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Background & Purpose: Primary prevention of COVID-19 has focused on encouraging compliance with specific behaviors that restrict contagion. This investigation sought to characterize engagement in these behaviors in U.S. adults early during the pandemic and to build explanatory models of the psychological processes that drive them. Methods: US adults were recruited through Qualtrics Research Panels (N = 324; 55% female; M[subscript age] = 50.91, SD = 15.98) and completed 10 days of online reports of emotion, COVID-19 perceived susceptibility and worry, and recommended behaviors (social distancing, hand washing, etc.). Factor analysis revealed behaviors loaded on two factors suggesting distinct motivational orientations: approach and avoidance. Results: Changes in approach and avoidance behaviors over the 10 days indicated large individual differences consistent with three types of participants. Discrete emotions, including fear, guilt/shame, and happiness were associated with more recommended behaviors. Fear and COVID-19 worry indirectly influenced each other to facilitate more behavioral engagement. While emotions and worry strongly predicted individual differences in behavior across the 10 days, they did not predict as well why behaviors occurred on one day versus another. Conclusions: These findings suggest how daily affective processes motivate behavior, improving the understanding of compliance and efforts to target behaviors as primary prevention of disease.

Prior research has found gender differences in spatial tasks in which men perform better, and are more confident, than women. Do gender differences also occur in people's confidence as they perform number-line estimation, a common spatial-numeric task predictive of math achievement? To investigate this question, we analyzed outcomes from six studies (N = 758 girls/women and boys/men with over 20,000 observations; grades 1-5 and adults) that involved a similar method: Participants estimated where a provided number (e.g., ¾, 37) was located on a bounded number line (e.g., 0-1; 0-100), then judged their confidence in that estimate. Boys/men were more precise (g = 0.52) and more confident (g = 0.30) in their estimates than were girls/women. Linear mixed model analyses of the trial-level data revealed that girls'/women's estimates had about 31% more error than did boys'/men's estimates, and even when controlling for precision, girls/women were about 7% less confident in their estimates than were boys/men. These outcomes should encourage researchers to consider gender differences for studies on math cognition and provide pathways for future research to address potential mechanisms underlying the present gender gaps. [This article was published in "Metacognition and Learning" (EJ1289459).]

People frequently encounter numeric information in medical and health contexts. In this paper, we investigated the math factors that are associated with decision-making accuracy in health and non-health contexts. This is an important endeavor given that there is relatively little cross-talk between math cognition researchers and those studying health decision making. Ninety adults (M = 37 years; 86% White; 51% male) answered hypothetical health decision-making problems, and 93 adults (M = 36 years; 75% White; 42% males) answered a non-health decision-making problem. All participants were recruited from an online panel. Each participant completed a battery of tasks involving objective math skills (e.g., whole number and fraction estimation, comparison, arithmetic fluency, objective numeracy, etc.) and subjective ratings of their math attitudes, anxiety, and subjective numeracy. In separate regression models, we identified which objective and subjective math measures were associated with health and non-health decision-making accuracy. Magnitude comparison accuracy, multi-step arithmetic accuracy, and math anxiety accounted for significant variance in health decision-making accuracy, whereas attention to math, as illustrated in open-ended strategy reports, was the only significant predictor of non-health decision-making accuracy. Importantly, reliable and valid measures from the math cognition literature were more strongly related to health decision-making accuracy than were commonly used subjective and objective measures of numeracy. These results have a practical implication: Understanding the math factors that are associated with health decision-making performance could inform future interventions to enhance comprehension of numeric health information.

Prior work exploring preschool-aged children's reasoning with repeating patterns has shown that patterning ability is an important predictor of math achievement; however, there is limited research exploring older children's growing pattern task performance. The current study tested whether presentation format impacts performance on growing pattern problems, and whether the effects of presentation format extend to transfer word problems for which no patterns are provided. Sixth grade students were randomly assigned to complete several growing pattern tasks in one of three presentation formats (sequences of values, or tables of values), and later completed transfer story problems with no figures, sequences, or tables provided. Findings suggest that presenting growing patterns as figures can benefit performance, although these benefits may depend on both pattern type and task. No differences were observed in performance on transfer problems, likely because students rarely spontaneously generated figures. Additional exploratory analyses suggest that performance on growing pattern problems may be related to both standardized math ability and fraction task performance, whereas inhibitory control may only be related to performance for specific patterning tasks. These findings have implications for educators because describing/expressing patterns is critical to algebra and higher-level mathematics.

