"Catastrophic" set size limits on infants' capacity to represent objects: A systematic review and Bayesian meta-analysis.

Decades of research has revealed that humans can concurrently represent small quantities of three-dimensional objects as those objects move through space or into occlusion. For infants (but not older children or adults), this ability apparently comes with a significant limitation: when the number of occluded objects exceeds three, infants experience what has been characterized as a "catastrophic" set size limit, failing to represent even the approximate quantity of the hidden array. Infants' apparent catastrophic representational failures suggest a significant information processing limitation in the first years of life, and the evidence has been used as support for prominent theories of the development of object and numerical cognition. However, the evidence for catastrophic failure consists of individual small-n experiments that use null hypothesis significance testing to obtain null results (i.e., p > 0.05). Whether catastrophic representational failures are robust or reliable across studies, methods, and labs is not known. Here we report a systematic review and Bayesian meta-analysis to examine the strength of the evidence in favor of catastrophic representational failures in infancy. Our analysis of 22 experiments across 12 reports, with a combined total of n = 367 infants aged 10-20 months, revealed strong support for the evidence for catastrophic set size limits. A complementary analysis found moderate support for infants' success when representing fewer than four objects. We discuss the implications of our findings for theories of object and numerical cognitive development. RESEARCH HIGHLIGHTS: Previous work has suggested that infants are unable to concurrently represent four or more objects-a "catastrophic" set size limit. We reviewed this work and conducted a Bayesian meta-analysis to examine the robustness of this limit across individual small-n experiments. We found strong support for the evidence for catastrophic set size limits, and moderate support for infants' success when representing fewer than four objects.

"Shape bias" goes social: Children categorize people by weight rather than race.

Children tend to categorize novel objects according to their shape rather than their color, texture, or other salient properties-known as "shape bias." We investigated whether this bias also extends to the social domain, where it should lead children to categorize people according to their weight (their body shape) rather than their race (their skin color). In Study 1, participants (n = 50 US 4- and 5-year-olds) were asked to extend a novel label from a target object/person to either an object/person who shared the target's shape/weight, color/race, or neither. Children selected the shape-/weight-matched individual over the color-/race-matched individual (dobjects  = 1.58, dpeople  = 0.99) and their shape biases were correlated across the two domains. In Study 2, participants (n = 20 US 4- and 5-year-olds) were asked to extend a novel internal property from a target person to either a person who shared the target's weight, race, or neither. Again, children selected the weight-matched individual (d = 1.98), suggesting they view an individual's weight as more predictive of their internal properties than their race. Overall, results suggest that children's early shape bias extends into the social domain. Implications for weight bias and early social cognition are discussed. RESEARCH HIGHLIGHTS: Preschoolers extend novel labels based on people's weight rather than their race. Preschoolers infer internal features based on people's weight rather than their race. Shape biases are present, and correlated, across the social and object domains.

Children's use of reasoning by exclusion to infer objects' identities in working memory.

Reasoning by exclusion allows us to form more complete representations of our environments, "filling in" inaccessible information by ruling out known alternatives. In two experiments (Experiment 1: N = 34 4- to 6-year-olds; Experiment 2: N = 85 4- to 8-year-olds), we examined children's ability to use reasoning by exclusion to infer the identity of an unknown object and investigated the role of working memory in this ability. Children were asked to encode a set of objects that were then hidden, and after a brief retention interval children were asked to select the identity of the object hidden in one of the locations from two alternatives. On some trials, all the images were visible during encoding, so selecting the correct identity when probed required successful working memory storage and retrieval. On other trials, all but one of the images was visible during encoding, so selecting the correct identity when probed also required maintaining a representation of an unknown object in working memory and then using reasoning by exclusion to fill in the missing information retroactively to complete that representation by ruling out known alternatives. To investigate the working memory cost of exclusive reasoning, we manipulated the working memory demands of the task. Our results suggest that children can use reasoning by exclusion to retroactively assign an identity to an incomplete object representation at least by 4 years of age but that this ability incurs some cognitive cost, which eases with development. These results provide new insights into children's representational capacities and on the foundational building blocks of fully developed exclusive reasoning.

