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How do children think about and plan for possible outcomes of events that could happen in the future? Previous work that has investigated children's ability to think about mutually exclusive possibilities has largely focused on children's reasoning about one type of possibility-the possible locations of an object. Here, we investigated children's reasoning about another type of possibility-mutually exclusive possible identities. In two experiments (N = 201 U.S. 3- and 4-year-olds), children were told that two animal characters (e.g., a bunny and a monkey) were going to take turns sliding down a playground slide. Children were told that the animals wanted to eat their favorite foods (e.g., carrots and bananas, respectively) as soon as they got to the bottom of the slide. In an Unambiguous Identity condition, we told children the identity of the animal that would slide down. In an Ambiguous Identity condition, we told children that which animal would slide down first was unknown. To examine children's representations of possible identities, we asked children to "get snack ready." We found that children in the Unambiguous Identity condition selected only one of the snacks (i.e., the favorite snack of the animal they were told would slide down), whereas children in the Ambiguous Identity condition selected both snacks, suggesting that they were accounting for both possible identities. These results extend the literature on the development of modal reasoning to include reasoning about possible identities and suggest that this ability may be available to children as young as 3 years., (Copyright © 2024 Elsevier Inc. All rights reserved.)

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., (© 2024 John Wiley & Sons Ltd.)

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., Competing Interests: Declaration of Competing Interest None., (Copyright © 2023. Published by Elsevier B.V.)

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 (d objects  = 1.58, d people  = 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., (© 2023 John Wiley & Sons Ltd.)

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., (Copyright © 2023 Elsevier Inc. All rights reserved.)

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., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2023 Cheng and Kibbe.)

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.

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., (© 2023 International Congress of Infant Studies.)

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., (© 2023 The Authors. Child Development © 2023 Society for Research in Child Development.)

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., (© 2023 Cognitive Science Society LLC.)

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., (© 2023 Massachusetts Institute of Technology.)

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., (Copyright © 2022 Elsevier Inc. All rights reserved.)

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., (Copyright © 2023. Published by Elsevier Inc.)

"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., (© 2022 Cognitive Science Society LLC.)

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., (© 2022 The Authors. Child Development © 2022 Society for Research in Child Development.)

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).

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., (Copyright © 2021 Elsevier Inc. All rights reserved.)

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., (Copyright © 2021 Elsevier B.V. All rights reserved.)

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).

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).

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., (Copyright © 2019 Elsevier Inc. All rights reserved.)

Stored memories may be drawn upon when accomplishing goals. In two experiments, we investigated limits on the ability to use episodic memories to support planning in 3- and 4-year-old children. We designed a new memory-guided planning task that required children to both retrieve memories and apply those memories to accomplish multiple, nested goals. We manipulated the difficulty of the task by varying the number of steps required to achieve the goals, and examined the impact of this manipulation on both memory retrieval and planning. We found that, overall, 4-year-olds outperformed 3-year-olds, but as task difficulty increased, all children made more errors. Analysis of these errors suggested that retrieval and planning processes might impose separate limits on memory-guided planning in early childhood, but that these limits may ease across early childhood.

Infants can infer agents' goals after observing agents' goal-directed actions on objects and can subsequently make predictions about how agents will act on objects in the future. We investigated the representations supporting these predictions. We familiarized 6-month-old infants to an agent who preferentially reached for one of two featurally distinct objects following a cue. At test, the objects were sequentially occluded from the infant in the agent's presence. We asked whether infants could generate action predictions without visual access to the relevant objects by measuring whether infants shifted their gaze to the location of the agent's hidden goal object following the cue. We also examined what infants represented about the hidden objects by removing one of the occluders to reveal either the original hidden object or the unexpected other object and measuring infants' looking time. We found that, even without visual access to the objects, infants made predictive gazes to the location of the agent's occluded goal object, but failed to represent the features of either hidden object. These results suggest that infants make goal-based action predictions when the relevant objects in the scene are occluded, but doing so may come at the expense of maintaining representations of the objects., (© International Congress of Infant Studies (ICIS).)