Children's informal and formal learning experiences with geometric shapes currently result in misconceptions that persist into adulthood. Here, we combine research from mathematics education as well as cognitive science pertaining to concepts, categories, and learning strategies to propose a more optimal progression that is better specified and justified than the current standards. To do so, we reframed what constitutes a "simple" shape from perceptual simplicity to simplicity of properties. Our Property-Based Shape Sequence uses property-based criteria of what makes shapes "simple" and progresses in a way that affords opportunities for learners to develop hierarchical conceptions of two-dimensional and three-dimensional shapes. Our goals are threefold: (1) recommend an optimal, mathematically-correct shape learning sequence, (2) correct misconceptions that adults and children harbor about shapes, and (3) encourage cross-disciplinary collaborations between mathematics education and psychology researchers to validate the proposed learning sequence.

We investigated whether three interventions -- studying incorrect worked examples, studying correct worked examples, or receiving feedback -- improved children's 0-1,000 (Experiment 1) and adults' 1 thousand--1 billion (Experiment 2) number-line estimation precision relative to a no intervention control group. At pretest, participants estimated numbers on number lines (without feedback or examples) and judged their confidence in each estimate. They were then assigned to an intervention group, completed intervention trials, and then estimated numbers and judged their confidence at posttest. Children's and adults' confidence judgments did not increase from pretest to posttest. However, consistent with prior research, feedback improved children's and adults' estimation precision from pretest-to-posttest. Importantly, studying correct worked examples also improved precision, but studying incorrect worked examples did not. Although not all children benefited from training, those who did were able to transfer their knowledge to a number-categorization task. Adults in the feedback group were also able to transfer their learning. These outcomes highlight benefits of studying worked examples for improving children's and adults' estimation precision, but to obtain benefits, corrective feedback must be included.

Objective: In May 2021, U.S. states began implementing "vaccination lotteries" encouraging COVID-19 vaccination. Drawing from Prospect Theory and math cognition research, we tested several monetary lottery structures and their framing to determine which would best motivate unvaccinated adults. Method: In two online experiments, U.S. adults were asked to imagine that their state implemented a vaccination lottery. In Experiment 1, participants (N = 589) were randomly assigned to 1 of 12 conditions varying the monetary amount and number of winners, holding constant a $5 million total payout. In Experiment 2, participants (N = 274) were randomly assigned to one of four conditions in a 2 (Message Framing: Gain versus Loss) by 2 (Numeric Framing: Big versus Small) factorial design; in all conditions, five people would each win $1 million. Participants rated their baseline vaccination willingness (1 = "not at all" to 4 = "very") and postmanipulation COVID-19 vaccination intentions "if their state offered this incentive" (0 = "definitely would not" to 100 = "definitely would"). Results: Intentions did not differ across conditions (Experiment 1: F[11, 561] = 1.29, p = 0.224, [partial eta squared] = 0.03; Experiment 2: Message Framing, F[1, 266)] = 0.01, p = 0.940, [partial eta squared] = 0.000; Numeric Framing, F[1, 266] = 1.40, p = 0.237, [partial eta squared] = 0.01; Interaction, F[1, 266] = 1.40, p = 0.238, [partial eta squared] = 0.01). When participants were shown a list of 12 lottery structures and asked which they preferred, participants on average preferred options that awarded less money to more people. However, 41.9% of participants across both experiments indicated they would not vaccinate for any lottery-based monetary incentive. Conclusions: Multiple lottery structures could be equally (un)motivating for unvaccinated adults. Structures that distribute incentives across more people or alternative public health strategies should be considered.

The advent of COVID-19 highlighted widespread misconceptions regarding people's accuracy in interpreting quantitative health information. How do people judge whether they accurately answered health-related math problems? Which individual differences predict these item-by-item metacognitive monitoring judgments? How does a brief intervention targeting math skills--which increased problem-solving accuracy--affect people's monitoring judgments? We investigated these pre-registered questions in a secondary analysis of data from a large Qualtrics panel of adults (N = 1,297). Pretest performance accuracy, math self-efficacy, gender, and math anxiety were associated with pretest item-level monitoring judgments. Participants randomly assigned to the intervention condition, relative to the control condition, made higher monitoring judgments post intervention. That is, these participants "believed" they were more accurate when answering problems. Regardless of experimental condition, those who actually were correct on health-related math problems made higher monitoring judgments than those who answered incorrectly. Finally, consistent with prior research, math anxiety explained additional variance in monitoring judgments beyond trait anxiety. Together, findings indicated the importance of considering both objective (e.g., problem accuracy) and subjective factors (e.g., math self-efficacy, math anxiety) to better understand adults' metacognitive monitoring.