Three-year-olds' ability to plan for mutually exclusive future possibilities is limited primarily by their representations of possible plans, not possible events.

The ability to prepare for mutually exclusive possible events in the future is essential for everyday decision making. Previous studies have suggested that this ability develops between the ages of 3 and 5 years, and in young children is primarily limited by the ability to represent the set of possible outcomes of an event as "possible". We tested an alternative hypothesis that this ability may be limited by the ability to represent the set of possible actions that could be taken to prepare for those possible outcomes. We adapted the inverted y-shaped tube task of Redshaw and Suddendorf (2016), in which children are asked to catch a marble that is dropped into the top of the tube and can emerge from either the left or right branch of the tube. While 4-year-olds typically place their hands under both openings to catch the marble, preparing for both possible outcomes (optimal action), 3-year-olds often cover only one opening, preparing for only one possible outcome (suboptimal action). In three Experiments, we asked whether first showing children the set of possible actions that could be taken on the tube would enable them to recognize the optimal action that should be used to catch the marble (Experiments 1 and 3, total n = 99 US 3- and 4-year-olds) and enable them to use the optimal action themselves (Experiment 2, n = 96 US 3- and 4-year-olds). We found that 3- and 4-year-olds performed similarly when they were given the opportunity to observe the set of possible actions beforehand. These findings suggest that 3-year-olds' competence at representing mutually exclusive possibilities may be masked by their developing ability to represent and deploy plans to act on these possibilities.

Development of precision of non-symbolic arithmetic operations in 4-6-year-old children.

Children can represent the approximate quantity of sets of items using the Approximate Number System (ANS), and can perform arithmetic-like operations over ANS representations. Previous work has shown that the representational precision of the ANS develops substantially during childhood. However, less is known about the development of the operational precision of the ANS. We examined developmental change in the precision of the solutions to two non-symbolic arithmetic operations in 4-6-year-old U.S. children. We asked children to represent the quantity of an occluded set (Baseline condition), to compute the sum of two sequentially occluded arrays (Addition condition), or to infer the quantity of an addend after observing an initial array and then the array incremented by the unknown addend (Unknown-addend condition). We measured the precision of the solutions of these operations by asking children to compare their solutions to visible arrays, manipulating the ratio between the true quantity of the solution and the comparison array. We found that the precision of ANS representations that were not the result of operations (in the Baseline condition) was higher than the precision of solutions to ANS operations (in the Addition and Unknown-addend conditions). Further, we found that precision in the Baseline and Addition conditions improved significantly between 4 and 6 years, while precision in the Unknown-Addend condition did not. Our results suggest that ANS operations may inject "noise" into the representations they operate over, and that the development of the precision of different operations may follow different trajectories in childhood.

The language-of-thought as a working hypothesis for developmental cognitive science.

A science of prelinguistic infant cognition must take seriously the language-of-thought (LoT) hypothesis. I show how the LoT framework enables us to identify the representational and computational capacities of infant minds and the developmental factors that act on these capacities, and explain how Quilty-Dunn et al.'s take on LoT has important upshots for developmental theory-building.

Objects in a social world: Infants' object representational capacity limits are shaped by objects' social relevance.

Several decades of research have revealed consistent signature limits on infants' ability to represent objects. However, these signature representational limits were established with methods that often removed objects from their most common context. In infants' everyday lives, objects are very often social artifacts: they are the targets of agents' goal-directed actions, communications, and beliefs, and may have social content or relevance themselves. In this chapter, we explore the relationship between infants' object representational capacity limits and their processing of the social world. We review evidence that the social content and context of objects can shift infants' object representational limits. We discuss how taking the social world into account can yield more robust and ecologically valid estimates of infants' early representational capacities.

Competition Between Object Topology and Surface Features in Children's Extension of Novel Nouns.

