Human cognition is founded, in part, on four systems for representing objects, actions, number, and space. It may be based, as well, on a ﬁfth system for representing social partners. Each system has deep roots in human phylogeny and ontogeny, and it guides and shapes the mental lives of adults. Converging research on human infants, non-human primates, children and adults in diverse cultures can aid both understanding of these systems and attempts to overcome their limits.
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.
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)
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)
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)
Does geometry constitues a core set of intuitions present in all humans, regarless of their language or schooling ? We used two non verbal tests to probe the conceptual primitives of geometry in the Munduruku, an isolated Amazonian indigene group. Our results provide evidence for geometrical intuitions in the absence of schooling, experience with graphic symbols or maps, or a rich language of geometrical terms.
All humans share a universal, evolutionarily ancient approximate number system (ANS) that estimates and combines the numbers of objects in sets with ratio-limited precision. Interindividual variability in the acuity of the ANS correlates with mathematical achievement, but the causes of this correlation have never been established. We acquired psychophysical measures of ANS acuity in child and adult members of an indigene group in the Amazon, the Mundurucú, who have a very restricted numerical lexicon and highly variable access to mathematics education. (...) By comparing Mundurucú subjects with and without access to schooling, we found that education significantly enhances the acuity with which sets of concrete objects are estimated. These results indicate that culture and education have an important effect on basic number perception. We hypothesize that symbolic and nonsymbolic numerical thinking mutually enhance one another over the course of mathematics instruction. (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)
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)
Previous research with adults suggests that a catalog of minimally counterintuitive concepts, which underlies supernatural or religious concepts, may constitute a cognitive optimum and is therefore cognitively encoded and culturally transmitted more successfully than either entirely intuitive concepts or maximally counterintuitive concepts. This study examines whether children's concept recall similarly is sensitive to the degree of conceptual counterintuitiveness (operationalized as a concept's number of ontological domain violations) for items presented in the context of a fictional narrative. Seven- to nine-year-old children (...) who listened to a story including both intuitive and counterintuitive concepts recalled the counterintuitive concepts containing one (Experiment 1) or two (Experiment 2), but not three (Experiment 3), violations of intuitive ontological expectations significantly more and in greater detail than the intuitive concepts, both immediately after hearing the story and 1 week later. We conclude that one or two violations of expectation may be a cognitive optimum for children: They are more inferentially rich and therefore more memorable, whereas three or more violations diminish memorability for target concepts. These results suggest that the cognitive bias for minimally counterintuitive ideas is present and active early in human development, near the start of formal religious instruction. This finding supports a growing literature suggesting that diverse, early-emerging, evolved psychological biases predispose humans to hold and perform religious beliefs and practices whose primary form and content is not derived from arbitrary custom or the social environment alone. (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)
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)
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)
A series of experiments investigated the effect of speakers’ language, accent, and race on children’s social preferences. When presented with photographs and voice recordings of novel children, 5-year-old children chose to be friends with native speakers of their native language rather than foreign-language or foreign-accented speakers. These preferences were not exclusively due to the intelligibility of the speech, as children found the accented speech to be comprehensible, and did not make social distinctions between foreign-accented and foreign-language speakers. Finally, children chose (...) same-race children as friends when the target children were silent, but they chose other-race children with a native accent when accent was pitted against race. A control experiment provided evidence that children’s privileging of accent over race was not due to the relative familiarity of each dimension. The results, discussed in an evolutionary framework, suggest that children preferentially evaluate others along dimensions that distinguished social groups in prehistoric human societies. (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)
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)
Four-month-old infants sometimes can perceive the unity of a partly hidden object. In each of a series of experiments, infants were habituated to one object whose top and bottom were visible but whose center was occluded by a nearer object. They were then tested with a fully visible continuous object and with two fully visible object pieces with a gap where the occluder had been. Pattems of dishabituation suggested that infants perceive the boundaries of a partly hidden object by analyzing (...) the movements of its surfaces: infants perceived a connected object when its ends moved in a common translation behind the occluder. Infants do not appear to perceive a connected object by analyzing the colors and forms of surfaces: they did not perceive a connected object when its visible parts were stationary, its color was homogeneous, its edges were aligned, and its shape was simple and regular. These findings do not support the thesis, from gestalt psychology, that object perception first arises as a consequence of a tendency to perceive the simplest, most regular configuration, or the Piagetian thesis that object perception depends on the prior coordination of action. Perception of objects may depend on an inherent conception of what an object is. (shrink)
Humans possess two nonverbal systems capable of representing numbers, both limited in their representational power: the first one represents numbers in an approximate fashion, and the second one conveys information about small numbers only. Conception of exact large numbers has therefore been thought to arise from the manipulation of exact numerical symbols. Here, we focus on two fundamental properties of the exact numbers as prerequisites to the concept of EXACT NUMBERS : the fact that all numbers can be generated by (...) a successor function and the fact that equality between numbers can be defined in an exact fashion. We discuss some recent findings assessing how speakers of Munduruc (an Amazonian language), and young Western children (3-4 years old) understand these fundamental properties of numbers. (shrink)
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)
Research on human infants, adult nonhuman primates, and children and adults in diverse cultures provides converging evidence for four systems at the foundations of human knowledge. These systems are domain specific and serve to represent both entities in the perceptible world (inanimate manipulable objects and animate agents) and entities that are more abstract (numbers and geometrical forms). Human cognition may be based, as well, on a fifth system for representing social partners and for categorizing the social world into groups. Research (...) on infants and children may contribute both to understanding of these systems and to attempts to overcome misconceptions that they may foster. (shrink)
& Behavioral and brain imaging research indicates that human infants, humans adults, and many nonhuman animals represent large nonsymbolic numbers approximately, discriminating between sets with a ratio limit on accuracy. Some behavioral evidence, especially with human infants, suggests that these representations differ from representations of small numbers of objects. To investigate neural signatures of this distinction, event-related potentials were recorded as adult humans passively viewed the sequential presentation of dot arrays in an adaptation paradigm. In two studies, subjects viewed successive (...) arrays of a single number of dots interspersed with test arrays presenting the same or a different number; numerical range (small numerical quantities 1–3 vs. large numerical.. (shrink)
Kant argued that Euclidean geometry is synthesized on the basis of an a priori intuition of space. This proposal inspired much behavioral research probing whether spatial navigation in humans and animals conforms to the predictions of Euclidean geometry. However, Euclidean geometry also includes concepts that transcend the perceptible, such as objects that are infinitely small or infinitely large, or statements of necessity and impossibility. We tested the hypothesis that certain aspects of nonperceptible Euclidian geometry map onto intuitions of space that (...) are present in all humans, even in the absence of formal mathematical education. Our tests probed intuitions of points, lines, and surfaces in participants from an indigene group in the Amazon, the Mundurucu, as well as adults and age-matched children controls from the United States and France and younger US children without education in geometry. The responses of Mundurucu adults and children converged with that of mathematically educated adults and children and revealed an intuitive understanding of essential properties of Euclidean geometry. For instance, on a surface described to them as perfectly planar, the Mundurucu's estimations of the internal angles of triangles added up to ∼180 degrees, and when asked explicitly, they stated that there exists one single parallel line to any given line through a given point. These intuitions were also partially in place in the group of younger US participants. We conclude that, during childhood, humans develop geometrical intuitions that spontaneously accord with the principles of Euclidean geometry, even in the absence of training in mathematics. (shrink)