Clarissa A Thompson

• Ph.D.
• Professor (Assistant) at Kent State University

Growing evidence highlights the predictive power of cross-notation magnitude comparison (e.g., 2/5 vs. 0.25) for math outcomes, but whether these relations persist into adulthood and the underlying mechanisms remain unknown. Across two studies during the 2021–2022 academic year, we investigated undergraduates’ cross-notation and within-notation com...

There is a pressing need for feasible, scalable interventions that address children’s and adults’ math anxiety and result in enhanced math learning. In this article, we suggest a pathway toward intervention development. First, we consider what is known about the mechanisms of math anxiety. To treat math anxiety, we must understand both how and why...

Dealing with numbers is an inherent aspect of interpreting health statistics, and negative emotions may interfere with medical decision making. One emotionally charged decision-making context is parents making medical decisions for their children. Knowing which factors–such as anxiety specific to math contexts–are associated with parents’ negative...

Background Dominant psychotherapies target how individuals experience and understand their daily emotion. Therefore, research examining how daily emotions influence long-term mental health outcomes may help inform treatment development. Methods This investigation applied a multi-cohort (n = 378; n = 460), longitudinal design to test how reports of...

Math proficiency is an important predictor of educational attainment and life success. However, developing mathematical competency is challenging, and some content (e.g., fractions) can be enigmatic. Numerous factors are suspected to influence math performance, including strategy knowledge, attention, and executive functions. In two online studies,...

Growing evidence points to the predictive power of cross-notation rational number understanding (e.g., 2/5 vs. 0.25) relative to within-notation understanding (e.g., 2/5 vs. 1/4) in predicting math outcomes. Though correlational in nature, these studies suggest that number sense training emphasizing integrating across notations may have more positi...

Given that risk beliefs predict engagement in behaviors to prevent disease, it is important to understand the factors associated with risk beliefs. In the present paper, we conducted path analyses to investigate the associations of belief systems (political orientation and cultural worldviews of individualism and hierarchy) with COVID‐19 risk belie...

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...

We examined U.S. college students’ ability to calculate hypothetical course grades as well as their perceptions and misconceptions about different grading scales (i.e., 100, 387, 400, and 1,000 total points). People often exhibit misconceptions, such as the whole number bias, when reasoning about rational numbers, such as fractions and decimals. On...

As a key part of the behavioral immune system, disgust is thought to have evolved to motivate the avoidance of pathogens. While evidence for such a role is accruing, naturalistic tests of this thesis are few and exactly how risk is implicated remains unclear. Two pre-registered studies tested whether objective or perceived risk for Covid-19 predict...

General Audience Summary Health information involving ratios, like those about COVID-19 case-fatality rates, can be challenging to understand because people sometimes misapply their reasoning about whole numbers. In the present study, we recruited 1,832 U.S. adults from a national panel and randomly assigned them to either a business-as-usual contr...

Mathematical problem solving is a process involving metacognitive (e.g., judging progress), cognitive (e.g., working memory), and affective (e.g., math anxiety) factors. Recent research encourages researchers who study math cognition to consider the role that the interaction between metacognition and math anxiety plays in mathematical problem solvi...

Growing evidence highlights the predictive power of cross-notation magnitude comparison (e.g., 2/5 vs. 0.25) for math outcomes, but the underlying mechanisms remain unknown. Across two studies, we investigated undergraduates’ cross-notation and within-notation comparison skills given equivalent fractions, decimals, and percentages (Study 1, N=220 a...

Metacognitive monitoring, recognizing when one is accurate or not, is important because judgments of one’s performance or knowledge often relate to control decisions, such as help seeking. Unfortunately, children and adults struggle to accurately monitor their performance during number-magnitude estimation. People’s accuracy in estimating number ma...

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 si...

There is continued interest in understanding what leads people to do CDC-recommended COVID-19 prevention behaviors. We tested whether fear and COVID-19 worry would replicate as the primary drivers of six CDC recommend prevention behaviors. We recruited 741 adult participants during the second major peak of the COVID-19 pandemic in the United States...

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 condi...

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 pand...

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-m...

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...

Children display an early sensitivity to implicit proportions (e.g., 1 of 5 apples vs. 3 of 4 apples), but have considerable difficulty in learning the explicit, symbolic proportions denoted by fractions (e.g., "1/5" vs. "3/4"). Theoretically, reducing the gap between representations of implicit versus explicit proportions would improve understandi...

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 targeti...

In mathematics, learners often spontaneously draw on prior knowledge when learning new ideas. In this study, we examined whether the specific diagrams used to represent more familiar (i.e., whole number division) and less familiar ideas (i.e., fraction division) shape successful transfer. Undergraduates (N = 177) were randomly assigned to demonstra...

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 impact health decision...

Magnitude understanding and metacognition are important in life and for academic achievement. In two studies, we examined children’s and adults’ metacognitive awareness of their whole-number and fraction magnitude estimates. There were few differences between grades or numerical ranges in third through fifth graders’ (8–12-year-olds’) and adults’ (...

