty preference elicited by a change in rate, both indicated that infants detected the synchronous changes, although they failed to use them as information for object unity. These ®ndings favor ecologically oriented accounts of object perception in which surface motion plays a privileged role. Ó 1999 Elsevier Science B.V. All rights reserved. (shrink)

For many centuries, philosophers and scientists have pondered the origins and nature of human intuitions about the properties of points, lines, and figures on the Euclidean plane, with most hypothesizing that a system of Euclidean concepts either is innate or is assembled by general learning processes. Recent research from cognitive and developmental psychology, cognitive anthropology, animal cognition, and cognitive neuroscience suggests a different view. Knowledge of geometry may be founded on at least two distinct, evolutionarily ancient, core cognitive systems for (...) representing the shapes of large-scale, navigable surface layouts and of small-scale, movable forms and objects. Each of these systems applies to some but not all perceptible arrays and captures some but not all of the three fundamental Euclidean relationships of distance (or length), angle, and direction (or sense). Like natural number (Carey, 2009), Euclidean geometry may be constructed through the productive combination of representations from these core systems, through the use of uniquely human symbolic systems. (shrink)

While endorsing Gopnik's proposal that studies of the emergence and modification of scientific theories and studies of cognitive development in children are mutually illuminating, we offer a different picture of the beginning points of cognitive development from Gopnik's picture of "theories all the way down." Human infants are endowed with several distinct core systems of knowledge which are theory-like in some, but not all, important ways. The existence of these core systems of knowledge has implications for the joint research program (...) between philosophers and psychologists that Gopnik advocates and we endorse. A few lessons already gained from this program of research are sketched. (shrink)

Research on human infants has begun to shed light on early-developing processes for segmenting perceptual arrays into objects. Infants appear to perceive objects by analyzing three-dimensional surface arrangements and motions. Their perception does not accord with a general tendency to maximize figural goodness or to attend to nonaccidental geometric relations in visual arrays. Object perception does accord with principles governing the motions of material bodies: Infants divide perceptual arrays into units that move as connected wholes, that move separately from one (...) another, that tend to maintain their size and shape over motion, and that tend to act upon each other only on contact. These findings suggest that o general representation of object unity and boundaries is interposed between representations of surfaces and representations of objects of familiar kinds. The processes that construct this representation may be related to processes of physical reasoning. (shrink)

Much research supports the existence of an Approximate Number System (ANS) that is recruited by infants, children, adults, and non-human animals to generate coarse, non-symbolic representations of number. This system supports simple arithmetic operations such as addition, subtraction, and ordering of amounts. The current study tests whether an intuition of a more complex calculation, division, exists in an indigene group in the Amazon, the Mundurucu, whose language includes no words for large numbers. Mundurucu children were presented with a video event (...) depicting a division transformation of halving, in which pairs of objects turned into single objects, reducing the array's numerical magnitude. Then they were tested on their ability to calculate the outcome of this division transformation with other large-number arrays. The Mundurucu children effected this transformation even when non-numerical variables were controlled, performed above chance levels on the very first set of test trials, and exhibited performance similar to urban children who had access to precise number words and a surrounding symbolic culture. We conclude that a halving calculation is part of the suite of intuitive operations supported by the ANS. (shrink)

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.

Complex cognitive skills such as reading and calculation and complex cognitive achievements such as formal science and mathematics may depend on a set of building block systems that emerge early in human ontogeny and phylogeny. These core knowledge systems show characteristic limits of domain and task specificity: Each serves to represent a particular class of entities for a particular set of purposes. By combining representations from these systems, however human cognition may achieve extraordinary flexibility. Studies of cognition in human infants (...) and in nonhuman primates therefore may contribute to understanding unique features of human knowledge. 2020 APA, all rights reserved). (shrink)

Experiments with young infants provide evidence for early-developing capacities to represent physical objects and to reason about object motion. Early physical reasoning accords with 2 constraints at the center of mature physical conceptions: continuity and solidity. It fails to accord with 2 constraints that may be peripheral to mature conceptions: gravity and inertia. These experiments suggest that cognition develops concurrently with perception and action and that development leads to the enrichment of conceptions around an unchanging core. The experiments challenge claims (...) that cognition develops on a foundation of perceptual or motor experience, that initial conceptions are inappropriate to the world, and that initial conceptions are abandoned or radically.. (shrink)

