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.     

Are there limits to collectivism? Culture and children's reasoning about lying to conceal a group transgression

This study explored the effects of collectivism on lying to conceal a group transgression. Seven‐, 9‐, and 11‐year‐old US and Chinese children (N=374) were asked to evaluate stories in which protagonists either lied or told the truth about their group's transgression and were then asked about either the protagonist's motivations or justification for their own evaluations. Previous research suggests that children in collectivist societies such as China find lying for one's group to be more acceptable than do children from individualistic societies such as the United States. The current study provides evidence that this is not always the case: Chinese children in this study viewed lies told to conceal a group's transgressions less favourably than did US children. An examination of children's reasoning about protagonists' motivations for lying indicated that children in both countries focused on an impact to self when discussing motivations for protagonists to lie for their group. Overall, results suggest that children living in collectivist societies do not always focus on the needs of the group. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical predictors of arithmetic success in grades 1–6

Math relies on mastery and integration of a wide range of simpler numerical processes and concepts. Recent work has identified several numerical competencies that predict variation in math ability. We examined the unique relations between eight basic numerical skills and early arithmetic ability in a large sample (N = 1391) of children across grades 1–6. In grades 1–2, children's ability to judge the relative magnitude of numerical symbols was most predictive of early arithmetic skills. The unique contribution of children's ability to assess ordinality in numerical symbols steadily increased across grades, overtaking all other predictors by grade 6. We found no evidence that children's ability to judge the relative magnitude of approximate, nonsymbolic numbers was uniquely predictive of arithmetic ability at any grade. Overall, symbolic number processing was more predictive of arithmetic ability than nonsymbolic number processing, though the relative importance of symbolic number ability appears to shift from cardinal to ordinal processing.     

Learning strategy differentially impacts memory connections in children and adults

Even once children can accurately remember their experiences, they nevertheless struggle to use those memories in flexible new ways—as in when drawing inferences. However, it remains an open question as to whether the developmental differences observed during both memory formation and inference itself represent a fundamental limitation on children's learning mechanisms, or rather their deployment of suboptimal strategy. Here, 7–9-year-old children (N = 154) and young adults (N = 130) first formed strong memories for initial (AB) associations and then engaged in one of three learning strategies as they viewed overlapping (BC) pairs. We found that being told to integrate—combine ABC during learning—both significantly improved children's ability to explicitly relate the indirectly associated A and C items during inference and protected the underlying pair memories from forgetting. However, this finding contrasted with implicit evidence for memory-to-memory connections: Adults and children both formed A-C links prior to any knowledge of an inference test—yet for children, such links were most apparent when they were told to simply encode BC, not integrate. Moreover, the accessibility of such implicit links differed between children and adults, with adults using them to make explicit inferences but children only doing so for well-established direct AB pairs. These results suggest that while a lack of integration strategy may explain a large share of the developmental differences in explicit inference, children and adults nevertheless differ in both the circumstances under which they connect interrelated memories and their ability to later leverage those links to inform flexible behaviours.

Research Highlights

• Children and adults view AB and BC pairs related through a shared item, B. This provides an opportunity for learners to connect A–C in memory.
• Being encouraged to integrate ABC during learning boosted performance on an explicit test of A–C connections (children and adults) and protected from forgetting (children).
• Children and adults differed in when implicit A–C connections were formed—occurring primarily when told to separately encode BC (children) versus integrate (adults), respectively.
• Adults used implicit A–C connections to facilitate explicit judgments, while children did not. Our results suggest developmental differences in the learning conditions promoting memory-to-memory connections.

