Fostering diversity in mathematics cognition.

Integrating diverse perspectives in psychological science can enhance innovation in research and allow research teams to better study diverse populations of individuals through an authentic lens. Despite recent efforts to better address issues of race and ethnicity in research samples, the field of psychology broadly-and the area of mathematics cognition specifically-has largely failed to support scientists from diverse racial and ethnic backgrounds. In this essay, we consider the unique contributions that scholars of color can make to psychological research in mathematics cognition. Next, we reveal common challenges faced by scholars of color and challenges to recruiting and maintaining scholars of color in our community with a focus on Black scholars. Finally, we propose actions for diversifying the "pipeline" of promising scholars.

From integers to fractions: The role of analogy in transfer and long-term learning.

Fractions are the gatekeepers to advanced mathematics but are difficult to learn. One powerful learning mechanism is analogy, which builds fraction understanding on a pre-existing foundation of integer knowledge. Indeed, a short intervention that aligned fractions and integers on number lines improved children's estimates of fractions (Yu et al., 2022). The breadth and durability of such gains, however, are unknown, and analogies to other sources (such as percentages) may be equally powerful. To investigate this issue, we randomly assigned 109 fourth and fifth graders to one of three experimental conditions with different analogical sources (integers, percentages, or fractions) or a control condition. During training, children in the experimental conditions solved pairs of aligned fraction number line problems and proportionally-equivalent problems expressed in integers, percentages, or fractions (e.g., 3/8 on a 0-1 number line aligned with 3 on a 0-8 number line). Children in the control group solved fraction number-line problems sequentially. At pretest and a two-week delayed posttest, children completed a broad fraction knowledge battery, including estimation, comparison, categorization, ordering, and arithmetic. Results showed that aligning integers and fractions on number lines facilitated better estimation of fractional magnitudes, and the training effect transferred to novel fraction problems after two weeks. Similar gains were not observed for analogies using percentages. These findings highlight the importance of building new mathematical knowledge through analogies to familiar, similar sources.

Adaptive variability in children's conceptual models of division.

This study examined whether different types of commonly used mathematical tasks affect how children think about whole number division problems. Prior research suggested that children tend to rely on the partitive model to understand whole number division, which is likely problematic when students transition to learning about fraction division. We assessed variability in correct whole number division problem-solving strategies among 63 elementary school children (41.5% female, 58.5% male, 0% nonbinary/gender expansive; 69.2% White, 10.7% multiracial, 6.1% Black, 4.6% Latino, 3.3% other/unidentified, 6.1% preferred not to answer). Each participant was asked to demonstrate four whole number division problems in each of three contexts (within participants): objects, story problems, and number lines. Most children displayed understanding of multiple conceptual models of division, but strategies varied by context. Story problems elicited partitive models, number lines elicited quotative models, and objects elicited both. Finally, elementary school children used strategies adaptively. Number line representations may afford conceptual connections between earlier-learned whole number concepts and analogous later-learned fraction concepts, supporting the integration of children's whole number and fraction knowledge.

Task features change the relation between math anxiety and number line estimation performance with rational numbers: Two large-scale online studies.

Math performance is negatively related to math anxiety (MA), though MA may impact certain math skills more than others. We investigated whether the relation between MA and math performance is affected by task features, such as number type (e.g., fractions, whole numbers, percentages), number format (symbolic vs. nonsymbolic), and ratio component size (small vs. large). Across two large-scale studies (combined n = 3,822), the MA-performance relation was strongest for large whole numbers and fractions, and stronger for symbolic than nonsymbolic fractions. The MA-performance relation was also stronger for smaller relative to larger components, and MA relating to specific number types may be a better predictor of performance than general MA for certain tasks. The relation between MA and estimation performance changes depending on task features, which suggests that MA may relate to certain math skills more than others, which may have implications for how people reason with numerical information and may inform future interventions. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Experimental tests of hypothetical lottery incentives on unvaccinated adults' COVID-19 vaccination intentions.

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 = .224, ηp² = .03; Experiment 2: Message Framing, F[1, 266)] = .01, p = .940, ηp² = .000; Numeric Framing, F[1, 266] = 1.40, p = .237, ηp² = .01; Interaction, F[1, 266] = 1.40, p = .238, ηp² = .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. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Emotional complexity under high stress: Do protective associations for risk behaviors persist even during a pandemic?

