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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.

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.

How does understanding the decimal system change with age and experience? Second, third, sixth graders, and adults (Experiment 1: N = 96, mean ages = 7.9, 9.23, 12.06, and 19.96 years, respectively) made number line estimates across 3 scales (0-1,000, 0-10,000, and 0-100,000). Generation of linear estimates increased with age but decreased with numerical scale. Therefore, the authors hypothesized highlighting commonalities between small and large scales (15:100::1500:10000) might prompt children to generalize their linear representations to ever-larger scales. Experiment 2 assigned second graders (N = 46, mean age = 7.78 years) to experimental groups differing in how commonalities of small and large numerical scales were highlighted. Only children experiencing progressive alignment of small and large scales successfully produced linear estimates on increasingly larger scales, suggesting analogies between numeric scales elicit broad generalization of linear representations.

The relation between short-term and long-term change (also known as learning and development) has been of great interest throughout the history of developmental psychology. Werner and Vygotsky believed that the two involved basically similar progressions of qualitatively distinct knowledge states; behaviorists such as Kendler and Kendler believed that the two involved similar patterns of continuous growth; Piaget believed that the two were basically dissimilar, with only development involving qualitative reorganization of existing knowledge and acquisition of new cognitive structures. This article examines the viability of these three accounts in accounting for the development of numerical representations. A review of this literature indicated that Werner's and Vygotsky's position (and that of modern dynamic systems and information processing theorists) provided the most accurate account of the data. In particular, both changes over periods of years and changes within a single experimental session indicated that children progress from logarithmic to linear representations of numerical magnitudes, at times showing abrupt changes across a large range of numbers. The pattern occurs with representations of whole number magnitudes at different ages for different numerical ranges; thus, children progress from logarithmic to linear representations of the 0-100 range between kindergarten and second grade, whereas they make the same transition in the 0-1,000 range between second and fourth grade. Similar changes are seen on tasks involving fractions; these changes yield the paradoxical finding that young children at times estimate fractional magnitudes more accurately than adults do. Several different educational interventions based on this analysis of changes in numerical representations have yielded promising results.

Health risks, when presented as ratios (e.g., two out of seven people), are challenging to understand, but visual displays can foster accurate understanding. We conducted three experiments to test how characteristics of numbers (Experiment 1), icon arrays (Experiments 1, 2, and 3), and number lines (Experiments 1 and 3) influenced people's ability to accurately estimate the risk of experiencing side effects. Participants in each experiment saw smaller‐ (e.g., 2 out of 7) and larger‐component (e.g., 264 out of 924) equivalent ratios in one of three conditions: with number lines only, with icon arrays only, or in the form of Arabic numerals with no accompanying visual. We found that risk estimates were more accurate when presented in 10 × 10 icon arrays, long horizontal 1 × 99 arrays, or number lines. We theorize that hypothetical risks can be estimated more accurately when the display affords easy translation to a percentage. [ABSTRACT FROM AUTHOR]

Adults use a variety of strategies to reason about fraction magnitudes, and this variability is adaptive. In two studies, we examined the relationships between mathematics anxiety, working memory, strategy variability and performance on two fraction tasks: fraction magnitude comparison and estimation. Adults with higher mathematics anxiety had lower accuracy on the comparison task and greater percentage absolute error (PAE) on the estimation task. Unexpectedly, mathematics anxiety was not related to variable strategy use. However, variable strategy use was linked to more accurate magnitude comparisons, especially among adults with lower working memory performance or those who use mathematics less frequently, as well as lower PAE on the estimation task. These findings shed light on the role of strategy variability in fraction problem solving and demonstrate a link between mathematics anxiety and fraction magnitude reasoning, a key predictor of general mathematics achievement. [ABSTRACT FROM AUTHOR]

• Brief picture-book interventions may improve adults' fraction understanding. • Parents' fraction performance benefited from both number lines and circle area models. • Caregivers were aware of their learning over time. • Caregivers may play a significant role in children's fraction understanding. Playful fraction picture books, together with math instructional content called "back matter," may promote fraction learning, which is crucial because fractions are difficult and often disliked content. However, open questions remain regarding how different types of back matter may affect caregivers' ability to use fraction picture books as a teaching tool. The current study offers a novel investigation into how back matter affects caregivers' (N = 160) fraction understanding (i.e., equivalence and arithmetic) and subjective beliefs about math using a pretest/posttest design. We contrasted existing back matter text with research-informed back matter text crossed with either circle area or number line visual displays. Caregivers' performance improved from pretest to posttest in the Researcher-Generated + Circles condition (fraction equivalence) and in the Existing + Circles, Researcher-Generated + Circles, and Researcher-Generated + Number Lines conditions (fraction arithmetic). In addition, caregivers were aware of their learning; they predicted improvements in their fraction arithmetic performance over time. These findings suggest that brief interventions, such as back matter in children's picture books, may improve adults' fraction understanding. [ABSTRACT FROM AUTHOR]