Five-year-old children categorized as skilled versus unskilled counters were given verbal estimation and number word comprehension tasks with numerosities 20 – 120. Skilled counters showed a linear relation between number words and nonsymbolic numerosities. Unskilled counters showed the same linear relation for smaller numbers to which they could count, but not for larger number words. Further tasks indicated that unskilled counters failed even to correctly order large number words differing by a 2 : 1 ratio, whereas they performed well on (...) this task with smaller numbers, and performed well on a nonsymbolic ordering task with the same numerosities. These findings provide evidence that large, approximate numerosity representations become linked to number words around the time that children learn to count to those words reliably. (shrink)

Although debates continue, studies of cognition in infancy suggest that knowledge begins to emerge early in life and constitutes part of humans' innate endowment. Early-developing knowledge appears to be both domain-specific and task-specific, it appears to capture fundamental constraints on ecologically important classes of entities in the child's environment, and it appears to remain central to the commonsense knowledge systems of adults.

What are the brain and cognitive systems that allow humans to play baseball, compute square roots, cook soufflés, or navigate the Tokyo subways? It may seem that studies of human infants and of non-human animals will tell us little about these abilities, because only educated, enculturated human adults engage in organized games, formal mathematics, gourmet cooking, or map-reading. In this chapter, we argue against this seemingly sensible conclusion. When human adults exhibit complex, uniquely human, culture-specific skills, they draw on a (...) set of psychological and neural mechanisms with two distinctive properties: they evolved before humanity and thus are shared with other animals, and they emerge early in human development and thus are common to infants, children, and adults. These core knowledge systems form the building blocks for uniquely human skills. Without them we wouldn’t be able to learn about different kinds of games, mathematics, cooking, or maps. To understand what is special about human intelligence, therefore, we must study both the core knowledge systems on which it rests and the mechanisms by which these systems are orchestrated to permit new kinds of concepts and cognitive processes. What is core knowledge? A wealth of research on non-human primates and on human infants suggests that a system of core knowledge is characterized by four properties (Hauser, 2000; Spelke, 2000). First, it is domain-specific: each system functions to represent particular kinds of entities such as conspecific agents, manipulable objects, places in the environmental layout, and numerosities. Second, it is task-specific: each system uses its representations to address specific questions about the world, such as “who is this?” [face recognition], “what does this do?” [categorization of artifacts], “where am I?” [spatial orientation], and “how many are here?” [enumeration]. Third, it is relatively encapsulated: each uses only a subset of the information delivered by an animal’s input systems and sends information only to a subset of the animal’s output systems. (shrink)

The mapping of numbers onto space is fundamental to measurement and to mathematics. Is this mapping a cultural invention or a universal intuition shared by all humans regardless of culture and education? We probed number-space mappings in the Mundurucu, an Amazonian indigene group with a reduced numerical lexicon and little or no formal education. At all ages, the Mundurucu mapped symbolic and nonsymbolic numbers onto a logarithmic scale, whereas Western adults used linear mapping with small or symbolic numbers and logarithmic (...) mapping when numbers were presented nonsymbolically under conditions that discouraged counting. This indicates that the mapping of numbers onto space is a universal intuition and that this initial intuition of number is logarithmic. The concept of a linear number line appears to be a cultural invention that fails to develop in the absence of formal education. (shrink)

A new method was devised to test object permanence in young infants. Fivemonth-old infants were habituated to a screen that moved back and forth through a 180-degree arc, in the manner of a drawbridge. After infants reached habituation, a box was centered behind the screen. Infants were shown two test events: a possible event and an impossible event. In the possible event, the screen stopped when it reached the occluded box; in the impossible event, the screen moved through the space (...) occupied by the box. The results indicated that infants looked reliably longer at the impossible than at the possible event. This hnding suggested that infants (1) understood that the box continued to exist, in its same location, after it was occluded by the screen, and (2) expected the screen to stop against the occluded box and were surprised, or puzzled, when it failed to do so. A control experiment in which the box was placed next to the screen provided support for this interpretation of the results. Together, the results of these experiments indicate that, contrary to Piaget’s (1954) claims, infants as young as 5 months of age understand that objects continue to exist when occluded. The results, also indicate that 5-month-old infants realize that solid objects do not move through the space occupied by other solid objects. (shrink)