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, t...

Is there an optimal grading scheme? Do psychology instructors prefer one grading scheme over another? These questions were recently posted on the Society for the Teaching of Psychology Facebook page. After reading the responses, we realized that research in the domain of math cognition might help to shed light on an optimal grading scheme and put s...

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 heal...

Prior work exploring preschool-aged children’s reasoning with repeating patterns has shown that patterning ability is an important predictor of math achievement; however, there is limited research exploring older children’s growing pattern task performance. The current study tested whether presentation format impacts performance on growing pattern...

Background: In May, 2021, U.S. states began implementing “vaccination lotteries” to encourage vaccine-hesitant individuals to get a COVID-19 vaccine. Purpose: Drawing on theories from math cognition and behavioral economics, we tested several monetary lottery structures and their framing to determine which would best motivate unvaccinated individua...

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...

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 compared rates for information related to COVID-19 (e.g., number of deaths and number of cases) in one of four randomly-assig...

Although evidence exists for a feedback loop between positive affect and self-care behaviors, it is unclear if findings generalize to the COVID-19 pandemic. A 10-day daily diary was completed by 324 adult participants in the United States during spring 2020 when national stay-at-home orders were in effect. We hypothesized a reciprocal within-person...

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 studie...

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 number...

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 studie...

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...

Understanding fraction magnitudes is especially important in daily life, but fraction reasoning is quite difficult. To accurately reason about fraction magnitudes, adults need to monitor what they know and what they do not know. However, little is known about which cues adults use to monitor fraction performance. Across two studies, we examined adu...

At the onset of the COVID-19 global pandemic, our interdisciplinary team hypothesized that a mathematical misconception--whole number bias (WNB)--contributed to incorrect beliefs that COVID-19 was less fatal than the flu. We created a novel, five-minute online educational intervention, leveraging evidence-based cognitive science research, to encour...

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 asse...

People’s attitudes toward mathematics are multifaceted. Across four studies, we found that children and adults have different attitudes about mathematics when asked specifically about whole numbers, as opposed to fractions. The vast majority of children and adults reported negative attitudes toward fractions despite having positive attitudes toward...

Analogies between old and new concepts are common during classroom instruction. Previous transfer studies focused on how features of initial learning guide later, spontaneous transfer to new problem solving. We argue for a shift in the focus of analogical-transfer research toward understanding how to best support analogical transfer from previous l...

The Common Core State Standards in Mathematics recommends that children should use visual models to represent fraction operations, such as fraction division. However, there is little experimental research on which visual models are the most effective for helping children to accurately solve and conceptualize these operations. In the current study,...

The Cambridge Handbook of Cognition and Education - edited by John Dunlosky February 2019

Cambridge Core - Cognition - The Cambridge Handbook of Cognition and Education - edited by John Dunlosky

The development of a classroom observation protocol for novice college educators.

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 low...

The magnitude comparison task and the number line estimation task are widely used in the literatures on numerical cognition, mathematical development and mathematics education. It has been suggested that these tasks assess a central component of mathematical competence and, thus, are useful tools for diagnosing mathematical competence and developme...

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 aske...

This study examined the relationship between math anxiety and fraction understanding. Students with higher math anxiety were less likely to accurately compare fraction magnitudes because they used fewer strategies across all trials. These students may have less strategy knowledge or may not use strategies adaptively.

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 th...

How do speed and accuracy trade off, and what components of information processing develop as children and adults make simple numeric comparisons? Data from symbolic and non-symbolic number tasks were collected from 19 first graders (Mage = 7.12 years), 26 second/third graders (Mage = 8.20 years), 27 fourth/fifth graders (Mage = 10.46 years), and 1...

Accurate monitoring and control are essential for effective self-regulated learning. These metacognitive abilities may be particularly important for developing math skills, such as when children are deciding whether a math task is difficult or whether they made a mistake on a particular item. The present experiments investigate children's ability t...

Children's number-line estimation has produced a lively debate about representational change, supported by apparently incompatible data regarding descriptive adequacy of logarithmic (Opfer, Siegler, & Young, 2011) and cyclic power models (Slusser, Santiago, & Barth, 2013). To test whether methodological differences might explain discrepant findings...

Mathematics achievement is strongly predicted by fractions knowledge past other contributors such as whole numbers knowledge and working memory (Siegler et al., 2012). However, both children and adults struggle with fractions knowledge. Does math anxiety (MA) contribute to this struggle? Since previous studies have examined children’s fractions kno...

Memory for numbers improves with age and experience. One potential source of improvement is a logarithmic-to-linear shift in children’s representations of magnitude. To test this, Kindergartners and second graders estimated the location of numbers on number lines and recalled numbers presented in vignettes (Study 1). Accuracy at number-line estimat...