Six-month-old infants can store representations of multiple objects in working memory but do not always remember the objects' features (e.g., shape). Here, we asked whether infants' object representations (a) may contain conceptual content and (b) may contain this content even if perceptual features are forgotten. We hid two conceptually distinct objects (a humanlike doll and a nonhuman ball) one at a time in two separate locations and then tested infants' memory for the first-hidden object by revealing either the original hidden object or an unexpected other object. Using looking time, we found that infants remembered the categorical identity of the hidden object but failed to remember its perceptual identity. Our results suggest that young infants may encode conceptual category in a representation of an occluded object, even when perceptual features are lost.

How distinct are visual memory representations from visual perception? Although evidence suggests that briefly remembered stimuli are represented within early visual cortices, the degree to which these memory traces resemble true visual representations remains something of a mystery. Here, we tested whether both visual memory and perception succumb to a seemingly ubiquitous neural computation: normalization. Observers were asked to remember the contrast of visual stimuli, which were pitted against each other to promote normalization either in perception or in visual memory. Our results revealed robust normalization between visual representations in perception, yet no signature of normalization occurring between working memory stores-neither between representations in memory nor between memory representations and visual inputs. These results provide unique insight into the nature of visual memory representations, illustrating that visual memory representations follow a different set of computational rules, bypassing normalization, a canonical visual computation.

What drives infants' attention in complex visual scenes? Early models of infant attention suggested that the degree to which different visual features were detectable determines their attentional priority. Here, we tested this by asking whether two targets - defined by different features, but each equally salient when evaluated independently - would drive attention equally when pitted head-to-head. In Experiment 1, we presented 6-month-old infants with an array of gabor patches in which a target region varied either in color or spatial frequency from the background. Using a forced-choice preferential-looking method, we measured how readily infants fixated the target as its featural difference from the background was parametrically increased. Then, in Experiment 2, we used these psychometric preference functions to choose values for color and spatial frequency targets that were equally salient (preferred), and pitted them against each other within the same display. We reasoned that, if salience is transitive, then the stimuli should be iso-salient and infants should therefore show no systematic preference for either stimulus. On the contrary, we found that infants consistently preferred the color-defined stimulus. This suggests that computing visual salience in more complex scenes needs to include factors above and beyond local salience values.

Solving for an unknown addend in problems like 5+x=17 is challenging for children. Yet, previous work (Kibbe & Feigenson, 2015) found that even before formal math education, young children, aged 4- to 6-years, succeeded when problems were presented using non-symbolic collections of objects rather than symbolic digits. This reveals that the Approximate Number System (ANS) can support pre-algebraic intuitions. Here, we asked whether children also could intuitively "solve for x" when problems contained arrays of four or fewer objects that encouraged representations of individual objects instead of ANS representations. In Experiment 1, we first confirmed that children could solve for an unknown addend with larger quantities, using the ANS. Next, in Experiment 2a, we presented addend-unknown problems containing arrays of four or fewer objects (e.g., 1+x=3). This time, despite the identical task conditions, children were unable to solve for the unknown addend. In Experiment 2b, we replicated this failure with a new sample of children. Finally, in Experiment 3, we confirmed that children's failures in Experiments 2a and b were not due to lack of motivation to compute with small arrays, or to the discriminability of the quantities used: children succeeded at solving for an unknown sum with arrays containing four or fewer objects. Together, these results suggest that children's ability to intuitively solve for an unknown addend may be limited to problems that can be represented using the ANS., (Copyright © 2016 Elsevier B.V. All rights reserved.)

