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.

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.

In order to navigate the social world, children need to understand and make predictions about how people will interact with one another. Throughout most of human history, social groups have been prominently marked by kinship relations, but few experiments have examined children’s knowledge of and reasoning about kinship relations. In the current studies, we investigated how 3- to 5-year-old children understand kinship relations, compared to non-kin relations between friends, with questions such as, “Who has the same grandmother?” We also tested how children expect people to interact based on their relations to one another, with questions such as “Who do you think Cara would like to share her treat with?” Both in a storybook context and in a richer context presenting more compelling cues to kinship using face morphology, 3- and 4-year-old children failed to show either robust explicit conceptual distinctions between kin and friends, or expectations of behavior favoring kin over friends, even when asked about their own social partners. By 5 years, children’s understanding of these relations improved, and they showed some expectation that others will preferentially aid siblings over friends. Together, these findings suggest that explicit understanding of kinship develops slowly over the preschool years.