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.

Using Hierarchical Linear Models to Examine Approximate Number System Acuity: The Role of Trial-Level and Participant-Level Characteristics.

The ability to intuitively and quickly compare the number of items in collections without counting is thought to rely on the Approximate Number System (ANS). To assess individual differences in the precision of peoples' ANS representations, researchers often use non-symbolic number comparison tasks in which participants quickly choose the numerically larger of two arrays of dots. However, some researchers debate whether this task actually measures the ability to discriminate approximate numbers or instead measures the ability to discriminate other continuous magnitude dimensions that are often confounded with number (e.g., the total surface area of the dots or the convex hull of the dot arrays). In this study, we used hierarchical linear models (HLMs) to predict 132 adults' accuracy on each trial of a non-symbolic number comparison task from a comprehensive set of trial-level characteristics (including numerosity ratio, surface area, convex hull, and temporal and spatial variations in presentation format) and participant-level controls (including cognitive abilities such as visual-short term memory, working memory, and math ability) in order to gain a more nuanced understanding of how individuals complete this task. Our results indicate that certain trial-level characteristics of the dot arrays contribute to our ability to compare numerosities, yet numerosity ratio, the critical marker of the ANS, remains a highly significant predictor of accuracy above and beyond trial-level characteristics and across individuals with varying levels of math ability and domain-general cognitive abilities.

Children's spontaneous focus on number before and after guided parent-child interactions in a children's museum.

Little is known about whether and how parents can foster their children's spontaneous focus on number, an unprompted measure of attention to small numbers of objects that predicts later math achievement. In the current study, we asked 54 preschool-aged children and their parents to play together in a children's museum exhibit using either a numerical prompt or a nonnumerical prompt (control condition). Before and after playing with their parent, children completed assessments to measure individual differences in their tendency to spontaneously focus on number. After playing with their parent, children whose parents received the numerical prompt showed greater spontaneous focus on number compared to children whose parents received the control prompt. These findings suggest that when parents interact in an informal play setting with their children in ways that involve numerical content, it sharpens children's later spontaneous attention to numerical information. (PsycINFO Database Record

When approximate number acuity predicts math performance: The moderating role of math anxiety.

Separate lines of research suggest that people who are better at estimating numerical quantities using the approximate number system (ANS) have better math performance, and that people with high levels of math anxiety have worse math performance. Only a handful of studies have examined both ANS acuity and math anxiety in the same participants and those studies report contradictory results. To address these inconsistencies, in the current study 87 undergraduate students completed assessments of ANS acuity, math anxiety, and three different measures of math. We considered moderation models to examine the interplay of ANS acuity and math anxiety on different aspects of math performance. Math anxiety and ANS acuity were both unique significant predictors of the ability to automatically recall basic number facts. ANS acuity was also a unique significant predictor of the ability to solve applied math problems, and this relation was further qualified by a significant interaction with math anxiety: the positive association between ANS acuity and applied problem solving was only present in students with high math anxiety. Our findings suggest that ANS acuity and math anxiety are differentially related to various aspects of math and should be considered together when examining their respective influences on math ability. Our findings also raise the possibility that good ANS acuity serves as a protective factor for highly math-anxious students on certain types of math assessments.

Intergenerational associations of the approximate number system in toddlers and their parents.

From birth, humans are able to discriminate quantities using the approximate number system (ANS). However, previous methods have only been suitable to examine ANS functioning in infancy and older children. The goals of this study were twofold: first, to modify an existing method of assessing ANS functioning for toddlerhood; and second, to investigate individual differences in toddlers' ANS performance by examining correlations with their parents' ANS acuity. Using a preferential looking paradigm, we found that 1- to 3-year-olds (N = 46) looked significantly longer to numerically changing images compared to numerically constant ones suggesting that the paradigm is a suitable measure of ANS functioning in toddlerhood. Furthermore, we found a positive relation between toddlers' ANS performance and that of their parents (assessed using a non-symbolic number comparison task) independent of children's vocabulary or parents' perceived math ability or preference for math. These findings are consistent with a specific intergenerational transmission of the ANS. Statement of contribution What is already known on this subject? Past methods used to examine ANS functioning were only suitable for infants and older children. Little research has examined sources underlying individual difference in ANS acuity. What does this study add? We developed a preferential looking task to assess ANS functioning in toddlerhood. Individual differences in toddlers' ANS functioning are correlated with their parents' ANS acuity.

No intrinsic gender differences in children's earliest numerical abilities.

Recent public discussions have suggested that the under-representation of women in science and mathematics careers can be traced back to intrinsic differences in aptitude. However, true gender differences are difficult to assess because sociocultural influences enter at an early point in childhood. If these claims of intrinsic differences are true, then gender differences in quantitative and mathematical abilities should emerge early in human development. We examined cross-sectional gender differences in mathematical cognition from over 500 children aged 6 months to 8 years by compiling data from five published studies with unpublished data from longitudinal records. We targeted three key milestones of numerical development: numerosity perception, culturally trained counting, and formal and informal elementary mathematics concepts. In addition to testing for statistical differences between boys' and girls' mean performance and variability, we also tested for statistical equivalence between boys' and girls' performance. Across all stages of numerical development, analyses consistently revealed that boys and girls do not differ in early quantitative and mathematical ability. These findings indicate that boys and girls are equally equipped to reason about mathematics during early childhood.

Understanding sources of individual variability in parents' number talk with young children.

Several studies suggest that parents' use of number words while talking with their children is positively related to children's understanding of certain mathematical concepts. In this study, we extended these findings and further examined several parent characteristics that could be related to individual differences in their number talk, including their subjective ratings of their math skills, preference for using math, beliefs about the importance of their children's math skills, and numerical approximation abilities, an early number skill present in children and adults. A sample of 44 5- and 6-year-old children and their parents completed a variety of laboratory-based tasks, including a 10-min free play session to assess number talk, a standardized math assessment for children, a nonsymbolic numerical comparison task for parents, and several questionnaires for parents. Parents' overall number talk was not related to children's performance on the math assessment; however, parents' use of numbers larger than 10 was positively and significantly related to children's math abilities even when controlling for parents' overall talk. Parents' large number talk was also associated with their numerical approximation abilities and subjective math ability, suggesting that math-specific characteristics of parents themselves can explain some of the individual variability in parents' use of number words, especially those larger than 10.

Infants discriminate number: Evidence against the prerequisite of visual object individuation and the primacy of continuous magnitude.

Leibovich et al. hypothesize that the absence of visual object individuation limits infants' numerical skills and necessitates a reliance on continuous magnitudes. We argue that parallels between infants' numerical discrimination in the visual and auditory modalities, their abilities to match numerosities across modalities, and their greater ability to discriminate changes in number compared with continuous magnitudes contradict the authors' assumptions.

Intergenerational associations in numerical approximation and mathematical abilities.

Although growing evidence suggests a link between children's math skills and their ability to estimate numerical quantities using the approximate number system (ANS), little is known about the sources underlying individual differences in ANS acuity and their relation with specific mathematical skills. To examine the role of intergenerational transmission of these abilities from parents to children, the current study assessed the ANS acuities and math abilities of 54 children (5-8 years old) and their parents, as well as parents' expectations about children's math skills. Children's ANS acuity positively correlated with their parents' ANS acuity, and children's math abilities were predicted by unique combinations of parents' ANS acuity and math ability depending on the specific math skill in question. These findings provide the first evidence of intergenerational transmission of an unlearned, non-verbal numerical competence and are an important step toward understanding the multifaceted parental influences on children's math abilities.