Person:

Spelke, Elizabeth

Although infants and animals respond to the approximate number of elements in visual, auditory, and tactile arrays, only human children and adults have been shown to possess abstract numerical representations that apply to entities of all kinds (e.g., 7 samurai, seas, or sins). Do abstract numerical concepts depend on language or culture, or do they form a part of humans' innate, core knowledge? Here we show that newborn infants spontaneously associate stationary, visual-spatial arrays of 4–18 objects with auditory sequences of events on the basis of number. Their performance provides evidence for abstract numerical representations at the start of postnatal experience.

Observations and experiments show that human adults preferentially share resources with close relations, with people who have shared with them (reciprocity), and with people who have shared with others (indirect reciprocity). These tendencies are consistent with evolutionary theory but could also reflect the shaping effects of experience or instruction in complex, cooperative and competitive societies. Here we report evidence for these three tendencies in 3.5 year old children, despite their limited experience with complex cooperative networks. Three pillars of mature cooperative behavior therefore appear to have roots extending deep into human development.

In learning mathematics, children must master fundamental logical relationships, including the inverse relationship between addition and subtraction. At the start of elementary school, children lack generalized understanding of this relationship in the context of exact arithmetic problems: they fail to judge, for example, that 12 + 9 − 9 yields 12. Here, we investigate whether preschool children’s approximate number knowledge nevertheless supports understanding of this relationship. Five-year-old children were more accurate on approximate large-number arithmetic problems that involved an inverse transformation than those that did not, when problems were presented in either non-symbolic or symbolic form. In contrast they showed no advantage for problems involving an inverse transformation when exact arithmetic was involved. Prior to formal schooling, children therefore show generalized understanding of at least one logical principle of arithmetic. The teaching of mathematics may be enhanced by building on this understanding.

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/her evaluation, reward and punishment. In a series of studies we investigate whether such rules guide the judgments of children. The first three studies demonstrate 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 three studies demonstrate that children as young as 3 years believe that lucky people are nicer than unlucky people. The final two studies find that Japanese children also demonstrate a robust preference for the lucky and their associates. These findings are discussed in relation to Lerner’s just world theory and Piaget’s immanent justice research and in relation to the development of intergroup attitudes.

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.

The performance of the Mundurucu on the number-space task may exemplify a general competence for drawing analogies between space and other linear dimensions, but Mundurucu participants spontaneously chose number when other dimensions were available. Response placement may not reflect the subjective scale for numbers, but Cantlon et al.’s proposal of a linear scale with scalar variability requires questionable additional hypotheses.

Geometric form perception has been extensively studied in human children, but it has not been systematically characterized from the perspective of formal geometry. Here, we present the findings of three experiments that use a deviant detection task to test children’s and adults’ sensitivity to geometric invariants in a variety of visual displays. Children as young as 4 years of age analyzed shapes by detecting relationships of distance and angle but not by detecting the relationships that distinguish an object from its mirror image (hereafter, sense). Patterns of visual form analysis showed high invariance over development: the properties that were least detectable by children also posed the greatest difficulty for adults. In general, sensitivity to all tested properties improved with age, with an asymptote at about 12 years, before the onset of instruction in formal geometry. When presented with a carefully controlled set of forms that varied exclusively in length, angle or sense, children were found to develop sensitivity to these properties at different rates, responding first to length, then to angle, and last to sense. Between 8 and 10 years of age, moreover, children began to confer a privileged status to the relation of perpendicularity. Geometric competence therefore appears to emerge as an interplay between developmentally invariant, core intuitions and later acquired distinctions.

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 Mundurucu (an Amazonian language), and young western children (3-4 years old) understand these fundamental properties of numbers.

Two experiments investigated the influence of socially conveyed emotions and speech on infants' choices among food. After watching films in which two unfamiliar actresses each spoke while eating a different kind of food, 12-month-old infants were allowed to choose between the two foods. In Experiment 1, infants selected a food endorsed by a speaker of their native language who displayed positive affect over a food endorsed by a foreign-language speaker who displayed negative affect. In Experiment 2, both actresses displayed positive affect, but they spoke in different languages, and infants again selected the food associated with the speaker of their native language. The findings contrast with previous research in which infants and toddlers have shown little selectivity when presented with foods that differ in their intrinsic properties such as color, texture, and familiarity. Although infants may lack capacities for evaluating foods on their own, they do look to other people for guidance in food selection.

Research on navigation has shown that humans and laboratory animals recover their sense of orientation primarily by detecting geometric properties of large-scale surface layouts (e.g. room shape), but the reasons for the primacy of layout geometry have not been clarified. In four experiments, we tested whether 4-year-old children reorient by the geometry of extended wall-like surfaces because such surfaces are large and perceived as stable, because they serve as barriers to vision or to locomotion, or because they form a single, connected geometric figure. Disoriented children successfully reoriented by the shape of an arena formed by surfaces that were short enough to see and step over. In contrast, children failed to reorient by the shape of an arena defined by large and stable columns or by connected lines on the floor. We conclude that preschool children's reorientation is not guided by the functional relevance of the immediate environmental properties, but rather by a specific sensitivity to the geometric properties of the extended three-dimensional surface layout.