     

Developmental changes in visual object recognition between 18 and 24 months of age

Two experiments examined developmental changes in children's visual recognition of common objects during the period of 18 to 24 months. Experiment 1 examined children's ability to recognize common category instances that presented three different kinds of information: (1) richly detailed and prototypical instances that presented both local and global shape information, color, textural and featural information, (2) the same rich and prototypical shapes but no color, texture or surface featural information, or (3) that presented only abstract and global representations of object shape in terms of geometric volumes. Significant developmental differences were observed only for the abstract shape representations in terms of geometric volumes, the kind of shape representation that has been hypothesized to underlie mature object recognition. Further, these differences were strongly linked in individual children to the number of object names in their productive vocabulary. Experiment 2 replicated these results and showed further that the less advanced children's object recognition was based on the piecemeal use of individual features and parts, rather than overall shape. The results provide further evidence for significant and rapid developmental changes in object recognition during the same period children first learn object names. The implications of the results for theories of visual object recognition, the relation of object recognition to category learning, and underlying developmental processes are discussed.     

The Shape of Things: The Origin of Young Children’s Knowledge of the Names and Properties of Geometric Forms

How do toddlers learn the names of geometric forms? Previous work suggests that preschoolers have fragmentary knowledge and that defining properties are not understood until well into elementary school. The current study investigated when children first begin to understand shape names and how they apply those labels to unusual instances. We tested 25- and 30-month-old children’s (N = 30 each) understanding of names for canonical shapes (commonly encountered instances, e.g., equilateral triangles), noncanonical shapes (more irregular instances, e.g., scalene triangles), and embedded shapes (shapes within a larger picture, e.g., triangular slices of pizza). At 25 months, children knew very few names, including those for canonical shapes. By 30 months, however, children had acquired more shape names and were beginning to apply them to some of the less typical instances of the shapes. Possible mechanisms driving this initial development of shape knowledge and implications of that development for school readiness are explored.     

Children's intuitive sense of number develops independently of their perception of area,density, length,and time

Young children can quickly and intuitively represent the number of objects in a visual scene through the Approximate Number System (ANS). The precision of the ANS – indexed as the most difficult ratio of two numbers that children can reliably discriminate – is well known to improve with development: whereas infants require relatively large ratios to discriminate number, children can discriminate finer and finer changes in number between toddlerhood and early adulthood. Which factors drive the developmental improvements in ANS precision? Here, we investigate the influence of four non‐numeric dimensions – area, density, line length, and time – on ANS development, exploring the degree to which the ANS develops independently from these other dimensions, from inhibitory control, and from domain‐general factors such as attention and working memory that are shared between these tasks. A sample of 185 children between the ages of 2 and 12 years completed five discrimination tasks: approximate number, area, density, length, and time. We report three main findings. First, logistic growth models applied to both accuracy and Weber fractions (w; an index of ANS precision) across age reveal distinct developmental trajectories across the five dimensions: while area and length develop by adolescence, time and density do not develop fully until early adulthood, with ANS precision developing at an intermediate rate. Second, we find that ANS precision develops independently of the other four dimensions, which in turn develop independently of the ANS. Third, we find that ANS precision also develops independently from individual differences in inhibitory control (indexed as the difference in accuracy and w between Congruent and Incongruent ANS trials). Together, these results are the first to provide evidence for domain‐specific improvements in ANS precision, and place children's maturing perception of number, space, and time into a broader developmental context.     

Spatial associations in relational reasoning: Evidence for a SNARC-like effect

Relational reasoning (A > B, B > C, therefore A > C) shares a number of similarities with numerical cognition, including a common behavioural signature, the symbolic distance effect. Just as reaction times for evaluating relational conclusions decrease as the distance between two ordered objects increases, people need less time to compare two numbers when they are distant (e.g., 2 and 8) than when they are close (e.g., 3 and 4). Given that some remain doubtful about such analogical representations in relational reasoning, we determine whether numerical cognition and relational reasoning have other overlapping behavioural effects. Here, using relational reasoning problems that require the alignment of six items, we provide evidence showing that the subjects' linear mental representation affects motor performance when evaluating conclusions. Items accessible from the left part of a linear representation are evaluated faster when the response is made by the left, rather than the right, hand and the reverse is observed for items accessible from the right part of the linear representation. This effect, observed with the prepositions to the left of and to the right of as well as with above and below, is analogous to the SNARC (Spatial Numerical Association of Response Codes) effect, which is characterized by an interaction between magnitude of numbers and side of response.     