Infants, like adults, can maintain only a few items in working memory, but can overcome this limit by creating more efficient representations, or "chunks." Previous research shows that infants can form chunks using shared features or spatial proximity between objects. Here we asked whether infants also can create chunked representations using regularities that unfold over time. Thirteen-month old infants first were familiarized with four objects of different shapes and colors, presented in successive pairs. For some infants, the identities of objects in each pair varied randomly across familiarization (Experiment 1). For others, the objects within a pair always co-occurred, either in consistent relative spatial positions (Experiment 2a) or varying spatial positions (Experiment 2b). Following familiarization, infants saw all four objects hidden behind a screen and then saw the screen lifted to reveal either four objects or only three. Infants in Experiment 1, who had been familiarized with random object pairings, failed to look longer at the unexpected 3-object outcome; they showed the same inability to concurrently represent four objects as in other studies of infant working memory. In contrast, infants in Experiments 2a and 2b, who had been familiarized with regularly co-occurring pairs, looked longer at the unexpected outcome. These infants apparently used the co-occurrence between individual objects during familiarization to form chunked representations that were later deployed to track the objects as they were hidden at test. In Experiment 3, we confirmed that the familiarization affected infants' ability to remember the occluded objects rather than merely establishing longer-term memory for object pairs. Following familiarization to consistent pairs, infants who were not shown a hiding event (but merely saw the same test outcomes as in Experiments 2a and b) showed no preference for arrays of three versus four objects. Finally, in Experiments 4 and 5, we asked whether infants also remembered the specific identities of the objects in each chunk. In Experiment 4, we confirmed that infants remembered objects' identities in smaller arrays that did not require chunking. Next, in Experiment 5, we asked whether infants also remembered objects' identities in larger arrays that had been chunked on the basis of temporal regularities. Following a familiarization phase identical to that in Experiment 2a, we hid all four objects and then revealed either these same four objects, or four objects of which two had unexpectedly changed shape and color. Surprisingly, infants failed to look longer at the identity change outcome. Taken together, our results suggest that infants can use temporal regularities between objects to increase memory for objects' existence, but not necessarily for objects' identities., (Copyright © 2015 Elsevier B.V. All rights reserved.)

The Approximate Number System (ANS) supports basic arithmetic computation in early childhood, but it is unclear whether the ANS also supports the more complex computations introduced later in formal education. 'Solving for x' in addend-unknown problems is notoriously difficult for children, who often struggle with these types of problems well into high school. Here we asked whether 4-6-year-old children could solve for an unknown addend using the ANS. We presented problems either symbolically, using Arabic numerals or verbal number words, or non-symbolically, using collections of objects while preventing verbal counting. Across five experiments, children failed to identify the value of the unknown addend when problems were presented symbolically, but succeeded when problems were presented non-symbolically. Our results suggest that, well before formal exposure to unknown-addend problems, children appear to 'solve for x' in an intuitive way, using the ANS., (© 2014 John Wiley & Sons Ltd.)

Working memory is severely limited in both adults and children, but one way that adults can overcome this limit is through the process of recoding. Recoding happens when representations of individual items are chunked together into a higher order representation, and the chunk is assigned a label. That label can then be decoded to retrieve the individual items from long-term memory. Whereas this ability has been extensively studied in adults (as, for example, in classic studies of memory in chess), little is known about recoding's developmental origins. Here we asked whether 2- to 3-year-old children also can recode-that is, can they restructure representations of individual objects into a higher order chunk, assign this new representation a verbal label, and then later decode the label to retrieve the represented individuals from memory. In Experiments 1 and 2, we showed children identical blocks that could be connected to make tools. Children learned a novel name for a tool that could be built from two blocks, and for a tool that could be built from three blocks. Later we told children that one of the tools was hidden in a box, with no visual information provided. Children were allowed to search the box and retrieve varying numbers of blocks. Critically, the retrieved blocks were identical and unconnected, so the only way children could know whether any blocks remained was by using the verbal label to recall how many objects comprised each tool (or chunk). We found that even children who could not yet count adjusted their searching of the box depending on the label they had heard. This suggests that they had recoded representations of individual blocks into higher-order chunks, attached labels to the chunks, and then later decoded the labels to infer how many blocks were hidden. In Experiments 3 and 4 we asked whether recoding also can expand the number of individual objects children could remember, as in the classic studies with adults. We found that when no information was provided to support recoding, children showed the standard failure to remember more than three hidden objects at once. But when provided recoding information, children successfully represented up to five individual objects in the box, thereby overcoming typical working memory limits. These results are the first demonstration of recoding by young children; we close by discussing their implications for understanding the structure of memory throughout the lifespan., (Copyright © 2014 Elsevier Inc. All rights reserved.)