Objects' topological properties play a central role in object perception, superseding objects' surface features in object representation and tracking from early in development. We asked about the role of objects' topological properties in children's generalization of novel labels to objects. We adapted the classic name generalization task of Landau et al. (1988, 1992). In three experiments, we showed children (n = 151; 3-8-year-olds) a novel object (the standard) and gave the object a novel label. We then showed children three potential target objects and asked children which of the objects shared the same label as the standard. In Experiment 1, the standard object either did or did not contain a hole, and we asked whether children would extend the standard's label to a target object that shared either metric shape or topology with the standard. Experiment 2 served as a control condition for Experiment 1. In Experiment 3, we pitted topology against another surface feature, color. We found that objects' topology competed with objects' surface features (both shape and color) in children's extension of labels to novel objects. We discuss possible implications for our understanding of the inductive potential of objects' topologies for making inferences about objects' categories across early development.

An object's categorizability impacts whether infants encode surface features into their object representations.

Infants encode the surface features of simple, unfamiliar objects (e.g., red triangle) and the categorical identities of familiar, categorizable objects (e.g., car) into their representations of these objects. We asked whether 16-18-month-olds ignore non-diagnostic surface features (e.g., color) in favor of encoding an object's categorical identity (e.g., car) when objects are from familiar categories. In Experiment 1 (n = 18), we hid a categorizable object inside an opaque box. In No Switch trials, infants retrieved the object that was hidden. In Switch trials, infants retrieved a different object: an object from a different category (Between-Category-Switch trials) or a different object from the same category (Within-Category-Switch trials). We measured infants' subsequent searching in the box. Infants' pattern of searching suggested that only infants who completed a Within-Category-Switch trial as their first Switch trial encoded objects' surface features, and an exploratory analysis suggested that infants who completed a Between-Category-Switch trial as their first Switch trial only encoded objects' categories. In Experiment 2 (n = 18), we confirmed that these results were due to objects' categorizability. These results suggest infants may tailor the way they encode categorizable objects depending on which object dimensions are perceived to be task relevant.

Is Nonsymbolic Arithmetic Truly "Arithmetic"? Examining the Computational Capacity of the Approximate Number System in Young Children.

Young children with limited knowledge of formal mathematics can intuitively perform basic arithmetic-like operations over nonsymbolic, approximate representations of quantity. However, the algorithmic rules that guide such nonsymbolic operations are not entirely clear. We asked whether nonsymbolic arithmetic operations have a function-like structure, like symbolic arithmetic. Children (n = 74 4- to -8-year-olds in Experiment 1; n = 52 7- to 8-year-olds in Experiment 2) first solved two nonsymbolic arithmetic problems. We then showed children two unequal sets of objects, and asked children which of the two derived solutions should be added to the smaller of the two sets to make them "about the same." We hypothesized that, if nonsymbolic arithmetic follows similar function rules to symbolic arithmetic, then children should be able to use the solutions of nonsymbolic computations as inputs into another nonsymbolic problem. Contrary to this hypothesis, we found that children were unable to reliably do so, suggesting that these solutions may not operate as independent representations that can be used inputs into other nonsymbolic computations. These results suggest that nonsymbolic and symbolic arithmetic computations are algorithmically distinct, which may limit the extent to which children can leverage nonsymbolic arithmetic intuitions to acquire formal mathematics knowledge.

"Plan chunking" expands 3-year-olds' ability to complete multiple-step plans.

The ability to use knowledge to guide the completion of goals is a critical cognitive skill, but 3-year-olds struggle to complete goals that require multiple steps. This study asked whether 3-year-olds could benefit from "plan chunking" to complete multistep goals. Thirty-two U.S. children (range = 35.75-46.59 months; 18 girls; 9 white, 3 mixed race, 20 unknown; tested between July 2020 and April 2021) were asked to complete "treasure maps," retrieving four colored map pieces by pressing specific buttons on a "rainbow box." Children completed more of the four-step sequence correctly when the steps were presented in a way that encouraged chunking the steps into pairs. These findings suggest a potential mechanism supporting memory-guided planning abilities in early childhood.

Explore versus store: Children strategically trade off reliance on exploration versus working memory during a complex task.