Being nice by choice: The effect of counterfactual reasoning on children's social evaluations

The ability to engage in counterfactual thinking (reason about what else could have happened) is critical to learning, agency, and social evaluation. However, not much is known about how individual differences in counterfactual reasoning may play a role in children's social evaluations. In the current study, we investigate how prompting children to engage in counterfactual thinking about positive moral actions impacts children's social evaluations. Eighty-seven 4-8-year-olds were introduced to a character who engaged in a positive moral action (shared a sticker with a friend) and asked about what else the character could have done with the sticker (counterfactual simulation). Children were asked to generate either a high number of counterfactuals (five alternative actions) or a low number of counterfactuals (one alternative action). Children were then asked a series of social evaluation questions contrasting that character with one who did not have a choice and had no alternatives (was told to give away the sticker to his friend). Results show that children who generated selfish counterfactuals were more likely to positively evaluate the character with choice than children who did not generate selfish counterfactuals, suggesting that generating counterfactuals most distant from the chosen action (prosociality) leads children to view prosocial actions more positively. We also found age-related changes: as children got older, regardless of the type of counterfactuals generated, they were more likely to evaluate the character with choice more positively. These results highlight the importance of counterfactual reasoning in the development of moral evaluations.

Research Highlights

• Older children were more likely to endorse agents who choose to share over those who do not have a choice.
• Children who were prompted to generate more counterfactuals were more likely to allocate resources to characters with choice.
• Children who generated selfish counterfactuals more positively evaluated agents with choice.
• Comparable to theories suggesting children punish willful transgressors more than accidental transgressors, we propose children also consider free will when making positive moral evaluations.

     

Three Kinds of Social Kinds

Could some social kinds be natural kinds? In this paper, I argue that there are three kinds of social kinds: 1) social kinds whose existence does not depend on human beings having any beliefs or other propositional attitudes towards them (e.g. recession, racism); 2) social kinds whose existence depends in part on specific attitudes that human beings have towards them, though attitudes need not be manifested towards their particular instances (e.g. money, war); 3) social kinds whose existence and that of their instances depend in part on specific attitudes that human beings have towards them (e.g. permanent resident, prime minister). Although all three kinds of social kinds are mind‐dependent, this does not make them ontologically subjective or preclude them from being natural kinds. Rather, what prevents the third kind of social kinds from being natural kinds is that their properties are conventionally rather than causally linked.     

Sensitivity to spacing changes in faces and nonface objects in preschool-aged children and adults

Sensitivity to variations in the spacing of features in faces and a class of nonface objects (i.e., frontal images of cars) was tested in 3- and 4-year-old children and adults using a delayed or simultaneous two-alternative forced choice matching-to-sample task. In the adults, detection of spacing information was robust against exemplar differences for faces but varied across exemplars for cars (Experiment 1A). The 4-year-olds performed above chance in both face and car discrimination even when differences in spacing were very small (within ±1.6 standard deviations [SDs]) and the task involved memory components (Experiment 1B), and the same was true for the 3-year-olds when tested with larger spacing changes (within ±2.5 SDs) in a task that posed no memory demands (Experiment 2). An advantage in the discrimination of faces over cars was found at 4 years of age, but only when spacing cues were made more readily available (within ±2.5 SDs). Results demonstrate that the ability to discriminate objects based on feature spacing (i.e., sensitivity to second-order information) is present at 3 years of age and becomes more pronounced for faces than cars by 4 years of age.     

