Intuitive Sociology: Children Recognize Decision-Making Structures and Prefer Groups With Less-Concentrated Power.

From an early age, children recognize that people belong to social groups. However, not all groups are structured in the same way. The current study asked whether children recognize and distinguish among different decision-making structures. If so, do they prefer some decision-making structures over others? In these studies, children were told stories about two groups that went camping. In the hierarchical group, one character made all the decisions; in the egalitarian group, each group member made one decision. Without being given explicit information about the group's structures, 6- to 8-year-old children, but not 4- and 5-year-old children, recognized that the two groups had different decision-making structures and preferred to interact with the group where decision-making was shared. Children also inferred that a new member of the egalitarian group would be more generous than a new member of the hierarchical group. Thus, from an early age, children's social reasoning includes the ability to compare social structures, which may be foundational for later complex political and moral reasoning.

Rationalization may improve predictability rather than accuracy.

We present a theoretical and an empirical challenge to Cushman's claim that rationalization is adaptive because it allows humans to extract more accurate beliefs from our non-rational motivations for behavior. Rationalization sometimes generates more adaptive decisions by making our beliefs about the world less accurate. We suggest that the most important adaptive advantage of rationalization is instead that it increases our predictability (and therefore attractiveness) as potential partners in cooperative social interactions.

Infants Choose Those Who Defer in Conflicts.

For humans and other social species, social status matters: it determines who wins access to contested resources, territory, and mates [1-11]. Human infants are sensitive to dominance status cues [12, 13]. They expect conflicts to be won by larger individuals [14], those with more allies [15], and those with a history of winning [16-18]. But being sensitive to status cues is not enough; individuals must also use status information when deciding whom to approach and whom to avoid [19]. In many non-human species, low-status individuals avoid high-status individuals and in so doing avoid the threat of aggression [20-23]. In these species, high-status individuals commit random acts of aggression toward subordinates [23] and even commit infanticide [24-26]. However, for less reactively aggressive species [27, 28], high-status individuals may be good coalition partners. This is especially true for humans, where high-status individuals can provide guidance, protection, and knowledge to subordinates [2, 29, 30]. Indeed, human adults [31-33], human toddlers [34], and adult bonobos [35] prefer high-status individuals to low-status ones. Here, we present 6 experiments testing whether 10- to 16-month-old human infants choose high- or low-status individuals-specifically, winners or yielders in zero-sum conflicts-and find that infants choose puppets who yield. Intriguingly, toddlers just 6 months older choose the winners of such conflicts [34]. This suggests that, although humans start out like many other species, avoiding high-status others, we shift in toddlerhood to approaching high-status individuals, consistent with the idea that, for humans, high-status individuals can provide benefits to low-status ones.

Toddlers prefer those who win but not when they win by force.

Social hierarchies occur across human societies, so all humans must navigate them. Infants can detect when one individual outranks another1-3, but it is unknown whether they approach others based on their social status. This paper presents a series of seven experiments investigating whether toddlers prefer high- or low-ranking individuals. Toddlers aged 21-31 months watched a zero-sum, right-of-way conflict between two puppets, in which one puppet 'won' because the other yielded the way. Of the 23 toddlers who participated, 20 reached for the puppet that 'won'. However, when one puppet used force and knocked the other puppet down in order to win, 18 out of 22 toddlers reached for the puppet that 'lost'. Five follow-up experiments ruled out alternative explanations for these results. The findings suggest that humans, from a very early age, not only recognize relative status but also incorporate status into their decisions about whether to approach or avoid others, in a way that differs from our nearest primate relatives4.

Exploring the relation between people's theories of intelligence and beliefs about brain development.

A person's belief about whether intelligence can change (called their implicit theory of intelligence) predicts something about that person's thinking and behavior. People who believe intelligence is fixed (called entity theorists) attribute failure to traits (i.e., "I failed the test because I'm not smart.") and tend to be less motivated in school; those who believe intelligence is malleable (called incremental theorists) tend to attribute failure to behavior (i.e., "I failed the test because I didn't study.") and are more motivated in school. In previous studies, researchers have characterized participants as either entity or incremental theorists based on their agreement or disagreement with three statements. The present study further explored the theories-of-intelligence (TOI) construct in two ways: first, we asked whether these theories are coherent, in the sense that they show up not only in participants' responses to the three standard assessment items, but on a broad range of questions about intelligence and the brain. Second, we asked whether these theories are discrete or continuous. In other words, we asked whether people believe one thing or the other (i.e., that intelligence is malleable or fixed), or if there is a continuous range of beliefs (i.e., people believe in malleability to a greater or lesser degree). Study (1) asked participants a range of general questions about the malleability of intelligence and the brain. Study (2) asked participants more specific questions about the brains of a pair of identical twins who were separated at birth. Results showed that TOI are coherent: participants' responses to the three standard survey items are correlated with their responses to questions about the brain. But the theories are not discrete: although responses to the three standard survey items fell into a bimodal distribution, responses to the broader range of questions fell into a normal distribution suggesting the theories are continuous.

