Impacts of number lines and circle visual displays on caregivers' 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.

Adults systematically underestimate decimals and whole number exposure induces further magnitude-based underestimation.

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 expressed in multiple ways (e.g., 0.8, 0.80, 0.800, etc.). Here, we used a number line task with carefully selected stimuli to investigate how equivalent decimals (e.g., 0.8 and 0.80 on a 0-1 number line) and proportionally equivalent whole numbers (e.g., 80 on a 0-100 number line) are estimated. We find that young adults (n = 88, Mage = 20.22 years, SD = 1.65, 57 female) have a linear response pattern for both decimals and whole numbers, but those 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, we find that exposing participants to 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 magnitude estimation is fragile and subject to greater underestimation when exposed to whole numbers. (PsycInfo Database Record (c) 2024 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).

Perceptions of ease and difficulty, but not growth mindset, relate to specific math attitudes.

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.

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).