Risk behaviors like substance use and binge eating are often used to cope with negative emotions. Engagement in these behaviors has been exacerbated by the COVID-19 pandemic. Past research suggests that complex emotion conceptualizations captured as emotion differentiation (ability to discriminate between emotional states) and polarity (ability to integrate positive and negative features of emotional experience) may be protective. We examined associations of mean affect intensity, emotion differentiation, and emotion polarity with frequency of daily substance use and binge eating across 10 days in a demographically diverse sample of U.S. adults (N = 353) recruited between March 24 and April 9, 2020, when stay-at-home orders were initiated. Owing to the nested data structure and excessive zero values, analyses were conducted using multilevel zero-inflated negative binomial regression. Consistent with past research, negative affect was positively associated with frequency of substance use and binge eating. Importantly, results indicated that negative emotion differentiation was protective, predicting greater likelihood of not using substances and binge eating at all across the sampling period. These effects remained even after controlling for mean affect intensity, emotion polarity, and positive emotion differentiation. Neither positive emotion differentiation nor emotion polarity were significantly associated with either behavior. Our results suggest that greater complexity in conceptualization of negative emotions facilitates some protection against risk behaviors such as substance use and binge eating, even during periods of high environmental stress. These findings have important implications for optimizing interventions to reduce engagement in risk behaviors. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Leveraging Math Cognition to Combat Health Innumeracy.

Rational numbers (i.e., fractions, percentages, decimals, and whole-number frequencies) are notoriously difficult mathematical constructs. Yet correctly interpreting rational numbers is imperative for understanding health statistics, such as gauging the likelihood of side effects from a medication. Several pernicious biases affect health decision-making involving rational numbers. In our novel developmental framework, the natural-number bias-a tendency to misapply knowledge about natural numbers to all numbers-is the mechanism underlying other biases that shape health decision-making. Natural-number bias occurs when people automatically process natural-number magnitudes and disregard ratio magnitudes. Math-cognition researchers have identified individual differences and environmental factors underlying natural-number bias and devised ways to teach people how to avoid these biases. Although effective interventions from other areas of research can help adults evaluate numerical health information, they circumvent the core issue: people's penchant to automatically process natural-number magnitudes and disregard ratio magnitudes. We describe the origins of natural-number bias and how researchers may harness the bias to improve rational-number understanding and ameliorate innumeracy in real-world contexts, including health. We recommend modifications to formal math education to help children learn the connections among natural and rational numbers. We also call on researchers to consider individual differences people bring to health decision-making contexts and how measures from math cognition might identify those who would benefit most from support when interpreting health statistics. Investigating innumeracy with an interdisciplinary lens could advance understanding of innumeracy in theoretically meaningful and practical ways.

Number lines can be more effective at facilitating adults' performance on health-related ratio problems than risk ladders and icon arrays.

Visual displays, such as icon arrays and risk ladders, are often used to communicate numerical health information. Number lines improve reasoning with rational numbers but are seldom used in health contexts. College students solved ratio problems related to COVID-19 (e.g., number of deaths and number of cases) in one of four randomly assigned conditions: icon arrays, risk ladders, number lines, or no accompanying visual display. As predicted, number lines facilitated performance on these problems-the number line condition outperformed the other visual display conditions, which did not perform any better than the no visual display condition. In addition, higher performance on the health-related ratio problems was associated with higher COVID-19 worry for oneself and others, higher perceptions of COVID-19 severity, and higher endorsement of intentions to engage in preventive health behaviors, even when controlling for baseline math skills. These findings have important implications for effectively presenting health statistics. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Self-care behaviors and affect during the early stages of the COVID-19 pandemic.

OBJECTIVE: Self-care behaviors aimed at maintaining physical and mental health are often recommended during stressful contexts. We tested emotional predictors of self-care behaviors (healthy eating, exercise, engaging in a hobby, relaxation/meditation, time spent with a supportive person, talking online with friends/family) during the COVID-19 pandemic and their emotional consequences. We hypothesized a reciprocal within-person process whereby positive affect increases self-care behaviors (Hypothesis 1) and self-care behaviors increase positive affect while decreasing negative affect (Hypothesis 2). METHOD: A 10-day daily diary was completed by 289 adult participants in the United States during spring 2020 when counties in 40 out of 50 states had some form of stay-at-home orders. RESULTS: Lagged analyses for Hypothesis 1 suggested that positive affect did not significantly predict residualized change in self-care behaviors; however, more intense negative affect predicted increased self-care behaviors from one day to the next. Concurrent analyses for Hypothesis 2 indicated most self-care behaviors were associated with more positive affect and some with less negative affect on the same day. Lagged analyses for Hypothesis 2 indicated that self-care behaviors largely did not predict residualized change in positive or negative affect from one day to the next. At the between-person level, people who experienced more positive affect engaged in more self-care behaviors across the sampling period. CONCLUSION: Self-care behaviors continue to have mental health benefits during stressful environments such as the COVID-19 pandemic and stay-at-home orders. Negative affect can play an adaptive role during times of stress by facilitating self-care. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Confidence in COVID problem solving: What factors predict adults' item-level metacognitive judgments on health-related math problems before and after an educational intervention?

