Boys' advantage on the fractions number line is mediated by visuospatial attention: Evidence for a parietal-spatial contribution to number line learning

The relation between number line performance and mathematics outcomes: Two meta-analyses

Understanding the magnitudes represented by numerals is a core component of early mathematical development and is often assessed by accuracy in situating numerals and fractions on a number line. Performance on these measures is consistently related to performance in other mathematics domains, but the strength of these relations may be overestimated because general cognitive ability has not been fully controlled in prior studies. The first of two meta-analyses (162 studies, 33,101 participants) confirmed a relation between performance on whole number (r = 0.33) and fractions number (r = 0.41) lines and overall mathematics performance. These relations were generally consistent across content domains (e.g., algebra and computation) and other moderators. The second (71 studies, 14,543 participants) used meta-analytic structural equation modeling to confirm these relations while controlling general cognitive ability (defined by IQ and working memory measures) and, in one analysis, general mathematics competence. The relation between number line performance and general mathematics competence remained significant but reduced (β = 0.13). Controlling general cognitive ability, whole number line performance consistently predicted competence with fractions but not performance on numeracy or computations measures. The results suggest an understanding of the magnitudes represented by whole numbers might be particularly important for students' fractions learning. RESEARCH HIGHLIGHTS: Two meta-analyses examined the link between the number line and mathematics performance. The first revealed significant relations across domains (e.g., algebra and computation). The second controlled for general cognitive ability and resulted in reduced but still significant relations. The relation between number line and fractions performance was stronger than relations to other domains.

Tracing the origins of the STEM gender gap: The contribution of childhood spatial skills

Despite some gains, women continue to be underrepresented in many science, technology, engineering, and math (STEM) fields. Using a national longitudinal dataset of 690 participants born in 1991, we tested whether spatial skills, measured in middle childhood, would help explain this gender gap. We modeled the relation between 4th-grade spatial skills and STEM majors while simultaneously accounting for competing cognitive and motivational mechanisms. Strong spatial skills in 4th grade directly increased the likelihood of choosing STEM college majors, above and beyond math achievement and motivation, verbal achievement and motivation, and family background. Additionally, 4th-grade spatial skills indirectly predicted STEM major choice via math achievement and motivation in the intervening years. Further, our findings suggest that gender differences in 4th-grade spatial skills contribute to women's underrepresentation in STEM majors. RESEARCH HIGHLIGHTS: Using a national longitudinal dataset, we found 4th-grade spatial skills directly predicted STEM college major choice after accounting for multiple cognitive and motivational mechanisms. Strong spatial skills in 4th grade also elevated STEM major choice via enhanced math achievement and motivation in the intervening years. Gender differences in 4th-grade spatial skills contributed to women's underrepresentation in STEM college majors.

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.

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.

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.

Boys' visuospatial abilities compensate for their relatively poor in-class attentive behavior in learning mathematics

The mathematics and reading achievement of 322 adolescents (159 boys) was assessed in seventh and eighth grades, as were their intelligence, working memory, and spatial abilities. Their seventh- and eighth-grade mathematics and English language arts teachers reported on their in-class attentive behavior. The latter emerged as an important predictor of achievement, but more so for mathematics than for reading. Boy were less attentive in classroom settings than girls (d = -.34) and performed better than expected in mathematics given their level of engagement in the classroom. Boys' better-than-expected mathematics achievement was related to advantages on visuospatial measures (ds = .28-.56), which fully mediated a sex difference in mathematics (ds = .27-.28) but not in reading achievement, with control of in-class attentive behavior. The results suggest that boys' advantages in visuospatial skills compensate for lower levels of classroom engagement in the learning of mathematics but not in reading competencies.

Mathematics Clusters Reveal Strengths and Weaknesses in Adolescents' Mathematical Competencies, Spatial Abilities, and Mathematics Attitudes

Pre-algebra mathematical competencies were assessed for a large and diverse sample of sixth graders (n = 1,926), including whole number and fractions arithmetic, conceptual understanding of equality and fractions magnitudes, and the fractions number line. The goal was to determine if there were clusters of students with similar patterns of pre-algebra strengths and weaknesses and if variation between clusters was related to mathematics attitudes, anxiety, or for a subsample (n = 342) some combination of intelligence, working memory, or spatial abilities. Critically, strengths and weaknesses were not uniform across the three identified clusters. Lower-performing students had pronounced deficits in their understanding of mathematical equality, fractions magnitudes, and the fractions number line. Higher-performing students had particular advantages in whole number and fractions arithmetic, and the fractions number line. Students could be reliably placed into clusters based on their mathematics self-efficacy and a combination of intelligence and spatial abilities. The results contribute to our understanding of key aspects of students' mathematical development, highlight areas in need of intervention for at-risk students, and identify cognitive areas in which scaffolds might be incorporated into these interventions.