Memory for numbers improves with age and experience. One potential source of improvement is a logarithmic-to-linear shift in children's representations of magnitude. To test this, Kindergartners and second graders estimated the location of numbers on number lines and recalled numbers presented in vignettes (Study 1). Accuracy at number-line estimat...

Cognitive development has yielded many findings with implications for improving classroom instruction and student learning. Improving learning in mathematics is a priority for the United States. This article describes stumbling blocks that preclude children from showing optimal learning and generalization of mathematics skills including misconcepti...

abstract: The current study surveyed students’ knowledge of and perceptions about general education requirements at a large research-intensive university. Findings revealed that students harbored misconceptions about general education requirements and illuminated the reasons why students were choosing to take required general education courses at o...

Students in an introductory psychology class rated their level of confidence in their answers to exam questions on four multiple-choice exams through the course of a semester. Correlations between confidence judgments and accuracy (correct vs. incorrect) at the individual item level showed modest but significant relationships for item sets scaled t...

Recent investigations into pedagogical training of novice graduate instructors (Beers, Hill, Thompson, & Tran, 2014) indicate that graduate teaching associates (GTAs) and faculty generally agree on training a subset of important teaching skills (e.g., public speaking, organization, and mastery of content). An analysis of the top three skills respon...

What pedagogical skills are necessary for first-time college instructors? Ninety-two faculty (M = 41.3 years old, 68% female, 90.2% white, 91% born in the US) and 64 graduate students (M = 28.3 years old, 83% female, 87.5% white, 81% born in the US) listed the top three skills they believed were essential to instructors’ success in the college clas...

Placing landmarks on number lines, such as marking each tenth on a 0–1 line with a hatch mark and the corresponding decimal, has been recommended as a useful tool for improving children’s number sense. Four experiments indicated that some landmarks do have beneficial effects, others have harmful effects, and yet others have no effects on representa...

Researchers debate whether one represents the magnitude of a fraction according to its real numerical value or just the discrete numerosity of its numerator or denominator. The present study examined three effects based on the notion that people possess a mental number line to explore how children represent fractions when they compare fractions wit...

Across cultures and age groups music has a powerful impact on human affective states. We examined the effect of these affective responses on children's and adults' ability to label musical excerpts as major or minor. Adults, 10-year-olds, and 5-year-olds rated affective quality of excerpts that differed by mode, tempo, pitch, and excerpt type and t...

Children (n = 130; M(age) = 8.51-15.68 years) and college-aged adults (n = 72; M(age) = 20.50 years) completed numerosity discrimination and lexical decision tasks. Children produced longer response times (RTs) than adults. R. Ratcliff's (1978) diffusion model, which divides processing into components (e.g., quality of evidence, decision criteria s...

This article proposes an integrated theory of acquisition of knowledge about whole numbers and fractions. Although whole numbers and fractions differ in many ways that influence their development, an important commonality is the centrality of knowledge of numerical magnitudes in overall understanding. The present findings with 11- and 13-year-olds...

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 num...

We investigated the relation between children's numerical-magnitude representations and their memory for numbers. Results of three experiments indicated that the more linear children's magnitude representations were, the more closely their memory of the numbers approximated the numbers presented. This relation was present for preschoolers and secon...

Numeric magnitudes often bias adults' spatial performance. Partly because the direction of this bias (left-to-right versus right-to-left) is culture-specific, it has been assumed that the orientation of spatial-numeric associations is a late development, tied to reading practice or schooling. Challenging this assumption, we found that preschoolers...

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 t...

Studies have reported high correlations in accuracy across estimation contexts, robust transfer of estimation training to novel numerical contexts, and adults drawing mistaken analogies between numerical and fractional values. We hypothesized that these disparate findings may reflect the benefits and costs of learning linear representations of nume...

Spontaneous transfer of learning is often difficult to elicit. This finding may be widespread partly because pretests proactively interfere with transfer. To test this hypothesis, 7-year-olds' transfer was examined across 2 numerical tasks (number line estimation and categorization) in which similar representational changes have been observed. As p...

Development of estimation has been ascribed to two sources: (1) a change from logarithmic to linear representations of number and (2) development of general estimation skills. To test the representational change hypothesis, we gave children and adults an estimation task in which an automatic, linear representation is less adaptive than the logarith...

Previous work has suggested that an important tool of adult numeric competence is a "mental number line" that codes increasing numeric magnitudes spatially and with a directional bias. Partly because the direction of this bias (left-to-right versus right-to-left) is culture-specific, it has been assumed that a directionally-biased mental number lin...

Categorization of musical excerpts was accurately predicted by subjects' association of emotional valence with musical properties. The strength of this association prior to training predicted greater category knowledge, predicted types of errors during category learning, and predicted age differences in learning. Training in this association led to...

The ability to carry out effortless structural alignment is a hallmark of human cognitive processing. We tested whether this mechanism might explain how humans learn to represent the ratio characteristics of the decimal system. Specifically, children were asked to align the familiar ratio structure of object sets (e.g., how 10 is more similar to 1...