Understanding the social-emotional components of our "number sense": insights from a novel non-symbolic numerical comparison task.

Introduction: A large body of work has identified a core sense of number supported by the Approximate Number System (ANS) that is present in infancy and across species. Although it is commonly assumed that the ANS directly processes perceptual input and is relatively independent from affective factors, some evidence points at a correlation between ANS performance and math anxiety. However, the evidence is mixed. We tested whether giving participants active control in completing a numerical task would change the relationship between math anxiety on performance. Methods: Adult participants (N = 103) completed a novel four-alternative-forced-choice non-symbolic numerical comparison task. In a repeated-measures design, participants either passively viewed different dot arrays or actively chose to view each array (i.e., active information-seeking) before deciding on the largest quantity. Participants also provided confidence judgments during the passive version of the task. Results: We replicated the ratio-dependent signature in participants' accuracy in both the passive and active versions of the task using this novel paradigm, as well as in trial-level confidence judgments and information-seeking behavior. Participants' self-reported math anxiety significantly correlated with their accuracy on the passive version of the task. Critically, the correlation disappeared in the active version of the task. Gender also emerged as a predictor of confidence judgments and a moderator of the effect of task on overall accuracy and the effect of active information seeking on accuracy in the active version of the task. Exploratory analysis of estimated Weber Fraction suggests that these results may be driven by auxiliary factors instead of changes in ANS acuity. Conclusion: These findings have implications for understanding the relationship between math anxiety and performance on numerical tasks.

"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.

What aspects of counting help infants attend to numerosity?

Recent work shows that 18-month old infants understand that counting is numerically relevant-infants who see objects counted are more likely to represent the approximate number of objects in the array than infants who see the objects labeled but not counted. Which aspects of counting signal infants to attend to numerosity in this way? Here we asked whether infants rely on familiarity with the count words in their native language, or on procedures instantiated by the counting routine, independent of specific tokens. In three experiments (N = 48), we found that 18-month old infants from English-speaking households successfully distinguished four hidden objects from two when the objects were counted correctly, regardless of their familiarity with the count words (i.e., when objects were counted in familiar English and in unfamiliar German). However, when the objects were counted using familiar English count words in ways that violated basic counting principles, infants no longer represented the arrays, failing to distinguish four hidden objects from two. Together with previous findings, these results suggest that children may link the procedure of counting with numerosity years before they learn the meanings of the count words.

Does virtual counting count for babies? Evidence from an online looking time study.

Infants who receive better counting input at home tend to become toddlers with better number knowledge in preschool. However, for many children, in-person counting experience is not always available, despite educational media becoming increasingly prevalent. Might virtual counting experience benefit the young mind? Using a novel online looking time paradigm, a cross-sectional sample of 14- to 19-month-old infants' (United States; N = 81; 35 females; 64% White; within-subject design) ability to keep track of objects presented on screen was measured. We found that infants were significantly more likely to detect a change in numerical quantity after watching the objects being pointed at and counted by an animated hand compared with when there was no counting. These findings provide initial evidence for numerical cognitive benefits from counting video relative to a no counting baseline before the second birthday. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

A cross-cultural investigation of people's intuitive beliefs about the origins of cognition.

Nature vs. nurture is an enduring theme of studies of the mind. Past studies on American children and adults have revealed a preference for thinking that even fundamental cognitive abilities documented in human infants and non-human species are late-emerging and reliant on learning and nurture. However, little is known about the generalizability of this "intuitive empiricist" belief and what factors may help explain it. Adult participants (N = 600) reported their beliefs about the emergence of several fundamental cognitive abilities demonstrated by preverbal infants. Studies 1A-1C showed that adults from both Japan and the US similarly estimated an older age of onset for cognitive abilities in human children as compared to the findings of cognitive science and consistently attributed acquisition of these abilities to learning rather than innateness in humans, and they made these learning attributions more so for humans than for non-human species. Study 2 showed that participants' beliefs about biological evolution versus creationism were related to their age onset estimates for fundamental cognitive abilities, and their beliefs about the malleability of intelligence were related to participants' explanations of the origin of fundamental cognitive abilities. These findings suggest generalizable preferences for nurture over nature across both Eastern and Western cultures (Japan and the United States), which may be related to people's beliefs about human origins and the power of learning.

Exploring individual differences in infants' looking preferences for impossible events: The Early Multidimensional Curiosity Scale.