Proficiency in math is critically important given its implications for education and daily life (e.g., finances, health). However, math is a challenging subject, and proficiency requires a complex interplay of content knowledge and general cognitive processes, including Executive Function (EF). In this exploratory study, we used heat maps to examine whether participants' self-reported attention to strategy-specific components of fraction arithmetic equations (i.e., operations, numerators, denominators) was related to their EF and task performance. Our results indicated that participants with stronger EF (indexed by a numerical stroop task) obtained higher fraction arithmetic scores and were also more likely to attend to strategy-specific components in the fraction problems. Additionally, a positive correlation was found between participants’ selection of strategy-specific components and their fraction arithmetic accuracy. Keywords: Fraction arithmetic; Strategy Reports; Executive Function; Inhibitory Control; Attention

Recent work has suggested that cross-notation understanding (e.g., 2/5 vs. 0.25) is important for math outcomes. In this study, equivalent fraction, decimal, and percent stimuli were used to examine individual differences in cross-notation and within-notation comparison in undergraduate students (N=183). Hierarchical linear regression analyses suggested that cross-notation magnitude comparison accuracy added explanatory power beyond that of within-notation magnitude comparison accuracy in predicting fraction arithmetic calculation and estimation skills, as well as ACT scores. Additionally, participants did not perceive equivalent rational numbers as equivalent when expressed in different notations (e.g., percentages were perceived as larger than equivalent fractions or decimals). Undergraduate students were also randomly assigned to one of two number line interventions: one focused on emphasizing connections among fractions, decimals, and percentages and another focused on developing fraction magnitude representations. Both interventions yielded improvements in rational number understanding, but there were some greater benefits of the cross-notation intervention.

Math anxiety (MA) is negatively related to math performance. One proposed intervention with potential to disrupt the MA-math performance link is expressive writing. The current study aimed to conceptually replicate Park and colleagues (2014). In that study, the authors concluded that expressive writing effectively boosted math anxious students’ performance. In our current sample of 168 college students, participants randomly assigned to the expressive writing condition were no more accurate at posttest than were other participants assigned to a math self-concept intervention, active control, or passive control. Additionally, participants in the math self-concept and active control conditions reported lower state MA immediately following the intervention; participants in the expressive writing and passive control conditions reported no differences between pretest and posttest state MA. The current study provides boundary conditions for the effectiveness of expressive writing interventions in ameliorating MA during difficult math tasks and illuminates potential mechanisms underlying MA.

Children display an early sensitivity to implicit proportions (e.g., 1 of 5 apples vs. 3 of 4 apples), but have considerable difficulty in learning the explicit, symbolic proportions denoted by fractions (e.g., "1/5" vs. "3/4"). Theoretically, reducing the gap between representations of implicit versus explicit proportions would improve understanding of fractions, but little is known about how the representations develop and interact with one another. To address this, we asked 177 third, fourth, and fifth graders (M = 9.85 years, 87 girls, 69% White, 19% low income) to estimate the position of proportionally equivalent integers and fractions on number lines (e.g., 3 on a 0-8 number line vs. 3/8 on a 0-1 number line, Study 1). With increasing age, children's estimates of implicit and explicit proportions became more coherent, such that a child's estimates of fractions on a 0-1 number-line was a linear function of the same child's estimates of equivalent integers. To further investigate whether preexisting integer knowledge can facilitate fraction learning through analogy, we assigned 100 third to fifth graders (M = 10.04 years, 55 girls, 76% White) to an Alignment condition, where children estimated fractions and integers on aligned number lines, or to a No Alignment condition (Study 2). Results showed that aligning integers and fractions on number lines facilitated a better understanding of fractional magnitudes, and increased children's fraction estimation accuracy to the level of college students'. Together, findings suggest that analogies can play an important role in building a coherent understanding of proportions.

