Infants recognize counting as numerically relevant

Early-emerging combinatorial thought: Human infants flexibly combine kind and quantity concepts

Combinatorial thought, or the ability to combine a finite set of concepts into a myriad of complex ideas and knowledge structures, is the key to the productivity of the human mind and underlies communication, science, technology, and art. Despite the importance of combinatorial thought for human cognition and culture, its developmental origins remain unknown. To address this, we tested whether 12-mo-old infants (N = 60), who cannot yet speak and only understand a handful of words, can combine quantity and kind concepts activated by verbal input. We proceeded in two steps: first, we taught infants two novel labels denoting quantity (e.g., "mize" for 1 item; "padu" for 2 items, Experiment 1). Then, we assessed whether they could combine quantity and kind concepts upon hearing complex expressions comprising their labels (e.g., "padu duck", Experiments 2-3). At test, infants viewed four different sets of objects (e.g., 1 duck, 2 ducks, 1 ball, 2 balls) while being presented with the target phrase (e.g., "padu duck") naming one of them (e.g., 2 ducks). They successfully retrieved and combined on-line the labeled concepts, as evidenced by increased looking to the named sets but not to distractor sets. Our results suggest that combinatorial processes for building complex representations are available by the end of the first year of life. The infant mind seems geared to integrate concepts in novel productive ways. This ability may be a precondition for deciphering the ambient language(s) and building abstract models of experience that enable fast and flexible learning.

"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.

Early access to language supports number mapping skills in deaf children

The ability to associate different types of number representations referring to the same quantity (symbolic Arabic numerals, signed/spoken number words, and nonsymbolic quantities), is an important predictor of overall mathematical success. This foundational skill-mapping-has not been examined in deaf and hard-of-hearing (DHH) children. To address this gap, we studied 188 4 1/2 to 9-year-old DHH and hearing children and systematically examined the relationship between their language experiences and mapping skills. We asked whether the timing of children's language exposure (early vs. later), the modality of their language (signed vs. spoken), and their rote counting abilities related to mapping performance. We found that language modality did not significantly relate to mapping performance, but timing of language exposure and counting skills did. These findings suggest that early access to language, whether spoken or signed, supports the development of age-typical mapping skills and that knowledge of number words is critical for this development.

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.

Self-regulation in toddlers and the emergence of pre-academic disparities

A growing body of research has examined how children's self-regulation during early and middle childhood mediates SES disparities in academic achievement. Evidence suggests that these self-regulation skills begin developing even earlier, during the toddler years, but more work is needed examining how different measures of self-regulation relate to key constructs such as socioeconomic status (SES) and toddlers' pre-academic skills. In this online study, we examine multiple approaches to measuring self-regulation using confirmatory factor analyses and assess the extent to which self-regulatory skills help explain SES differences in early math and language skills among a sample of 158 two- and three-year-old children. Self-regulation was assessed through a battery of parent- and examiner-ratings. Children's counting, cardinality, and vocabulary skills were measured online through direct assessments and parent surveys. Two self-regulation factors emerged representing parent-reported and observational measures, and only observational measures of self-regulation mediated associations between SES and children's math and language skills. Parent-reported self-regulation was not uniquely related to SES or children's pre-academic skills, underscoring the need for careful consideration of how self-regulation is measured among toddlers when examining its associations with pre-academic skills.

Predicting children's emerging understanding of numbers

How do children construct a concept of natural numbers? Past research addressing this question has mainly focused on understanding how children come to acquire the cardinality principle. However, at that point children already understand the first number words and have a rudimentary natural number concept in place. The question therefore remains; what gets children's number learning off the ground? We therefore, based on previous empirical and theoretical work, tested which factors predict the first stages of children's natural number understanding. We assessed if children's expressive vocabulary, visuospatial working memory, and ANS (Approximate number system) acuity at 18 months of age could predict their natural number knowledge at 2.5 years of age. We found that early expressive vocabulary and visuospatial working memory were important for later number knowledge. The results of the current study add to a growing body of literature showing the importance of language in children's learning about numbers.

Measuring Emerging Number Knowledge in Toddlers

Recent evidence suggests that infants and toddlers may recognize counting as numerically relevant long before they are able to count or understand the cardinal meaning of number words. The Give-N task, which asks children to produce sets of objects in different quantities, is commonly used to test children’s cardinal number knowledge and understanding of exact number words but does not capture children’s preliminary understanding of number words and is difficult to administer remotely. Here, we asked whether toddlers correctly map number words to the referred quantities in a two-alternative forced choice Point-to-X task (e.g., “Which has three?”). Two- to three-year-old toddlers (N = 100) completed a Give-N task and a Point-to-X task through in-person testing or online via videoconferencing software. Across number-word trials in Point-to-X, toddlers pointed to the correct image more often than predicted by chance, indicating that they had some understanding of the prompted number word that allowed them to rule out incorrect responses, despite limited understanding of exact cardinal values. No differences in Point-to-X performance were seen for children tested in-person versus remotely. Children with better understanding of exact number words as indicated on the Give-N task also answered more trials correctly in Point-to-X. Critically, in-depth analyses of Point-to-X performance for children who were identified as 1- or 2-knowers on Give-N showed that 1-knowers do not show a preliminary understanding of numbers above their knower-level, whereas 2-knowers do. As researchers move to administering assessments remotely, the Point-to-X task promises to be an easy-to-administer alternative to Give-N for measuring children’s emerging number knowledge and capturing nuances in children’s number-word knowledge that Give-N may miss.

What Counts? Sources of Knowledge in Children's Acquisition of the Successor Function

Although many U.S. children can count sets by 4 years, it is not until 5½-6 years that they understand how counting relates to number-that is, that adding 1 to a set necessitates counting up one number. This study examined two knowledge sources that 3½- to 6-year-olds (N = 136) may leverage to acquire this "successor function": (a) mastery of productive rules governing count list generation; and (b) training with "+1" math facts. Both productive counting and "+1" math facts were related to understanding that adding 1 to sets entails counting up one number in the count list; however, even children with robust successor knowledge struggled with its arithmetic expression, suggesting they do not generalize the successor function from "+1" math facts.

The Effect of Language-Specific Characteristics on English and Japanese Speakers' Ability to Recall Number Information

The current paper presents two experiments investigating the effect of presence versus absence of compulsory number marking in a native language on a speaker's ability to recall number information from photos. In Experiment 1, monolingual English and Japanese adults were shown a sequence of 110 photos after which they were asked questions about the photos. We found that the English participants showed a significantly higher accuracy rate for questions testing recall for number information when the correct answer was "2" (instead of "1") than Japanese participants. In Experiment 2, English and Japanese adults engaged in the same task as in Experiment 1 with an addition that explored reasons for the results found in Experiment 1. The results of Experiment 2 were in line with the results of Experiment 1, but also suggested that the results could not be attributed to differences in guessing patterns between the two groups or the type of linguistic constructions used in the test situations. The current study suggests that native language affects speakers' ability to recall number information from scenes and thus provides evidence for the Whorfian hypothesis.

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.