What leads humans to divide the social world into groups, preferring their own group and disfavoring others? Experiments with infants and young children suggest these tendencies are based on predispo- sitions that emerge early in life and depend, in part, on natural language. Young infants prefer to look at a person who previously spoke their native language. Older infants preferentially accept toys from native-language speakers, and preschool children preferentially select native-language speakers as friends. Variations in accent are sufficient to evoke (...) these social preferences, which are observed in infants before they produce or comprehend speech and are exhibited by children even when they comprehend the foreign-accented speech. Early-developing preferences for native-language speakers may serve as a foundation for later-developing preferences and conflicts among social groups. (shrink)

Three experiments investigated changes from 15 to 30 months of age in children’s (N = 114) mastery of relations between an object and an aperture, supporting surface, or form. When choosing between objects to insert into an aperture, older children selected objects of an appropriate size and shape, but younger children showed little selectivity. Further experiments probed the sources of younger children’s difficulty by comparing children’s performance placing a target object in a hole, on a 2-dimensional form, or atop another (...) solid object. Together, the findings suggest that some factors limiting adults’ object representations, including the difficulty of comparing the shapes of positive and negative spaces and of representing shapes in 3 dimensions, contribute to young children’s errors in manipulating objects. (shrink)

For millennia, human beings have believed that it is morally wrong to judge others by the fortuitous or unfortunate events that befall them or by the actions of another person. Rather, an individual’s own intended, deliberate actions should be the basis of his or her evaluation, reward, and punishment. In a series of studies, the authors investigated whether such rules guide the judgments of children. The first 3 studies demonstrated that children view lucky others as more likely than unlucky others (...) to perform intentional good actions. Children similarly assess the siblings of lucky others as more likely to perform intentional good actions than the siblings of unlucky others. The next 3 studies demonstrated that children as young as 3 years believe that lucky people are nicer than unlucky people. The final 2 studies found that Japanese children also demonstrate a robust preference for the lucky and their associates. These findings are discussed in relation to M. J. Lerner’s (1980) just-world theory and J. Piaget’s (1932/1965) immanent-justice research and in relation to the development of intergroup attitudes. (shrink)

This article considers 3 claims that cognitive sex differ- ences account for the differential representation of men and women in high-level careers in mathematics and sci- ence: (a) males are more focused on objects from the beginning of life and therefore are predisposed to better learning about mechanical systems; (b) males have a pro- file of spatial and numerical abilities producing greater aptitude for mathematics; and (c) males are more variable in their cognitive abilities and therefore predominate at the upper (...) reaches of mathematical talent. Research on cogni- tive development in human infants, preschool children, and students at all levels fails to support these claims. Instead, it provides evidence that mathematical and scientific rea- soning develop from a set of biologically based cognitive capacities that males and females share. These capacities lead men and women to develop equal talent for mathe- matics and science. (shrink)

Because human languages vary in sound and meaning, children must learn which distinctions their language uses. For speech perception, this learning is selective: initially infants are sensitive to most acoustic distinctions used in any language1–3, and this sensitivity reflects basic properties of the auditory system rather than mechanisms specific to language4–7; however, infants’ sensitivity to non-native sound distinctions declines over the course of the first year8. Here we ask whether a similar process governs learning of word meanings. We investigated the (...) sensitivity of 5-month-old infants in an English-speaking environment to a conceptual distinction that is marked in Korean but not English; that is, the distinction between ‘tight’ and ‘loose’ fit of one object to another9,10. Like adult Korean speakers but unlike adult English speakers, these infants detected this distinction and divided a continuum of motion-into-contact actions into tightand loose-fit categories. Infants’ sensitivity to this distinction is linked to representations of object mechanics11that are shared by non-human animals12–14. Language learning therefore seems to develop by linking linguistic forms to universal, pre-existing representations of sound and meaning. Our research focuses on the crosscutting conceptual distinctions between actions producing loose- and tight-fitting contact relationships (compare left and right columns in Fig. 1a) and actions producing containment versus support relationships (compare first and second rows in Fig. 1a). As early as Korean and English children begin to talk about such actions, they categorize them differently from one another and similarly to Korean- and Englishspeaking adults9,15. Moreover, English and Korean adults differ in their performance on non-linguistic categorization tasks involving heterogeneous examples of these actions, in accord with the differing semantics of their languages16,17, whereas the performance of young children on such tasks has been mixed9,10,18,19.. (shrink)

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. (shrink)