Large numbers cause magnitude neglect: The case of government expenditures.

Four studies demonstrate that the public's understanding of government budgetary expenditures is hampered by difficulty in representing large numerical magnitudes. Despite orders of magnitude difference between millions and billions, study participants struggle with the budgetary magnitudes of government programs. When numerical values are rescaled as smaller magnitudes (in the thousands or lower), lay understanding improves, as indicated by greater sensitivity to numerical ratios and more accurate rank ordering of expenses. A robust benefit of numerical rescaling is demonstrated across a variety of experimental designs, including policy relevant choices and incentive-compatible accuracy measures. This improved sensitivity ultimately impacts funding choices and public perception of respective budgets, indicating the importance of numerical cognition for good citizenship.

A Practical Significance Bias in Laypeople's Evaluation of Scientific Findings.

People often rely on scientific findings to help them make decisions-however, failing to report effect magnitudes might lead to a potential bias in assuming findings are practically significant. Across two online studies (Prolific; N = 800), we measured U.S. adults' endorsements of expensive interventions described in media reports that led to effects that were small, large, or of unreported magnitude between groups. Participants who viewed interventions with unreported effect magnitudes were more likely to endorse interventions compared with those who viewed interventions with small effects and were just as likely to endorse interventions as those who viewed interventions with large effects, suggesting a practical significance bias. When effect magnitudes were reported, participants on average adjusted their evaluations accordingly. However, some individuals, such as those with low numeracy skills, were more likely than others to act on small effects, even when explicitly prompted to first consider the meaningfulness of the effect.

Choice Consistency in Discrete Choice Experiments: Does Numeracy Skill Matter? (VIH-2023-0494.R2).

OBJECTIVES: This study investigated the relationship between numeracy skills and choice consistency in discrete choice experiments (DCEs). METHODS: A DCE was conducted to explore patients' preferences for kidney transplantation in Italy. Patients completed the DCE and answered three-item numeracy questions. A Heteroskedastic Multinomial Logit (HMNL) model was used to investigate the effect of numeracy on choice consistency. RESULTS: Higher numeracy skills were associated with greater choice consistency, increasing the scale to 1.63 (p<0.001), 1.39 (p<0.001), and 1.18 (p<0.001) for patients answering 3/3, 2/3, and 1/3 questions correctly, respectively, compared to those with no correct answers. This corresponded to 63%, 39%, and 18% more consistent choices, respectively. Accounting for choice consistency resulted in varying willingness-to-wait (WTW) estimates for kidney transplant attributes. Patients with the lowest numeracy (0/3) were willing to wait approximately 42 months [95% CI: 29.37, 54.68] for standard infectious risk, compared to 33 months [95% CI: 28.48, 38.09] for 1/3, 28 months [95% CI: 25.13, 30.32] for 2/3, and 24 months [95% CI: 20.51, 27.25] for 3/3 correct answers. However, WTW differences for an additional year of graft survival and neoplastic risk were not statistically significant across numeracy levels. Supplementary analyses of two additional DCEs on COVID-19 vaccinations and rheumatoid arthritis, conducted online, supported these findings: higher numeracy skills were associated with more consistent choices across different disease contexts and survey formats. CONCLUSIONS: The findings suggested that combining patients with varying numeracy skills could bias WTW estimates, highlighting the need to consider numeracy in DCE data analysis and interpretation.

Successful Aging is Associated with Better Health Literacy in Older Adults with HIV Disease.

People with HIV (PWH) are susceptible to neurocognitive, physical, and mental health problems that may decrease their likelihood of experiencing successful aging. This cross-sectional, retrospective study estimated the extent to which health literacy is associated with successful aging among 116 older PWH and 60 persons without HIV. Successful aging was defined using indicators of biological health, cognitive efficiency, mental health, and productivity. Health literacy was measured using the Rapid Estimate of Adult Literacy in Medicine, Newest Vital Sign, Brief Health Literacy Screening, and Beliefs Related to Medication Adherence. A series of logistic regressions covarying for education showed that better health literacy was associated with a higher frequency of successful aging among older PWH. Older PWH were approximately three times less likely to experience successful aging as compared to older adults without HIV. Future studies may examine whether improving health literacy among younger PWH increases the likelihood of successful aging.