During the COVID-19 pandemic, people across the globe have been exposed to large amounts of statistical data. Previous studies have shown that individuals' mathematical understanding of health-related information affects their attitudes and behaviours. Here, we investigate the relation between: (1) basic numeracy; (2) COVID-19 health numeracy; and (3) COVID-19 health-related attitudes and behaviours. An online survey measuring these three variables was distributed in Canada, the United States (US) and the United Kingdom (UK) (n = 2032). In line with predictions, basic numeracy was positively related to COVID-19 health numeracy. However, predictions, neither basic numeracy nor COVID-19 health numeracy was related to COVID-19 health related attitudes and behaviours (e.g. follow experts' recommendations on social distancing, wearing masks etc.). Multi-group analysis was used to investigate mean differences and differences in the strength of the correlation across countries. Results indicate there were no between-country differences in the correlations between the main constructs but there were between-country differences in latent means. Overall, results suggest that while basic numeracy is related to one's understanding of data about COVID-19, better numeracy alone is not enough to influence a population's health-related attitudes about disease severity and to increase the likelihood of following public health advice.

Do children spontaneously represent spatial-numeric features of a task, even when it does not include printed numbers (Mix et al., 2016)? Sixty first grade students completed a novel spatial estimation task by seeking and finding pages in a 100-page book without printed page numbers. Children were shown pages 1 through 6 and 100, and then were asked, "Can you find page X?" Children's precision of estimates on the page finder task and a 0-100 number line estimation task was calculated with the Percent Absolute Error (PAE) formula (Siegler and Booth, 2004), in which lower PAE indicated more precise estimates. Children's numerical knowledge was further assessed with: (1) numeral identification (e.g., What number is this: 57?); (2) magnitude comparison (e.g., Which is larger: 54 or 57?); and (3) counting on (e.g., Start counting from 84 and count up 5 more). Children's accuracy on these tasks was correlated with their number line PAE. Children's number line estimation PAE predicted their page finder PAE, even after controlling for age and accuracy on the other numerical tasks. Children's estimates on the page finder and number line tasks appear to tap a general magnitude representation. However, the page finder task did not correlate with numeral identification and counting-on performance, likely because these tasks do not measure children's magnitude knowledge. Our results suggest that the novel page finder task is a useful measure of children's magnitude knowledge, and that books have similar spatial-numeric affordances as number lines and numeric board games.

Children display an early sensitivity to implicit proportions (e.g., 1 of 5 apples vs 3 of 4 apples) but have considerabledifficulty in learning the explicit, symbolic proportions denoted by fractions (e.g., 1/5 vs 3/4). Theoretically, reducingthe gap between representations of implicit vs explicit proportions would improve understanding of fractions, but littleis known about how the representations develop and interact with one another. To address this, we asked 163 third tofifth graders to estimate the position of proportionally-equivalent integers and fractions on number lines (e.g., 3 on 0-8number line vs 3/8 on 0-1 number line). We found that, with increasing age, children were more accurate and linear inrepresenting both integers and fractions. More importantly, childrens estimates of implicit and explicit proportions becamemore coherent, such that a childs estimates of fractions on a 0-1 number-line was a linear function of the same childsestimates of equivalent integers. This representational coherence independently predicted childrens fraction proficiency inother tasks, suggest- ing that building a coherent understanding of proportions is an educationally-important goal.

East Asian students routinely outperform American peers in mathematics. One source of this learning gap may be linguis-tic, such as explicitly naming part-whole relations in fractions (e.g., of four parts, one in Korean vs. one-fourth in English).Our study examined whether adopting such language would improve American children’s number-line estimates. To testthis, 83 10-year-olds were read fractions using either Korean-style or English names over pretest, training, and posttest. Inboth conditions, number-line problems either had no landmarks, landmarks that matched the denominator, or landmarksthat did not match the denominator. As expected, we observed a session by problem type interaction (F=2.71, p¡.05),indicating that feedback improved accuracy most for problems involving matching landmarks. Surprisingly, the effect ofKorean naming was to reduce accuracy across all problems and test phases (ps ¡ .01). Results offer an important warningagainst linguistic reform that may be harmful for American students.

