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.

Metacognitive Cues, Working Memory, and Math Anxiety: The Regulated Attention in Mathematical Problem Solving (RAMPS) Framework.

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 solving. Problem solvers can make many metacognitive judgments during a math problem, ranging from global judgments such as, "Do I care to solve this problem?" to minor cue-based judgments such as, "Is my current strategy successful in making progress toward the correct solution?" Metacognitive monitoring can hinder accurate mathematical problem solving when the monitoring is task-irrelevant; however, task-relevant metacognitive experiences can lead to helpful control decisions in mathematical problem solving such as checking work, considering plausibility of an answer, and considering alternate strategies. Worry and negative thoughts (i.e., math anxiety) can both interfere with the accuracy of metacognitive experiences as cues in mathematical problem solving and lead to avoidance of metacognitive control decisions that could otherwise improve performance. The current paper briefly reviews and incorporates prior literature with current qualitative reports (n = 673) to establish a novel framework of regulated attention in mathematical problem solving (RAMPS).

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).

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.

Structural basis for the autoinhibition and STI-571 inhibition of c-Kit tyrosine kinase.

The activity of the c-Kit receptor protein-tyrosine kinase is tightly regulated in normal cells, whereas deregulated c-Kit kinase activity is implicated in the pathogenesis of human cancers. The c-Kit juxtamembrane region is known to have an autoinhibitory function; however the precise mechanism by which c-Kit is maintained in an autoinhibited state is not known. We report the 1.9-A resolution crystal structure of native c-Kit kinase in an autoinhibited conformation and compare it with active c-Kit kinase. Autoinhibited c-Kit is stabilized by the juxtamembrane domain, which inserts into the kinase-active site and disrupts formation of the activated structure. A 1.6-A crystal structure of c-Kit in complex with STI-571 (Imatinib or Gleevec) demonstrates that inhibitor binding disrupts this natural mechanism for maintaining c-Kit in an autoinhibited state. Together, these results provide a structural basis for understanding c-Kit kinase autoinhibition and will facilitate the structure-guided design of specific inhibitors that target the activated and autoinhibited conformations of c-Kit kinase.

Crystal structure of Pasteurella haemolytica ferric ion-binding protein A reveals a novel class of bacterial iron-binding proteins.

Pasteurellosis caused by the Gram-negative pathogen Pasteurella haemolytica is a serious disease leading to death in cattle. To scavenge growth-limiting iron from the host, the pathogen utilizes the periplasmic ferric ion-binding protein A (PhFbpA) as a component of an ATP-binding cassette transport pathway. We report the 1.2-A structure of the iron-free (apo) form of PhFbpA, which is a member of the transferrin structural superfamily. The protein structure adopts a closed conformation, allowing us to reliably assign putative iron-coordinating residues. Based on our analysis, PhFbpA utilizes a unique constellation of binding site residues and anions to octahedrally coordinate an iron atom. A surprising finding in the structure is the presence of two formate anions on opposite sides of the iron-binding pocket. The formate ions tether the N- and C-terminal domains of the protein and stabilize the closed structure, also providing clues as to probable candidates for synergistic anions in the iron-loaded state. PhFbpA represents a new class of bacterial iron-binding proteins.

A fully integrated protein crystallization platform for small-molecule drug discovery.

Structure-based drug discovery in the pharmaceutical industry benefits from cost-efficient methodologies that quickly assess the feasibility of specific, often refractory, protein targets to form well-diffracting crystals. By tightly coupling construct and purification diversity with nanovolume crystallization, the Structural Biology Group at Syrrx has developed such a platform to support its small-molecule drug-discovery program. During the past 18 months of operation at Syrrx, the Structural Biology Group has executed several million crystallization and imaging trials on over 400 unique drug-discovery targets. Here, key components of the platform, as well as an analysis of some experimental results that allowed for platform optimization, will be described.

Structures of the cancer-related Aurora-A, FAK, and EphA2 protein kinases from nanovolume crystallography.

Protein kinases are important drug targets in human cancers, inflammation, and metabolic diseases. This report presents the structures of kinase domains for three cancer-associated protein kinases: ephrin receptor A2 (EphA2), focal adhesion kinase (FAK), and Aurora-A. The expression profiles of EphA2, FAK, and Aurora-A in carcinomas suggest that inhibitors of these kinases may have inherent potential as therapeutic agents. The structures were determined from crystals grown in nanovolume droplets, which produced high-resolution diffraction data at 1.7, 1.9, and 2.3 A for FAK, Aurora-A, and EphA2, respectively. The FAK and Aurora-A structures are the first determined within two unique subfamilies of human kinases, and all three structures provide new insights into kinase regulation and the design of selective inhibitors.

Structural genomics of the Thermotoga maritima proteome implemented in a high-throughput structure determination pipeline.

Structural genomics is emerging as a principal approach to define protein structure-function relationships. To apply this approach on a genomic scale, novel methods and technologies must be developed to determine large numbers of structures. We describe the design and implementation of a high-throughput structural genomics pipeline and its application to the proteome of the thermophilic bacterium Thermotoga maritima. By using this pipeline, we successfully cloned and attempted expression of 1,376 of the predicted 1,877 genes (73%) and have identified crystallization conditions for 432 proteins, comprising 23% of the T. maritima proteome. Representative structures from TM0423 glycerol dehydrogenase and TM0449 thymidylate synthase-complementing protein are presented as examples of final outputs from the pipeline.