Is there really a link between exact-number knowledge and approximate number system acuity in young children?

Although everyone perceives approximate numerosities, some people make more accurate estimates than others. The accuracy of this estimation is called approximate number system (ANS) acuity. Recently, several studies have reported that individual differences in young children's ANS acuity are correlated with their knowledge of exact numbers such as the word 'six' (Mussolin et al., 2012, Trends Neurosci. Educ., 1, 21; Shusterman et al., 2011, Connecting early number word knowledge and approximate number system acuity; Wagner & Johnson, 2011, Cognition, 119, 10; see also Abreu-Mendoza et al., 2013, Front. Psychol., 4, 1). This study argues that this correlation should not be trusted. It seems to be an artefact of the procedure used to assess ANS acuity in children. The correlation arises because (1) some experimental designs inadvertently allow children to answer correctly based on the size (rather than the number) of dots in the display and/or (2) young children with little exact-number knowledge may not understand the phrase 'more dots' to mean numerically more. When the task is modified to make sure that children respond on the basis of numerosity, the correlation between ANS acuity and exact-number knowledge in normally developing children disappears.

On the relation between grammatical number and cardinal numbers in development.

This mini-review focuses on the question of how the grammatical number system of a child's language may help the child learn the meanings of cardinal number words (e.g., "one" and "two"). Evidence from young children learning English, Russian, Japanese, Mandarin, Slovenian, or Saudi Arabic suggests that trajectories of number-word learning differ for children learning different languages. Children learning English, which distinguishes between singular and plural, seem to learn the meaning of the cardinal number "one" earlier than children learning Japanese or Mandarin, which have very little singular/plural marking. Similarly, children whose languages have a singular/dual/plural system (Slovenian and Saudi Arabic) learn the meaning of "two" earlier than English-speaking children. This relation between grammatical and cardinal number may shed light on how humans acquire cardinal-number concepts. There is an ongoing debate about whether mental symbols for small cardinalities (concepts for "oneness," "twoness," etc.) are innate or learned. Although an effect of grammatical number on number-word learning does not rule out nativist accounts, it seems more consistent with constructivist accounts, which portray the number-learning process as one that requires significant conceptual change.

Are bilingual children better at ignoring perceptually misleading information? A novel test.

Does speaking more than one language help a child perform better on certain types of cognitive tasks? One possibility is that bilingualism confers either specific or general cognitive advantages on tasks that require selective attention to one dimension over another (e.g. Bialystok, ; Hilchey & Klein, ). Other studies have looked for such an advantage but found none (e.g. Morton & Harper, ; Paap & Greenberg, ). The present study compared monolingual and bilingual children's performance on a numerical discrimination task, which required children to ignore area and attend to number. Ninety-two children, ages 3 to 6 years, were asked which of two arrays of dots had 'more dots'. Half of the trials were congruent, where the numerically greater array was also larger in total area, and half were incongruent, where the numerically greater array was smaller in total area. All children performed better on congruent than on incongruent trials. Older children were more successful than younger children at ignoring area in favor of number. Bilingual children did not perform differently from monolingual children either in number discrimination itself (i.e. identifying which array had more dots) or at selectively attending to number. The present study thus finds no evidence of a bilingual advantage on this task for children of this age.

Children's number-line estimation shows development of measurement skills (not number representations).

Children's understanding of numbers is often assessed using a number-line task, where the child is shown a line labeled with 0 at one end and a higher number (e.g., 100) at the other end. The child is then asked where on the line some intermediate number (e.g., 70) should go. Performance on this task changes predictably during childhood, and this has often been interpreted as evidence of a change in the child's psychological representation of integer quantities. The present article presents theoretical and empirical evidence that the change in number-line performance actually reflects the development of measurement skills used in the task. We compare 2 versions of the number-line task: the bounded version used in the literature and a new, unbounded version. Results indicate that it is only children's performance on the bounded task (which requires subtraction or division) that changes markedly with age. In contrast, children's performance on the unbounded task (which requires only addition) remains fairly constant as they get older. Thus, developmental changes in performance on the traditional bounded number-line task likely reflect the growth of task-specific measurement skills rather than changes in the child's understanding of numerical quantities.