Mapping skills between symbols and quantities in preschoolers: The role of finger patterns.

Mapping skills between different codes to represent numerical information, such as number symbols (i.e., verbal number words and written digits) and non-symbolic quantities, are important in the development of the concept of number. The aim of the current study is to investigate children's mapping skills by incorporating another numerical code that emerges at early stages in development, finger patterns. Specifically, the study investigates (i) the order in which mapping skills develop and the association with young children's understanding of cardinality; and (ii) whether finger patterns are processed similarly to symbolic codes or rather as non-symbolic quantities. Preschool children (3-year-olds, N = 113, Mage = 40.8 months, SDage = 3.6 months; 4-year-olds, N = 103, Mage = 52.9 months, SDage = 3.4 months) both cardinality knowers and subset-knowers, were presented with twelve tasks that assessed the mappings between number words, Arabic digits, finger patterns, and quantities. The results showed that children's ability to map symbolic numbers precedes the understanding that such symbols reflect quantities, and that children recognize finger patterns above their cardinality knowledge, suggesting that finger patterns are symbolic in essence. RESEARCH HIGHLIGHTS: Children are more accurate in mapping between finger patterns and symbols (number words and Arabic digits) than in mapping finger patterns and quantities, indicating that fingers are processed holistically as symbolic codes. Children can map finger patterns to symbols above their corresponding cardinality level even in subset-knowers. Finger patterns may play a role in the process by which children learn to map symbols to quantities. Fingers patterns' use in the classroom context may be an adequate instructional and diagnostic tool.

Neural evidence of core foundations and conceptual change in preschool numeracy.

Symbolic numeracy first emerges as children learn the meanings of number words and how to use them to precisely count sets of objects. This development starts before children enter school and forms a foundation for lifelong mathematics achievement. Despite its importance, exactly how children acquire this basic knowledge is unclear. Here we test competing theories of early number learning by measuring event-related brain potentials during a novel number word-quantity comparison task in 3-4-year-old preschool children (N = 128). We find several qualitative differences in neural processing of number by conceptual stage of development. Specifically, we find differences in early attention-related parietal electrophysiology (N1), suggesting that less conceptually advanced children process arrays as individual objects and more advanced children distribute attention over the entire set. Subsequently, we find that only more conceptually advanced children show later-going frontal (N2) sensitivity to the numerical-distance relationship between the number word and visual quantity. The nature of this response suggested that exact rather than approximate numerical meanings were being associated with number words over frontal sites. No evidence of numerical distance effects was observed over posterior scalp sites. Together these results suggest that children may engage parallel individuation of objects to learn the meanings of the first few number words, but, ultimately, create new exact cardinal value representations for number words that cannot be defined in terms of core, nonverbal number systems. More broadly, these results document an interaction between attentional and general cognitive mechanisms in cognitive development. RESEARCH HIGHLIGHTS: Conceptual development in numeracy is associated with a shift in attention from objects to sets. Children acquire meanings of the first few number words through associations with parallel attentional individuation of objects. Understanding of cardinality is associated with attentional processing of sets rather than individuals. Brain signatures suggest children attribute exact rather than approximate numerical meanings to the first few number words. Number-quantity relationship processing for the first few number words is evident in frontal but not parietal scalp electrophysiology of young children.

Contributions of preschool behavioral self-regulation and social skills to growth in different domains of early math knowledge.

The current study explored the relative contribution of individual differences in children's behavioral self-regulation and social skills (often referred to as learning-related skills) in the fall of preschool to children's rate of growth in different domains of early math knowledge through the spring of kindergarten. Participants were 684 children (Mage = 57.6 months, SD = 3.8, at Time 1 [fall of preschool]; 48% female; 43% Black, 32% White, 13% Latine, 11% multiracial, and 1% Asian). All children were from families with low incomes and lived in the midwestern United States. The math domains of informal numeracy, formal numeracy, and math language were assessed at four time points: fall and spring of preschool and fall and spring of kindergarten. Contrary to expectations, we did not find that either learning-related skill positively predicted rate of growth in math knowledge or observe differential relations by math domain. Rather, the relative contribution of behavioral self-regulation and social skills in the fall of preschool to rate of growth in math knowledge followed similar patterns across all math domains: an early advantage for children with higher initial social skills that stayed consistent over time (i.e., a nonsignificant slope effect) and an early advantage for children with higher initial behavioral self-regulation that diminished over time (i.e., a negative slope effect).