Infants are drawn to events that violate their expectations about the world: they look longer at physically impossible events, such as when a car passes through a wall. Here, we examined whether individual differences in infants' visual preferences for physically impossible events reflect an early form of curiosity, and asked whether caregivers' behaviors, parenting styles, and everyday routines relate to these differences. In Study 1, we presented infants (N = 47, Mage = 16.83 months, range = 10.29-24.59 months) with events that violated physical principles and closely matched possible events. We measured infants' everyday curiosity and related experiences (i.e., caregiver curiosity-promoting activities) through a newly developed curiosity scale, The Early Multidimensional Curiosity Scale (EMCS). Infants' looking preferences for physically impossible events were positively associated with their score on the EMCS, but not their temperament, vocabulary, or caregiver trait curiosity. In Study 2A, we set out to better understand the relation between the EMCS and infants' looking preferences for physically impossible events by assessing the underlying structure of the EMCS with a larger sample of children (N = 211, Mage = 47.63 months, range = 10.29-78.97 months). An exploratory factor analysis revealed that children's curiosity was comprised four factors: Social Curiosity, Broad Exploration, Persistence, and Information-Seeking. Relatedly, caregiver curiosity-promoting activities were composed of five factors: Flexible Problem-Solving, Cognitive Stimulation, Diverse Daily Activities, Child-Directed Play, and Awe-Inducing Activities. In Study 2B (N = 42 infants from Study 1), we examined which aspects of infant curiosity and caregiver behavior predicted infants' looking preferences using the factor structures of the EMCS. Findings revealed that infants' looking preferences were uniquely related to infants' Broad Exploration and caregivers' Awe-Inducing Activities (e.g., nature walks with infants, museum outings). These exploratory findings indicate that infants' visual preferences for physically impossible events may reflect an early form of curiosity, which is related to the curiosity-stimulating environments provided by caregivers. Moreover, this work offers a new comprehensive tool, the Early Multidimensional Curiosity Scale, that can be used to measure both curiosity and factors related to its development, starting in infancy and extending into childhood.

Children With More Uncertainty in Their Intuitive Theories Seek Domain-Relevant Information.

How do changes in learners' knowledge influence information seeking? We showed preschoolers (N = 100) uncertain outcomes for events and let them choose which event to resolve. We found that children whose intuitive theories were at immature stages were more likely to seek information to resolve uncertainty about an outcome in the related domains, but children with more mature knowledge were not. This result was replicated in a second experiment but with the nuance that children at intermediate stages of belief development-when the causal outcome would be most ambiguous-were the most motivated to resolve the uncertainty. This effect was not driven by general uncertainty at the framework level but, rather, by the impact that framework knowledge has in accessing uncertainty at the model level. These results are the first to show the relationship between a learning preference and the developmental stage of a child's intuitive theory.

Dynamic changes in numerical acuity in 4-month-old infants.

Preverbal infants represent the approximate numerosity of visual and auditory arrays: By 6 months old, they reliably discriminate eight dots or tones from 16 (a 1:2 ratio), but not eight from 12 (a 2:3 ratio). The precision of this approximate number sense improves gradually over childhood and into adulthood. However, less is known about numerical abilities in younger infants, and in particular, whether there is developmental change in the number sense in the first half year of life. Here, in four experiments, we measured numerical precision in 4-month-old infants (N = 128) using a visual habituation task comparable to that in studies of older infants. We found that 4-month-olds exhibited poorer numerical discrimination than the 6-month-olds tested in previous studies, dishabituating to a 1:4 change in numerical ratio, but not a 1:3 change. Like older infants, 4-month-olds' numerical precision improved when they were provided with redundant visual and auditory input; when both visual and auditory information were present, 4-month-olds discriminated a 1:3 but not a 1:2 ratio. These results suggest that Approximate Number System precision develops in early infancy and may be sensitive to intersensory redundancy as early as four months of age.

Emergence of the Link Between the Approximate Number System and Symbolic Math Ability.

Experimentally manipulating Approximate Number System (ANS) precision has been found to influence children's subsequent symbolic math performance. Here in three experiments (N = 160; 81 girls; 3-5 year old) we replicated this effect and examined its duration and developmental trajectory. We found that modulation of 5-year-olds' ANS precision continued to affect their symbolic math performance after a 30-min delay. Furthermore, our cross-sectional investigation revealed that children 4.5 years and older experienced a significant transfer effect of ANS manipulation on math performance, whereas younger children showed no such transfer, despite experiencing significant changes in ANS precision. These findings support the existence of a causal link between nonverbal numerical approximation and symbolic math performance that first emerges during the preschool years.

Infants recognize counting as numerically relevant.