During complex tasks, we use working memory to actively maintain goal sets and direct attention toward goal-relevant information in the environment. However, working memory is severely limited, and storing information in working memory is cognitively effortful. Previous work by Kibbe and Kowler [2011, Journal of Vision, 11(3), Article 14] showed that adults strategically modulate reliance on working memory during complex, goal-oriented tasks, varying the amount of information they store in working memory depending both on the cognitive demands of the task and on the ease with which task-relevant information can be accessed from the environment. We asked whether children, whose working memory and executive functions are undergoing significant developmental change, also use working memory strategically during complex tasks. Forty-six 8-10-year-old children searched through arrays of hidden objects to find three that belonged to a given category defined over the objects' features. We manipulated the cognitive demands of the task by increasing the complexity of the category. We manipulated the exploration costs of the task by varying the rate at which task-relevant information could be accessed. We measured children's search patterns to gain insights into how the children used working memory during the task. We found that as the cognitive demands of the task increased, children stored less information in working memory, relying more on exploration. When exploration was costlier, children explored less, storing more in working memory. These results suggest that developing children, like adults, make strategic decisions about when to explore versus when to store during a complex, goal-oriented task.

Problems and Mysteries of the Many Languages of Thought.

"What is the structure of thought?" is as central a question as any in cognitive science. A classic answer to this question has appealed to a Language of Thought (LoT). We point to emerging research from disparate branches of the field that supports the LoT hypothesis, but also uncovers diversity in LoTs across cognitive systems, stages of development, and species. Our letter formulates open research questions for cognitive science concerning the varieties of rules and representations that underwrite various LoT-based systems and how these variations can help researchers taxonomize cognitive systems.

Tracking what went where across toddlerhood: Feature-location bound object representations in 2- to 3-year-olds' working memory.

Two experiments examined the development of the ability to encode, maintain, and update integrated representations of occluded objects' locations and featural identities in working memory across toddlerhood. Sixty-eight 28- to 40-month-old US toddlers (13 Asian or Pacific Islander, 6 Black, 48 White, 1 multiracial; 40 girls; tested between February 2015 and July 2017) tracked the locations of different color beads that were hidden simultaneously (Experiment 1) or sequentially (Experiment 2). Toddlers' ability to reliably store feature-location bound object representations in working memory varied as a function of age, memory load, and task demands. These results bridge a developmental gap between infancy and early childhood and provide new insights into sources of limitation and developmental change in children's early object representational capacities.

Development of updating in working memory in 4-7-year-old children.

Children live in a dynamic environment, in which objects continually change locations and move into and out of occlusion. Children must therefore rely on working memory to store information from the environment and to update those stored representations as the environment changes. Previous work suggests that the ability to store information in working memory increases through infancy and childhood. However, less is known about the development of the ability to update stored information. Participants were 63 4-7-year-old children (37 girls; 34 caregivers completed optional demographic forms, and those children were reported as Asian [one], Asian/White [four], Black [one], Middle East/Arab [one], or White [27]; two were Hispanic/Latinx). We asked children to keep track of arrays of hidden items that either remained where they were hidden (static trials) or swapped locations (swap trials) and then to identify from two alternatives which item was hidden in a particular location. We manipulated the number of items in the arrays and the number of times the items swapped locations in order to investigate how increasing storage and updating load impacted children's performance. We found that children's ability to update working memory developed significantly across our age range. Updating appeared to impose a significant one-time cost to working memory performance, regardless of the number of times items swapped. Our results yield new insights into the developmental trajectories of storage and updating in working memory across early childhood. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Two-year-olds use past memories to accomplish novel goals.

Memory-guided planning involves retrieving relevant memories and applying that information in service of a goal. Previous studies have shown substantial development in this ability from 3 to 4 years of age. We investigated the emergence of memory-guided planning by asking whether 2-year-olds could draw on episodic memories of past experiences to generate and execute plans. In Experiments 1 and 2 (N = 32, ds > .7), 2-year-olds successfully did so, and this ability developed significantly across the third year of life. Furthermore, in Experiment 3 (N = 19, d = 0.63), 2-year-olds successfully applied episodic memories to guide plans in a novel problem context, suggesting flexibility in this ability. Together, these results suggest that some form of memory-guided planning emerges during the third year of life and may form the cognitive basis for episodic prospection later in development.