The roles of mathematical language and emergent literacy skills in the longitudinal prediction of specific early numeracy skills.

Mathematical language (i.e., content-specific language used in mathematics) and emergent literacy skills predict children's broad numeracy development. However, little work has examined whether these domains predict development of individual numeracy skills (e.g., cardinality, number order). Thus, the aim of the current study was to examine longitudinal relations among mathematical language, emergent literacy skills, and specific early numeracy skills. Participants included 114 preschool children aged 3.12 to 5.26 years (M = 4.17 years, SD = 0.59). Specifically, this study examined whether mathematical language and three emergent literacy skills (print knowledge, phonological awareness, and general vocabulary) in the fall of preschool predicted 12 individual early numeracy skills in the spring, controlling for age, sex, rapid automatized naming, parent education, and autoregressors. Results indicated that mathematical language predicted development of most of the early numeracy skills (e.g., set comparison, numeral comparison, numeral identification), but findings for emergent literacy skills were not robust. Among the three emergent literacy skills, only print knowledge was a significant predictor of development in some specific numeracy skills, including verbal counting, number order, and story problems. Results highlight the important role of mathematical language in children's numeracy development and provide the foundation for future work in designing interventions to improve early numeracy skills.

Assessing the association between parents' math talk and children's math performance: A preregistered meta-analysis.

The home math environment has gained considerable attention as a potential cause of variation in children's math performance, and recent research has suggested positive associations between parents' math talk and children's mathematical performance. However, the extent to which associations reflect robust causal effects is difficult to test. In a preregistered meta-analysis, we assess the association between parents' math talk and children's math performance. Our initial search identified 24,291 potential articles. After screening, we identified 22 studies that were included in analyses (k = 280 effect sizes, n = 35,917 participants). A multilevel random effects meta-analysis was employed, finding that parents' math talk is significantly associated with children's math performance (b = 0.10, SE = 0.03, p = .002). We tested whether associations differ as a function of sample characteristics, observation context, observation length, type of math talk and math performance measured, and modeling approaches to math talk variable analysis. In addition, we tested whether associations are robust to the inclusion of strong baseline covariates and found that effects attenuated when children's domain-general and/or prior math abilities are included. We discuss plausible bounds of the effects of parents' math talk on children's mathematical performance to inform power analyses and experimental work on the impact of parents' math language on children's math learning.

New measures of number line estimation performance reveal children's ordinal understanding of numbers.

Children's performance on the number line estimation task, often measured by the percentage of absolute error, predicts their later mathematics achievement. This task may also reveal (a) children's ordinal understanding of the target numbers in relation to each other and the benchmarks (e.g., endpoints, midpoint) and (b) the ordinal skills that are a necessary precursor to children's ability to understand the interval nature of a number line as measured by percentage of absolute error. Using data from 104 U.S. kindergartners, we measured whether children's estimates were correctly sequenced across trials and correctly positioned relative to given benchmarks within trials at two time points. For both time points, we found that each ordinal error measure revealed a distinct pattern of data distribution, providing opportunities to tap into different aspects of children's ordinal understanding. Furthermore, children who made fewer ordinal errors scored higher on the Test of Early Mathematics Ability and showed greater improvement on their interval understanding of numbers as reflected by a larger reduction of percentage of absolute error from Time 1 to Time 2. The findings suggest that our number line measures reveal individual differences in children's ordinal understanding of numbers, and that such understanding may be a precursor to their interval understanding and later mathematics performance.

Math talk by mothers, fathers, and toddlers: Differences across materials and associations with children's math understanding.