The idea of an exact number: children's understanding of cardinality and equinumerosity.

Understanding what numbers are means knowing several things. It means knowing how counting relates to numbers (called the cardinal principle or cardinality); it means knowing that each number is generated by adding one to the previous number (called the successor function or succession), and it means knowing that all and only sets whose members can be placed in one-to-one correspondence have the same number of items (called exact equality or equinumerosity). A previous study (Sarnecka & Carey, 2008) linked children's understanding of cardinality to their understanding of succession for the numbers five and six. This study investigates the link between cardinality and equinumerosity for these numbers, finding that children either understand both cardinality and equinumerosity or they understand neither. This suggests that cardinality and equinumerosity (along with succession) are interrelated facets of the concepts five and six, the acquisition of which is an important conceptual achievement of early childhood.

A number of options: rationalist, constructivist, and Bayesian insights into the development of exact-number concepts.

The question of how human beings acquire exact-number concepts has interested cognitive developmentalists since the time of Piaget. The answer will owe something to both the rationalist and constructivist traditions. On the one hand, some aspects of numerical cognition (e.g. approximate number estimation and the ability to track small sets of one to four individuals) are innate or early-developing and are shared widely among species. On the other hand, only humans create representations of exact, large numbers such as 42, as distinct from both 41 and 43. These representations seem to be constructed slowly, over a period of months or years during early childhood. The task for researchers is to distinguish the innate representational resources from those that are constructed, and to characterize the construction process. Bayesian approaches can be useful to this project in at least three ways: (1) As a way to analyze data, which may have distinct advantages over more traditional methods (e.g. making it possible to find support for a nuli hypothesis); (2) as a way of modeling children's performance on specific tasks: Peculiarities of the task are captured as a prior; the child's knowledge is captured in the way the prior is updated; and behavior is captured as a posterior distribution; and (3) as a way of modeling learning itself, by providing a formal account of how learners might choose among alternative hypotheses.

Number-concept acquisition and general vocabulary development.

How is number-concept acquisition related to overall language development? Experiments 1 and 2 measured number-word knowledge and general vocabulary in a total of 59 children, ages 30-60 months. A strong correlation was found between number-word knowledge and vocabulary, independent of the child's age, contrary to previous results (D. Ansari et al., 2003). This result calls into question arguments that (a) the number-concept creation process is scaffolded mainly by visuo-spatial development and (b) that language only becomes integrated after the concepts are created (D. Ansari et al., 2003). Instead, this may suggest that having a larger nominal vocabulary helps children learn number words. Experiment 3 shows that the differences with previous results are likely due to changes in how the data were analyzed.

An Excel sheet for inferring children's number-knower levels from give-N data.

Number-knower levels are a series of stages of number concept development in early childhood. A child's number-knower level is typically assessed using the give-N task. Although the task procedure has been highly refined, the standard ways of analyzing give-N data remain somewhat crude. Lee and Sarnecka (Cogn Sci 34:51-67, 2010, in press) have developed a Bayesian model of children's performance on the give-N task that allows knower level to be inferred in a more principled way. However, this model requires considerable expertise and computational effort to implement and apply to data. Here, we present an approximation to the model's inference that can be computed with Microsoft Excel. We demonstrate the accuracy of the approximation and provide instructions for its use. This makes the powerful inferential capabilities of the Bayesian model accessible to developmental researchers interested in estimating knower levels from give-N data.

Find the picture of eight turtles: a link between children's counting and their knowledge of number word semantics.

An essential part of understanding number words (e.g., eight) is understanding that all number words refer to the dimension of experience we call numerosity. Knowledge of this general principle may be separable from knowledge of individual number word meanings. That is, children may learn the meanings of at least a few individual number words before realizing that all number words refer to numerosity. Alternatively, knowledge of this general principle may form relatively early and proceed to guide and constrain the acquisition of individual number word meanings. The current article describes two experiments in which 116 children (2½- to 4-year-olds) were given a Word Extension task as well as a standard Give-N task. Results show that only children who understood the cardinality principle of counting successfully extended number words from one set to another based on numerosity-with evidence that a developing understanding of this concept emerges as children approach the cardinality principle induction. These findings support the view that children do not use a broad understanding of number words to initially connect number words to numerosity but rather make this connection around the time that they figure out the cardinality principle of counting.

Number-knower levels in young children: insights from Bayesian modeling.