Background: People report negative attitudes towards fractions and percentages relative to whole numbers (WNs, Sidney, Thompson, Fitzsimmons, & Taber, 2021), and these attitudes may relate to an individual's interpretation of what experiences with these number types signify. Because fractions are challenging, individual differences related to beliefs about challenge, such as endorsement of a growth versus fixed mindset (Dweck, 2006) and interpretations of easy or difficult experiences (Fisher & Oyserman, 2017), could relate to attitudes towards fractions relative to other number types. Aims: Two studies tested whether gender, math skills, mindset beliefs, and perceptions of difficulty relate to negative math attitudes towards specific number types. Samples: Two samples of college students (Study 1: N = 491; Study 2: N = 415), approximately 19 years of age (17% male, 51% first year students) participated. Methods: Participants rated attitudes pertaining to WNs, fractions, and percentages, endorsement of a growth mindset, and perceptions of ease and difficulty. Results: Replicating prior work (Sidney, Thompson, Fitzsimmons, & Taber, 2021), college students endorsed more negative attitudes about fractions than WNs and percentages. Self-reported ACT scores related to all number-type attitudes, endorsement of the belief that 'difficult tasks/goals are important' related to fraction attitudes, and endorsement of the belief that 'easy tasks/goals are possible' related to whole number attitudes. Endorsement of a growth mindset did not relate to specific math attitudes. Conclusions: People struggle to integrate their whole number and rational number representations, and one reason people hold negative attitudes about fractions may be that they view them as difficult and even impossible.

We investigated the relation between children's numerical-magnitude representations and their memory for numbers. Results of three experiments indicated that the more linear children's magnitude representations were, the more closely their memory of the numbers approximated the numbers presented. This relation was present for preschoolers and second graders, for children from low-income and middle-income backgrounds, for the ranges 0 through 20 and 0 through 1,000, and for four different tasks (number line, measurement, numerosity, and categorization) measuring numerical-magnitude representations. Other types of numerical knowledge--numeral identification and counting--were unrelated to recall of the same numerical information. The results also indicated that children's representations vary from trial to trial with the numbers they need to represent and remember and that general strategy-choice mechanisms may operate in selection of numerical representations, as in other domains. [This article was published in "Psychological Science," v21 n9 p1274-1281 2010.]

Fractions knowledge is essential to everyday life, yet manychildren and adults struggle to accurately represent fractions.This is the first study to investigate adults’ confidencejudgments and eye fixations as they solved fractions numberline estimation, magnitude comparison, and magnitudeordering tasks. Educational implications are discussed.

Comparing health risks is challenging. We tested whether a worked-example intervention with number line (NL) visual displays improved adults' risk comparison accuracy, whether pretest confidence moderated learning, and which individual differences related to accuracy. Replicating prior work, U.S. adults randomly assigned to the intervention (n = 883) were more accurate than control participants (n = 949) at solving health-related math problems with number line visual displays and a transfer problem without a visual display. One day later, most participants were accurate and there were no differences between conditions, potentially because participants with better math skills and attitudes participated at follow-up. However, there was a small effect on accuracy 1 day later among those who learned from the intervention. Adults were more likely to learn from the intervention if they made a low-confidence pretest error. Identifying as male, accurately estimating numbers on number lines, lower math anxiety, higher educational attainment, and being older were associated with greater risk comparison accuracy. General Audience Summary: Health information involving ratios, like those about COVID-19 case-fatality rates, can be challenging to understand because people sometimes misapply their reasoning about whole numbers. In the present study, we recruited 1,832 U.S. adults from a national panel and randomly assigned them to either a business-as-usual control condition or a brief, online educational intervention, which included a step-by-step worked example aimed at teaching adults how to calculate and compare case-fatality rates for COVID-19 versus the flu. Participants were more accurate at comparing health risks, such as between COVID-19 and the flu, when problems were accompanied by number line visual displays if they engaged with the intervention compared to those who were in a control condition. The intervention participants were also more accurate than control participants on a problem that did not include a visual display. And, among those who learned to accurately compare case-fatality rates without a visual display support, they were able to solve a similar problem 1 day later. We also found that people were more likely to learn from the intervention if, prior to the intervention, they made an error with low relative to high confidence. Finally, we found that people who identified as male, who estimated numbers more accurately on number lines, who reported lower math anxiety, who were more highly educated and older, were more accurate in comparing risks in health-related math problems. [ABSTRACT FROM AUTHOR]