Learning words for numbers, shapes, spatial relations, and magnitudes-"math talk"-relies on input from caregivers. Language interactions between caregivers and children are situated in activity contexts and likely affected by available materials. Here, we examined how play materials influence the math talk directed to and produced by young children. We video-recorded parents (mothers and fathers; English- and/or Spanish-speaking) and their 24- to 36-month-olds during play with four sets of materials, transcribed and coded types of parent and toddler math words/phrases, and assessed toddlers' understanding of number, shape, and spatial relations terms. Categories of math words varied by materials. Numeracy talk (e.g., "one," "two," "first," "second") was more frequent during interactions with a picture book and toy grocery shopping set than with a shape sorter or magnet board; the reverse held for spatial talk (e.g., "out," "bottom," "up," "circle"). Parent math talk predicted toddler math talk, and both parent and toddler math talk predicted toddlers' understanding of spatial and number words. Different materials provide unique opportunities for toddlers to learn abstract math words during interactions with caregivers, and such interactions support early math cognition.

"R" you getting this? Factors contributing to the public's understanding, evaluation, and use of basic reproduction numbers for infectious diseases.

BACKGROUND: We (1) examined the effects of evaluative labels and visual aids on people's understanding, evaluation, and use of the COVID-19 reproduction number (or "r-number"), (2) examined whether people's perceived susceptibility and (intended) adherence to preventive measures changed after being exposed to the r-number, and (3) explored whether these effects and changes depended on people's numeracy skills. METHODS: In an online experiment, participants from a large Dutch representative sample (N = 1,168) received information about the COVID-19 r-number displayed on the corona dashboard of the Dutch Ministry of Health, Welfare and Sport. The r-number was either presented with or without a categorical line display (i.e., evaluative label) and with or without an icon-based tree diagram (i.e., visual aid) explaining how the number works. Regarding people's use of the statistic, we measured perceived susceptibility to COVID-19 and adherence (intention) to five preventive measures before and after exposure to the r-number. After exposure, we also measured participants' understanding, perceived usefulness, affective and cognitive evaluation, and objective numeracy. RESULTS: About 56% of participants correctly interpreted the r-number, with highly numerate people having better understanding than less numerate people. Information about the r-number was perceived as more useful when presented with a visual aid. There were no differences across experimental conditions in people's understanding, affective, and cognitive evaluations. Finally, independent of experimental conditions, intention to adhere to preventive measures was higher after seeing the r-number, but only among highly numerate people. CONCLUSIONS: Although evaluative labels and visual aids did not facilitate people's understanding and evaluation of the r-number, our results show that the statistic is perceived as useful and may be used to stimulate adherence to preventive measures. Policy makers and public health communicators are advised to clearly explain why they are giving these numbers to - especially - the less numerate people, but also how people could use them for behavior change to combat the spread of virus during a pandemic.

Collective overclaiming is related to collective narcissism and numeracy.

When asked to estimate how much their state or nation has contributed to history, people typically provide unreasonably large estimates, claiming that their group has contributed much more to history than nongroup members would estimate, demonstrating collective overclaiming. Why does such overclaiming occur? In the current study we examined factors that might predict collective overclaiming. Participants from 12 U.S. states estimated how much their home state contributed to U.S. history, completed measures of collective narcissism and numeracy, and rated the importance of 60 specific historical events. There was a positive relationship between collective overclaiming and collective narcissism, a negative relationship between collective overclaiming and numeracy, and a positive relationship between collective overclaiming and the importance ratings of the specific events. Together, these results indicate that overclaiming is partially and positively related to collective narcissism and negatively related to people's ability to work with numbers. We conclude that collective overclaiming is likely determined by several factors, including the availability heuristic and ego protection mechanisms, in addition to collective narcissism and relative innumeracy.

Home Learning Environment and Screen Time Differentially Mediate the Relationship Between Socioeconomic Status and Preschoolers' Learning and Behavioural Profiles.