Development of time sensitivity: Duration ratios in time bisection

This study investigated the development of children's abilities to discriminate durations as a function of their ratio and examined whether the ability to discriminate durations that differed by a very difficult ratio is related to the development of attention capacities. Children aged 5 and 8 years, as well as adults, performed a series of temporal bisection tasks with a ratio between the short and the long anchor duration that was changed to control the difficulty of the task (5:6, 2:3, and 1:2) in two duration ranges (<1 s and >3 s). In addition, they completed neuropsychological tests in order to assess their short-term memory, working memory, and visual attention abilities. The results showed that, at ratios of 2:3 and 1:2, most participants were able to discriminate the anchor durations in bisection. However, their sensitivity to time improved, whatever the duration range, both as the distance between the anchor durations increased and with increasing age. For the smallest duration ratio (5:6), few of the children were able to discriminate the anchor durations in the bisection task in comparison to adults. Hierarchical regression analyses performed on the neuropsychological tests revealed that, for the 2:3 ratio between anchor durations, the participants' visual attention scores explained a large part of the variance in time sensitivity. The children's lower temporal sensitivity was probably due to their limited visual attention abilities, thus explaining the difficulty they experienced in discriminating very close durations (5:6).     

In any way,shape, or form? Toddlers’ understanding of shapes

Using the intermodal preferential looking paradigm, two-year-old children’s ability to discriminate valid (typical and atypical) squares, rectangles, triangles, and circles from invalid distractors was examined. The cognitive and environmental factors that might predict this ability were also investigated. Two-year-old children (N = 33) were able to discriminate squares, triangles, and circles, but not rectangles. No significant cognitive or environmental predictors of this ability were found. The results suggest that the ability to shape discriminate at age two is under considerable development and that other factors may be responsible for children’s ability to discriminate shapes.     

An experiment on measuring awareness of stuttering in individuals with Down syndrome

BackgroundAwareness of stuttering is likely to depend upon the development of the metalinguistic skill to discriminate between fluent speech and stuttering and the ability to identify one’s own speech as fluent or stuttered. Presently, little is known about these abilities in individuals with Down syndrome (DS).PurposeThis study investigates whether individuals with DS and typically developing (TD) children who stutter and who do not stutter differ in their ability to discriminate between fluent speech and stuttering. The second purpose of this study is to discover if this ability is correlated with their self-identification ability.MethodAn experiment to investigate awareness with tasks for discrimination of stuttering and self-identification was developed. It was administered to 28 individuals (7–19 years) with DS, 17 of them stutter and 11 do not, and 20 TD children (3–10 years), 8 of them stutter and 12 do not. Skills to discriminate stuttering were compared between these groups and correlated with self-identification within these groups. The influence of stuttering severity and developmental/chronological age on their ability to discriminate was also investigated.ResultsThe ability to discriminate does not differ significantly between the DS and TD group, but is highly influenced by developmental age. This ability correlates with self-identification but only for the TD individuals who speak fluently.ConclusionThe ability to discriminate matures around the age of 7 and conscious awareness may rely on this ability. Differences between the present findings and earlier studies suggest that differentiation in levels and types of awareness is warranted.     

Evaluations of moral and conventional intergroup transgressions

To investigate children's understanding of intergroup transgressions, children (3–8 years, N = 84) evaluated moral and conventional transgressions that occurred among members of the same gender group (ingroup) or members of different gender groups (outgroup). All participants judged moral transgressions to be more wrong than conventional transgressions. However, when asked to make a judgment after being told an authority figure did not see the transgression, younger participants still judged that moral violations were less acceptable than conventional transgressions, but judged both moral and conventional transgressions with an outgroup victim as more acceptable than the corresponding transgressions with an ingroup victim. Older children did not demonstrate the same ingroup bias; rather they focused only on the domain of the transgressions. The results demonstrate the impact intergroup information has on children's evaluations about both moral and conventional transgressions.     

