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.

We propose that integrated number sense, the ability to fluidly translate and compare magnitudes within and across notations, is central to understanding of rational numbers. Consistent with this hypothesis, two studies of 6th through 8th grade students (N=264 and N=46) indicated that accuracy comparing magnitudes within and across notations predicted overall math achievement and fraction number line and arithmetic estimation accuracy. Cross-notation magnitude comparison accuracy (i.e., fraction vs. decimal, percentage vs. fraction, and percentage vs. decimal) accounted for variance in math outcomes beyond that explained by magnitude representations of individual notations. The findings also revealed a percentages-are-larger bias, in which percentages are perceived as larger than equivalent fractions and decimals. Theoretical and instructional implications are discussed.

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.

Decimal numbers are generally assumed to be a straightforward extension of the base-ten system for whole numbers given their shared place value structure. However, in decimal notation, unlike whole numbers, the same magnitude can be represented in infinite ways (e.g., 0.8, 0.80, 0.800, etc.). Here, we used carefully selected stimuli to investigate how equivalent decimals and whole numbers are represented on the number line. We find that young adults (N = 88, Mage = 20.22 Years, SD = 1.65, 57 female) have linear representations for both decimals and whole numbers, but that double-digit decimals (e.g., 0.08, 0.82, 0.80) are systematically underestimated relative to proportionally equivalent whole numbers (e.g., 8, 82, 80). Moreover, decimal string length worsens the underestimation, such that single-digit decimals (e.g., 0.8) are perceived as smaller than their equivalent double-digit decimals (e.g., 0.80). Finally, using a natural priming design, we find that presenting whole number stimuli before decimal stimuli induces magnitude-based underestimation, that is, greater underestimation for larger decimals. Together, these results suggest a small but persistent underestimation bias for decimals less than one, and further that decimal representation is fragile and subject to greater underestimation when exposed to whole numbers.

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.