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. Supplementary Information: The online version contains supplementary material available at 10.1007/s11409-022-09300-3.

What Drives Preventive Health Behavior During a Global Pandemic? Emotion and Worry.

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; Mage = 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.

Math matters: A novel, brief educational intervention decreases whole number bias when reasoning about COVID-19.

At the onset of the coronavirus disease (COVID-19) global pandemic, our interdisciplinary team hypothesized that a mathematical misconception-whole number bias (WNB)-contributed to beliefs that COVID-19 was less fatal than the flu. We created a brief online educational intervention for adults, leveraging evidence-based cognitive science research, to promote accurate understanding of rational numbers related to COVID-19. Participants from a Qualtrics panel (N = 1,297; 75% White) were randomly assigned to an intervention or control condition, solved health-related math problems, and subsequently completed 10 days of daily diaries in which health cognitions and affect were assessed. Participants who engaged with the intervention, relative to those in the control condition, were more accurate and less likely to explicitly mention WNB errors in their strategy reports as they solved COVID-19-related math problems. Math anxiety was positively associated with risk perceptions, worry, and negative affect immediately after the intervention and across the daily diaries. These results extend the benefits of worked examples in a practically relevant domain. Ameliorating WNB errors could not only help people think more accurately about COVID-19 statistics expressed as rational numbers, but also about novel future health crises, or any other context that involves information expressed as rational numbers. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Do adults treat equivalent fractions equally? Adults' strategies and errors during fraction reasoning.

Understanding fraction magnitudes is important for achievement and in daily life. However, adults' fraction reasoning sometimes appears to reflect whole number bias and other times reflects accurate reasoning. In the current experiments, we examined how contextual factors and individual differences in executive functioning (Experiment 1), knowledge of fraction equivalence (both experiments), and strategy use (Experiment 2) influenced adults' fraction reasoning. Adults were only biased by fraction components when reasoning about fractions as holistic magnitudes was difficult: when estimating under a time constraint, when estimating fractions with large components, or when comparing fractions close in decimal distance. However, adults' knowledge of fraction equivalence moderated the effects of whole number components on their fraction estimation performance: when modeled at low levels of equivalence knowledge, adults were biased by fraction components when estimating. Adults with more knowledge of fraction equivalence were able to reason about fractions as holistic magnitudes through adaptive strategy choices. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Math anxiety, but not induced stress, is associated with objective numeracy.

Many daily activities require a basic understanding of math. Numeracy, which refers to individual differences in the ability to understand numerical concepts and work with probabilities, has been linked to health-related decision-making and medical and financial outcomes. Whether affective influences impact numeracy has not been experimentally assessed, although research has shown that emotions impact judgments and decision-making. Stress is one commonly experienced affective influence that could impact numeracy. We examined whether objective and subjective numeracy were influenced by stress induced from anticipating giving a speech in a laboratory setting. We also examined the association of self-reported math anxiety, or apprehension pertaining to mathematics, with objective and subjective numeracy. Two experiments were conducted; the second was a direct replication. Undergraduate students (Experiment 1, n = 99; Experiment 2, n = 139) were randomly assigned to one of two conditions: a stress induction or a neutral condition. Whereas neither objective nor subjective numeracy significantly differed across conditions, math anxiety was a consistent predictor of objective and subjective numeracy. Math anxiety and baseline perceived stress did not consistently moderate any effects. These findings have implications for health care, educational, and financial contexts in which people must make decisions that involve complex numbers. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Are Books Like Number Lines? Children Spontaneously Encode Spatial-Numeric Relationships in a Novel Spatial Estimation Task.

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.

From continuous magnitudes to symbolic numbers: The centrality of ratio.

Leibovich et al.'s theory neither accounts for the deep connections between whole numbers and other classes of number nor provides a potential mechanism for mapping continuous magnitudes to symbolic numbers. We argue that focusing on non-symbolic ratio processing abilities can furnish a more expansive account of numerical cognition that remedies these shortcomings.