Environmental variables related to the home context, including home literacy and numeracy, screen exposure and Socioeconomic Status (SES) are potential risks or protective factors for children's academic achievements and behaviour. The present multi-informant study aims to contribute to this issue by investigating SES's direct and indirect relationships in early learning (i.e., literacy, numeracy, and cognitive) and behavioural skills within a large sample of young children. One parent and one teacher for each of 1660 preschoolers filled out a questionnaire investigating SES, tablet and TV use, home learning activities, behavioural problems/strengths (parents' questionnaire), and children's learning skills and behaviour (teachers' questionnaire). Results of path analysis showed that tablet time and home learning environment mediate the effect of SES on early learning as assessed by teachers; as for the home learning environment, it was also a mediator of the relationship between SES and behavioural problems. Implications of these results for research in the field and educational policies are discussed.

Young children with intellectual disabilities and their mathematical attainments: Do parents' attitudes toward mathematics, home numeracy, and literacy practices matter?

This study explored potential factors of numeracy acquisition in young children with intellectual disabilities (IDs). Those factors are determined to assess parents' academic expectations and home practices that they use with their children daily. The sample consisted of 187 Greek-speaking couples, comprising a total number of 374 parents. All of them had a child with mild IDs aged between 4 and 7 years old. Since Greece is placed among European countries with the lowest median disposable income it is significant to assess the potential effects of each family's socioeconomic status. We employed structural equation modeling to identify potential factors affecting a child's with IDs numeracy outcomes. Analysis of moments structures (AMOS) revealed that there is a good fit for the suggested second-order structural equation model. Results are discussed regarding their practical implications.

Task-independent neural bases of peer presence effect on cognition in children and adults.

There is ample behavioral evidence that others' mere presence can affect any behavior in human and non-human animals, generally facilitating the expression of mastered responses while impairing the acquisition of novel ones. Much less is known about i) how the brain orchestrates the modulation of such a wide array of behaviors by others' presence and ii) when these neural underpinnings mature during development. To address these issues, fMRI data were collected in children and adults alternately observed and unobserved by a familiar peer. Subjects performed a numerosity comparison task and a phonological comparison task. While the former involves number-processing brain areas, the latter involves language-processing areas. Consistent with previous behavioral findings, adults' and children's performance improved in both tasks when observed by a peer. Across all participants, task-specific brain regions showed no reliable change in activity under peer observation. Rather, we found task-independent changes in domain-general brain regions typically involved in mentalizing, reward, and attention. Bayesian analyses singled out the attention network as the exception to the close child-adult resemblance of peer observation neural substrates. These findings suggest that i) social facilitation of some human education-related skills is primarily orchestrated by domain-general brain networks, rather than by task-selective substrates, and ii) apart from attention, peer presence neural processing is largely mature in children.

Mathematics Skills in Epilepsy: A Systematic Review and Meta-Analysis.

Mathematics incorporates a broad range of skills, which includes basic early numeracy skills, such as subitizing and basic counting to more advanced secondary skills including mathematics calculation and reasoning. The aim of this review was to undertake a detailed investigation of the severity and pattern of early numeracy and secondary mathematics skills in people with epilepsy. Searches were guided by the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement. Twenty adult studies and 67 child studies were included in this review. Overall, meta-analyses revealed significant moderate impairments across all mathematics outcomes in both adults (g= -0.676), and children (g= -0.593) with epilepsy. Deficits were also observed for specific mathematics outcomes. For adults, impairments were found for mathematics reasoning (g= -0.736). However, two studies found that mathematics calculation was not significantly impaired, and an insufficient number of studies examined early numeracy skills in adults. In children with epilepsy, significant impairments were observed for each mathematics outcome: early numeracy (g= -0.383), calculation (g= -0.762), and reasoning (g= -0.572). The gravity of impairments also differed according to the site of seizure focus for children and adults, suggesting that mathematics outcomes were differentially vulnerable to the location of seizure focus.

Quantifying quality: The impact of measures of school quality on children's academic achievement across diverse societies.