Face processing at birth: a Thatcher illusion study

The present study was aimed at exploring newborns’ ability to recognize configural changes within real face images by testing newborns’ sensitivity to the Thatcher illusion. Using the habituation procedure, newborns’ ability to discriminate between an unaltered face image and the same face with the eyes and the mouth 180° rotated (i.e. thatcherized) was investigated. Newborns were able to discriminate an unaltered from the thatcherized version of the same face when stimuli were presented in the canonical upright orientation (Experiment 1), but failed to discriminate the same stimuli when they were presented upside‐down (Experiment 2). The results indicate that sensitivity to fine spatial information (defined as second‐order relational information) in processing upright faces is already present at birth.     

Children's judgements of social withdrawal behaviours

Ding et al. (Brit. J. Dev. Psychol., 2015; 33, 159–173) demonstrated that Chinese children discriminate between the three subtypes of social withdrawal: Shyness, unsociability, and social avoidance. This commentary on the Ding et al.'s paper highlights the need to further explore the following: (1) children's understanding of the implications of being shy, unsociable, or socially avoidant, including assessing these which we know are associated with outcomes for socially withdrawn children; (2) what additional subtypes might exist naturally within the Chinese culture; and (3) consider the implications of social withdrawal on children's developing social skills.     

Small and large number processing in infants and toddlers with Williams syndrome

Previous studies have suggested that typically developing 6‐month‐old infants are able to discriminate between small and large numerosities. However, discrimination between small numerosities in young infants is only possible when variables continuous with number (e.g. area or circumference) are confounded. In contrast, large number discrimination is successful even when variables continuous with number are systematically controlled for. These findings suggest the existence of different systems underlying small and large number processing in infancy. How do these develop in atypical syndromes? Williams syndrome (WS) is a rare neurocognitive developmental disorder in which numerical cognition has been found to be impaired in older children and adults. Do impairments of number processing have their origins in infancy? Here this question is investigated by testing the small and large number discrimination abilities of infants and toddlers with WS. While infants with WS were able to discriminate between 2 and 3 elements when total area was confounded with numerosity, the same infants did not discriminate between 8 and 16 elements, when number was not confounded with continuous variables. These findings suggest that a system for tracking the features of small numbers of object (object‐file representation) may be functional in WS, while large number discrimination is impaired from an early age onwards. Finally, we argue that individual differences in large number processing in infancy are more likely than small number processing to be predictive of later development of numerical cognition.     

Think‐Aloud Process Superior to Thought‐Listing in Increasing Children's Critical Processing of Advertising

This study develops and tests a model of children's critical processing of advertising. Within this model, 2 paths to reduced advertising susceptibility (i.e., attitude toward the advertised brand) were hypothesized: a cognitive path and an affective path. The secondary aim was to compare these paths for different thought verbalization processes: think‐aloud and thought‐listing. The model was tested on a sample of 8‐ to 12‐year‐old children (N = 163). Structural equation modeling revealed that, for children in the think‐aloud group, both cognitive and affective paths were successful in reducing advertising susceptibility. However, for children in the thought‐listing group, only the affective path was successful. These findings suggest that the think‐aloud process increased children's motivation and ability to critically process advertising messages.     

Differences in mathematical reasoning between typically achieving and gifted children

Mathematical giftedness refers to mastery in a specific mathematical domain at an earlier than expected age. The present study examined which cognitive processes accounted for differences in mathematical reasoning between gifted children (MRG) and their typically achieving peers (TA). Naming speed, phonological awareness, short-term memory, executive functioning, and working memory were examined in 51 children aged approximately 7 years. A series of stepwise regression models, using a contrast variable to capture differences in mathematical reasoning between MRG and TA children, were created to examine which cognitive domains accounted for differences in mathematical reasoning. Short-term memory (r²?=?.08) and visual-spatial working memory (r²?=?.39) emerged as the only cognitive predictors within a model that included gender, age, and fluid intelligence. This model captured all of the variance distinguishing mathematics reasoning between MRG and TA children, explaining an overall contribution of 70% of the variance in mathematical reasoning.