We examined the perception of virtual curved surfaces explored with a tool. We found a reliable curvature aftereffect, suggesting neural representation of the curvature in the absence of direct touch. Intermanual transfer of the aftereffect suggests that this representation is somewhat independent of the hand used to explore the surface.

Infants have a bandwidth-limited object working memory (WM) that can both individuate and identify objects in a scene, (answering 'how many?' or 'what?', respectively). Studies of infants' WM for objects have typically looked for limits on either 'how many' or 'what', yielding different estimates of infant capacity. Infants can keep track of about three individuals (regardless of identity), but appear to be much more limited in the number of specific identities they can recall. Why are the limits on 'how many' and 'what' different? Are the limits entirely separate, do they interact, or are they simply two different aspects of the same underlying limit? We sought to unravel these limits in a series of experiments which tested 9- and 12-month-olds' WM for object identities under varying degrees of difficulty. In a violation-of-expectation looking-time task, we hid objects one at a time behind separate screens, and then probed infants' WM for the shape identity of the penultimate object in the sequence. We manipulated the difficulty of the task by varying both the number of objects in hiding locations and the number of means by which infants could detect a shape change to the probed object. We found that 9-month-olds' WM for identities was limited by the number of hiding locations: when the probed object was one of two objects hidden (one in each of two locations), 9-month-olds succeeded, and they did so even though they were given only one means to detect the change. However, when the probed object was one of three objects hidden (one in each of three locations), they failed, even when they were given two means to detect the shape change. Twelve-month-olds, by contrast, succeeded at the most difficult task level. Results show that WM for 'how many' and for 'what' are not entirely separate. Individuated objects are tracked relatively cheaply. Maintaining bindings between indexed objects and identifying featural information incurs a greater attentional/memory cost. This cost reduces with development. We conclude that infant WM supports a small number of featureless object representations that index the current locations of objects. These can have featural information bound to them, but only at substantial cost., (Copyright © 2013 Elsevier Inc. All rights reserved.)

What does an infant remember about a forgotten object? Although at age 6 months, infants can keep track of up to three hidden objects, they can remember the featural identity of only one. When infants forget the identity of an object, do they forget the object entirely, or do they retain an inkling of it? In a looking-time study, we familiarized 6-month-olds with a disk and a triangle placed on opposite sides of a stage. During test trials, we hid the objects one at a time behind different screens, and after hiding the second object, we removed the screen where the first object had been hidden. Infants then saw the expected object, the unexpected other object, or the empty stage. Bayes factor analysis showed that although the infants did not notice when the object changed shape, they were surprised when it vanished. This finding indicates that infants can represent an object without its features.

Limitations of working memory force a reliance on motor exploration to retrieve forgotten features of the visual array. A category search task was devised to study tradeoffs between exploration and memory in the face of significant cognitive and motor demands. The task required search through arrays of hidden, multi-featured objects to find three belonging to the same category. Location contents were revealed briefly by either a: (1) mouseclick, or (2) saccadic eye movement with or without delays between saccade offset and object appearance. As the complexity of the category rule increased, search favored exploration, with more visits and revisits needed to find the set. As motor costs increased (mouseclick search or oculomotor search with delays) search favored reliance on memory. Application of the model of J. Epelboim and P. Suppes (2001) to the revisits produced an estimate of immediate memory span (M) of about 4-6 objects. Variation in estimates of M across category rules suggested that search was also driven by strategies of transforming the category rule into concrete perceptual hypotheses. The results show that tradeoffs between memory and exploration in a cognitively demanding task are determined by continual and effective monitoring of perceptual load, cognitive demand, decision strategies and motor effort.