Recent decades have seen a rapid acceleration in global participation in formal education, due to worldwide initiatives aimed to provide school access to all children. Research in high income countries has shown that school quality indicators have a significant, positive impact on numeracy and literacy-skills required to participate in the increasingly globalized economy. Schools vary enormously in kind, resources, and teacher training around the world, however, and the validity of using diverse school quality measures in populations with diverse educational profiles remains unclear. First, we assessed whether children's numeracy and literacy performance across populations improves with age, as evidence of general school-related learning effects. Next, we examined whether several school quality measures related to classroom experience and composition, and to educational resources, were correlated with one another. Finally, we examined whether they were associated with children's (4-12-year-olds, N = 889) numeracy and literacy performance in 10 culturally and geographically diverse populations which vary in historical engagement with formal schooling. Across populations, age was a strong positive predictor of academic achievement. Measures related to classroom experience and composition were correlated with one another, as were measures of access to educational resources and classroom experience and composition. The number of teachers per class and access to writing materials were key predictors of numeracy and literacy, while the number of students per classroom, often linked to academic achievement, was not. We discuss these results in the context of maximising children's learning environments and highlight study limitations to motivate future research. RESEARCH HIGHLIGHTS: We examined the extent to which four measures of school quality were associated with one another, and whether they predicted children's academic achievement in 10 culturally and geographically diverse societies. Across populations, measures related to classroom experience and composition were correlated with one another as were measures of access to educational resources to classroom experience and composition. Age, the number of teachers per class, and access to writing materials were key predictors of academic achievement across populations. Our data have implications for designing efficacious educational initiatives to improve school quality globally.

Difficulties with mathematics experienced by adults with epilepsy in daily life: An online study.

OBJECTIVE: Mathematics encompass a variety of skills, broadly grouped into basic numeracy to complex secondary mathematical skills. In children with epilepsy difficulties with mathematics are common and related to a multicomponent working memory capacity. Little is known about mathematical skills of adults with epilepsy in daily life. Hence, we aimed to compare basic and secondary mathematical skills of adults with epilepsy to controls, examine relations between mathematical skills and working memory, and explored relationships between mathematical skills and epilepsy variables (age of onset, seizure frequency, and anti-seizure medication). METHODS: Eighty four people with epilepsy and 86 healthy controls completed questionnaires on their subjective experience of using mathematics and working memory skills in daily life: The Dyscalculia Checklist (DC) and Working Memory Questionnaire (WMQ; including attention, storage, and executive scales), respectively. Questionnaires also collected demographic and epilepsy variables. RESULTS: Adults with epilepsy reported greater difficulties in basic and secondary mathematical skills on the DC compared with controls. Only one epilepsy variable, a younger age of epilepsy onset, related to higher DC scores (greater mathematical difficulties), but was not significantly related in regression analyses. Instead, the WMQ explained 33% of the variance on the DC; the poorer storage and attention (but not executive) on the WMQ were associated with the higher DC score, when demographic and epilepsy variables were accounted for. SIGNIFICANCE: Adults with epilepsy reported significant difficulties with mathematics in daily life, which were not explained by epilepsy variables but by poor working memory. While our findings suggest that daily difficulties with mathematics may be comorbid with epilepsy rather than epilepsy related, it is important to be cognizant of mathematical difficulties experienced by patients with epilepsy as they have potential to impact understanding of numerical information provided in patient care, such as risks associated with different epilepsy treatments.

The home numeracy environment and children's math skills: The moderating role of parents' math anxiety.

Evidence suggests that parents' math anxiety moderates the association between parents' help in mathematics homework and first graders' mathematics skills. Understanding whether similar associations are evident in younger children, in regard to the home numeracy environment (HNE) is essential, given that early math skills are strong predictors of later academic outcomes, and children's skills prior to kindergarten are fostered principally by their parents. Thus, the purpose of this study was to examine the association and interaction between the HNE and parents' math anxiety related to preschool children's numeracy performance. Participants were 121 parent-child dyads. Results from hierarchical multiple regression models demonstrated that parents' math anxiety and the HNE, included as separate predictors of children's math skills, were not statistically significant. However, the interaction between HNE and parents' math anxiety was statistically significant, such that the positive association between HNE and children's numeracy skills emerged when parents felt less anxious about math. These findings highlight the importance of accounting for parents' math anxiety when exploring the home influences on children's numeracy skills.