Children's understanding of economic demand: A dissociation between inference and choice.

Adults infer that resources that become scarce over time are in higher demand, and use this "demand inference" to guide their own economic decisions. However, it is unclear when children begin to understand and use economic demand. In six experiments, we investigated the development of demand inference and demand-based economic decisions in 4- to 10-year-old children and adults in the United States. In Experiments 1-5, we showed children two boxes with the same number of compartments but containing different numbers of face-down stickers and varied the information provided about how those differences arose (e.g. that other children had taken the stickers). In separate experiments, we asked children to buy or trade to get a sticker for themselves or to predict what other children would do. We also asked them which set of stickers they thought the other children had preferred to assess their ability to make a demand inference separately from their own choice. Across experiments, children were able to make a demand inference about children's past preferences by 6 years of age. However, children did not use this demand information when making choices for themselves or when predicting what another child would select in the future. In Experiment 6, we adapted the task for adults and found that adult participants inferred that the set containing fewer resources was in higher demand, and selected the higher demand resource for themselves at rates significantly above chance. The overall pattern of results suggests a dissociation between economic inference and economic decisions during early-to-middle childhood. We discuss implications for our understanding of the development of economic reasoning.

Young children monitor the fidelity of visual working memory.

The ability to concurrently maintain representations of multiple objects and their locations in visual working memory is severely limited. Thus, making optimal use of visual working memory requires continual, moment-to-moment monitoring of its fidelity: High-fidelity representations can be relied upon, whereas incomplete or fuzzy representations must be refreshed or ignored. Previous work showed that adults track the fidelity of their visual working memory. Here, we asked whether children, whose capacities for visual working memory are undergoing protracted development, also can do so. We showed 5- and 6-year-olds sets of 2-5 single-feature (Experiment 1) or multifeature (Experiment 2) objects hidden simultaneously in separate locations. We asked children to recall the location of one of the objects, then bet 0-3 resources on whether they were correct. In both experiments, we found that children's confidence in their visual working memory, as indexed by their bets, was correlated with their accuracy on each trial, controlling for task difficulty: Children bet higher when they were correct and lower when they were incorrect. Our results suggest that metacognitive awareness of the representational limits of visual working memory may emerge before working memory reaches stable capacity. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Development of multiple object tracking via multifocal attention.

Multifocal attention is the ability to simultaneously attend to multiple objects, and is critical for typical functioning. Although adults are able to use multifocal attention, little is known about the development of this ability. In two experiments, we investigated multifocal attention in 6-8-year-old children and adults using a child-friendly, computerized multiple object tracking task designed to encourage the use of multifocal attention. We also investigated whether multifocal attention in children is deployed independently across left and right hemifields of vision, as in adults. Our results suggest that children's capacity for multifocal attention increases significantly across middle childhood. We also found evidence that at least one signature of hemifield-independent multifocal attention, the bilateral field advantage, can be observed in children. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Altruistic self-regulation in young children.

We investigated whether children would be willing to sustain delaying their own gratification in order to benefit someone else. We used a modified version of the classic "marshmallow task," in which children must sustain delaying gratification in the presence of the immediate reward for an unspecified amount of time in order to receive a larger reward later. Children were assigned to one of three conditions. In the Self condition, children were given a food item and were told that if they waited to eat it, they would receive a second food item. In the Prosocial condition, children also were given a food item but were told that if they waited to eat their food item, another child would get a food item. In the Nonsocial Control condition, children were given a food item but were told that waiting to eat it would not benefit anyone. We found that children waited significantly longer in both the Self and Prosocial conditions than in the Nonsocial Control condition, and children's wait durations in the Self and Prosocial conditions were not significantly different. Our results suggest that children are willing to engage in effortful self-regulation in order to benefit another child.