Lee and Sarnecka (2010) developed a Bayesian model of young children's behavior on the Give-N test of number knowledge. This paper presents two new extensions of the model, and applies the model to new data. In the first extension, the model is used to evaluate competing theories about the conceptual knowledge underlying children's behavior. One, the knower-levels theory, is basically a "stage" theory involving real conceptual change. The other, the approximate-meanings theory, assumes that the child's conceptual knowledge is relatively constant, although performance improves over time. In the second extension, the model is used to ask whether the same latent psychological variable (a child's number-knower level) can simultaneously account for behavior on two tasks (the Give-N task and the Fast-Cards task) with different performance demands. Together, these two demonstrations show the potential of the Bayesian modeling approach to improve our understanding of the development of human cognition.

A Model of Knower-Level Behavior in Number-Concept Development.

We develop and evaluate a model of behavior on the Give-N task, a commonly-used measure of young children's number knowledge. Our model uses the knower-level theory of how children represent numbers. To produce behavior on the Give-N task, the model assumes children start out with a base-rate that make some answers more likely a priori than others, but is updated on each experimental trial in a way that depends on the interaction between the experimenter's request and the child's knower-level. We formalize this process as a generative graphical model, so that the parameters-including the base-rate distribution and each child's knower-level-can be inferred from data using Bayesian methods. Using this approach, we evaluate the model on previously published data from 82 children spanning the whole developmental range. The model provides an excellent fit to these data, and the inferences about the base-rate and knower-levels are interpretable and insightful. We discuss how our modeling approach can be extended to other developmental tasks, and can be used to help evaluate alternative theories of number representation against the knower-level theory.

Levels of number knowledge during early childhood.

Researchers have long disagreed about whether number concepts are essentially continuous (unchanging) or discontinuous over development. Among those who take the discontinuity position, there is disagreement about how development proceeds. The current study addressed these questions with new quantitative analyses of children's incorrect responses on the Give-N task. Using data from 280 children, ages 2 to 4 years, this study showed that most wrong answers were simply guesses, not counting or estimation errors. Their mean was unrelated to the target number, and they were lower-bounded by the numbers children actually knew. In addition, children learned the number-word meanings one at a time and in order; they treated the number words as mutually exclusive; and once they figured out the cardinal principle of counting, they generalized this principle to the rest of their count list. Findings support the 'discontinuity' account of number development in general and the 'knower-levels' account in particular.

How counting represents number: what children must learn and when they learn it.

This study compared 2- to 4-year-olds who understand how counting works (cardinal-principle-knowers) to those who do not (subset-knowers), in order to better characterize the knowledge itself. New results are that (1) Many children answer the question "how many" with the last word used in counting, despite not understanding how counting works; (2) Only children who have mastered the cardinal principle, or are just short of doing so, understand that adding objects to a set means moving forward in the numeral list whereas subtracting objects mean going backward; and finally (3) Only cardinal-principle-knowers understand that adding exactly 1 object to a set means moving forward exactly 1 word in the list, whereas subset-knowers do not understand the unit of change.

Generic Language in Parent-Child Conversations.

Generic knowledge concerns kinds of things (e.g., birds fly; a chair is for sitting; gold is a metal). Past research demonstrated that children spontaneously develop generic knowledge by preschool age. The present study examines when and how children learn to use the multiple devices provided by their language to express generic knowledge. We hypothesize that children assume, in the absence of specifying information or context, that nouns refer to generic kinds, as a default. Thus, we predict that (a) Children should talk about kinds from an early age. (b) Children should learn generic forms with only minimal parental scaffolding. (c) Children should recognize a variety of different linguistic forms as generic. Results from longitudinal samples of adult-child conversations support all three hypotheses. We also report individual differences in the use of generics, suggesting that children differ in their tendency to form the abstract generalizations so expressed.

From grammatical number to exact numbers: early meanings of 'one', 'two', and 'three' in English, Russian, and Japanese.

This study examined whether singular/plural marking in a language helps children learn the meanings of the words 'one,' 'two,' and 'three.' First, CHILDES data in English, Russian (which marks singular/plural), and Japanese (which does not) were compared for frequency, variability, and contexts of number-word use. Then young children in the USA, Russia, and Japan were tested on Counting and Give-N tasks. More English and Russian learners knew the meaning of each number word than Japanese learners, regardless of whether singular/plural cues appeared in the task itself (e.g., "Give two apples" vs. "Give two"). These results suggest that the learning of "one," "two" and "three" is supported by the conceptual framework of grammatical number, rather than that of integers.