Children do not understand the meanings of count words like "two" and "three" until the preschool years. But even before knowing the meanings of these individual words, might they recognize that counting is "about" the dimension of number? Here in five experiments, we asked whether infants already associate counting with quantities. We measured 14- and 18-month olds' ability to remember different numbers of hidden objects that either were or were not counted by an experimenter before hiding. As in previous research, we found that infants failed to differentiate four hidden objects from two when the objects were not counted-suggesting an upper limit on the number of individual objects they could represent in working memory. However, infants succeeded when the objects were simply counted aloud before hiding. We found that counting also helped infants differentiate four hidden objects from six (a 2:3 ratio), but not three hidden objects from four (a 3:4 ratio), suggesting that counting helped infants represent the arrays' approximate cardinalities. Hence counting directs infants' attention to numerical aspects of the world, showing that they recognize counting as numerically relevant years before acquiring the meanings of number words.

Is Empiricism Innate? Preference for Nurture Over Nature in People's Beliefs About the Origins of Human Knowledge.

The origins of human knowledge are an enduring puzzle: what parts of what we know require learning, and what depends on intrinsic structure? Although the nature-nurture debate has been a central question for millennia and has inspired much contemporary research in psychology and neuroscience, it remains unknown whether people share intuitive, prescientific theories about the answer. Here we report that people (N = 1,188) explain fundamental perceptual and cognitive abilities by appeal to learning and instruction, rather than genes or innateness, even for abilities documented in the first days of life. U.S. adults, adults from a culture with a belief in reincarnation, children, and professional scientists-including psychologists and neuroscientists, all believed these basic abilities emerge significantly later than they actually do, and ascribed them to nurture over nature. These findings implicate a widespread intuitive empiricist theory about the human mind, present from early in life.

Approximate number sense correlates with math performance in gifted adolescents.

Nonhuman animals, human infants, and human adults all share an Approximate Number System (ANS) that allows them to imprecisely represent number without counting. Among humans, people differ in the precision of their ANS representations, and these individual differences have been shown to correlate with symbolic mathematics performance in both children and adults. For example, children with specific math impairment (dyscalculia) have notably poor ANS precision. However, it remains unknown whether ANS precision contributes to individual differences only in populations of people with lower or average mathematical abilities, or whether this link also is present in people who excel in math. Here we tested non-symbolic numerical approximation in 13- to 16-year old gifted children enrolled in a program for talented adolescents (the Center for Talented Youth). We found that in this high achieving population, ANS precision significantly correlated with performance on the symbolic math portion of two common standardized tests (SAT and ACT) that typically are administered to much older students. This relationship was robust even when controlling for age, verbal performance, and reaction times in the approximate number task. These results suggest that the Approximate Number System is linked to symbolic math performance even at the top levels of math performance.

Better together: Multiple lines of evidence for a link between approximate and exact number representations: A reply to Merkley, Matejko, and Ansari.

The results of our recent experiments suggest that temporarily modulating children's approximate number system (ANS) precision leads to a domain-specific change in their symbolic math performance (Journal of Experimental Child Psychology, 2016, Vol. 147, pp. 82-99). We interpreted these results as evidence for a causal relationship between ANS precision and symbolic math. In a commentary on our work, Merkley, Matejko, and Ansari argue that our methodology limits the interpretation of our results, primarily because our experiments did not meet the criteria for an intervention study as set out by What Works Clearinghouse and others. Here, we clarify the goals and limitations of our study and emphasize the variety of approaches to demonstrating causality. We argue that our goal was not to design and test an intervention or to compare the effectiveness of different treatments. Instead, we aimed to experimentally manipulate one variable (i.e., ANS acuity) and, in a randomized sample of children, observe whether this manipulation had any statistically significant effect on a dependent variable (i.e., performance on a set of symbolic math questions). We provide further analyses to support our assertion that a temporary manipulation of ANS performance does lead to a change in math performance. These results point to a causal relationship between ANS precision and math, and they suggest that further investigation of this relationship will be fruitful.

Changing the precision of preschoolers' approximate number system representations changes their symbolic math performance.

From early in life, humans have access to an approximate number system (ANS) that supports an intuitive sense of numerical quantity. Previous work in both children and adults suggests that individual differences in the precision of ANS representations correlate with symbolic math performance. However, this work has been almost entirely correlational in nature. Here we tested for a causal link between ANS precision and symbolic math performance by asking whether a temporary modulation of ANS precision changes symbolic math performance. First, we replicated a recent finding that 5-year-old children make more precise ANS discriminations when starting with easier trials and gradually progressing to harder ones, compared with the reverse. Next, we show that this brief modulation of ANS precision influenced children's performance on a subsequent symbolic math task but not a vocabulary task. In a supplemental experiment, we present evidence that children who performed ANS discriminations in a random trial order showed intermediate performance on both the ANS task and the symbolic math task, compared with children who made ordered discriminations. Thus, our results point to a specific causal link from the ANS to symbolic math performance.