Unpacking the challenges and predictors of elementary-middle school students' use of the distributive property.

The distributive property plays a pivotal role in advancing students' understanding of multiplication, enabling the decomposition of problems and the acquisition of new facts. However, this property of multiplication is difficult for students to understand. We used two unique data sets to explore middle school students' use of the distributive property. Study 1 involved data from 1:1 structured interviews of students (N = 24) discussing worked examples and solving associated practice problems. We examined whether or not students used the distributive property to solve the problems and whether or not interviewers followed the recommended distributive property prompts or defaulted to more conventional methods. Despite exposure to worked examples using the distributive property and a protocol calling for attention to it, students and interviewers favored methods like PEMDAS (parentheses, exponents, multiplication, division, addition, subtraction) or long multiplication. Study 2 used a data set with middle school students' (N = 131) item-level responses on Kirkland's (2022; doctoral dissertation, University of Notre Dame) Brief Assessment of Mature Number Sense along with several related measures of domain-general and domain-specific skills. We extracted problems involving the distributive property for analysis. Surprisingly, there was no evidence that students' use of the distributive property improved from sixth grade to eighth grade. However, both grade-level mathematics achievement and cognitive reflection uniquely predicted the correct use of the distributive property. Results suggest that middle school students who exhibit stronger reflective thinking tend to perform better on distributive property problems. Findings highlight cognitive reflection as a potentially important construct involved in the understanding and use of the distributive property.

Kindergarten predictors of formal understanding of mathematical equivalence in second grade.

A longitudinal study was conducted to identify unique sources of individual differences in later understanding of the equal sign as a relational symbol of equivalence (i.e., formal understanding of mathematical equivalence). The sample included 141 children from a mid-sized city in the Midwestern United States (Mage = 6 years, 2 months in kindergarten; 88 boys, 53 girls; 71% white, 8% Hispanic or Latine, 7% Black, 3% Asian, 11% multiracial or other race/ethnicity; 42% qualified for free/reduced lunch). Children were assessed on three categories of skills in kindergarten including number knowledge, relational thinking, and executive functioning. These skills were hypothesized to provide a foundation for a formal understanding of mathematical equivalence (assessed in second grade) by preventing a specific, narrow misunderstanding of the equal sign that hinders learning. Results showed that kindergarten relational thinking, particularly tasks assessing nonsymbolic equivalence understanding, uniquely and positively predicted formal understanding of mathematical equivalence and negatively predicted the specific misunderstanding of the equal sign in second grade, controlling for IQ, gender, and free/reduced lunch status. Exploratory analyses unpacking the categories of skills into individual tasks also indicated specific areas of kindergarten instructional focus that may help children construct understanding of mathematical equivalence in future years. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Features in children's counting books that lead dyads to both count and label sets during shared book reading.

This study examined how book features influence talk during shared book reading. We used data from a study in which parent-child dyads (n = 157; child's Mage  = 43.99 months; 88 girls, 69 boys; 91.72% of parents self-reported as white) were randomly assigned to read two number books. The focus was comparison talk (i.e., talk in which dyads count a set and also label its total), as this type of talk has been shown to promote children's understanding of cardinality. Replicating previous findings, dyads produced relatively low levels of comparison talk. However, book features influenced the talk. Books containing a greater number of numerical representations (e.g., number word, numeral, and non-symbolic set) and a greater word count elicited more comparison talk.

Novel irreversible peptidic inhibitors of transglutaminase 2.

Transglutaminase 2 (TG2), also referred to as tissue transglutaminase, plays crucial roles in both protein crosslinking and cell signalling. It is capable of both catalysing transamidation and acting as a G-protein, these activities being conformation-dependent, mutually exclusive, and tightly regulated. The dysregulation of both activities has been implicated in numerous pathologies. TG2 is expressed ubiquitously in humans and is localized both intracellularly and extracellularly. Targeted TG2 therapies have been developed but have faced numerous hurdles including decreased efficacy in vivo. Our latest efforts in inhibitor optimization involve the modification of a previous lead compound's scaffold by insertion of various amino acid residues into the peptidomimetic backbone, and derivatization of the N-terminus with substituted phenylacetic acids, resulting in 28 novel irreversible inhibitors. These inhibitors were evaluated for their ability to inhibit TG2 in vitro and their pharmacokinetic properties, and the most promising candidate 35 (k inact/K I = 760 × 103 M-1 min-1) was tested in a cancer stem cell model. Although these inhibitors display exceptional potency versus TG2, with k inact/K I ratios nearly ten-fold higher than their parent compound, their pharmacokinetic properties and cellular activity limit their therapeutic potential. However, they do serve as a scaffold for the development of potent research tools.

Structure-activity relationships of N-terminal variants of peptidomimetic tissue transglutaminase inhibitors.

Tissue transglutaminase (TG2) is a multifunctional protein that catalyses protein crosslinking in the extracellular matrix, and functions as an intracellular G-protein. While both activities have been associated with human diseases, its role as a G-protein has been linked to cancer stem cell survival and maintenance of a metastatic phenotype. Recently we have shown that targeted covalent inhibitors (TCIs) can react selectively with the enzyme active site of TG2, to allosterically abolish its ability to bind GTP. In the present work, we focused on the variation of the N-terminal group of these peptidomimetic inhibitors, in order to enhance efficiency, while reducing log P and the number of rotatable bonds. This approach led to the synthesis and evaluation of 41 novel inhibitors, some of which had greatly improved efficiency and affinity for TG2 (e.g. TCI 72: KI = 1.0 µM, kinact/KI = 4.4 × 105 M-1 min-1). Molecular modelling provided a hypothetical binding mode for these TCIs. The most efficient inhibitors were evaluated further and shown to have excellent isozyme selectivity, to block GTP binding, and to have improved pharmacokinetic properties, as expected. Their biological activity was also confirmed, in a cellular invasion assay, although with less potency than expected.

Question Design Affects Students' Sense-Making on Mathematics Word Problems.

Mathematics word problems provide students with an opportunity to apply what they are learning in their mathematics classes to the world around them. However, students often neglect their knowledge of the world and provide nonsensical responses (e.g., they may answer that a school needs 12.5 buses for a field trip). This study examined if the question design of word problems affects students' mindset in ways that affect subsequent sense-making. The hypothesis was that rewriting standard word problems to introduce inherent uncertainty about the result would be beneficial to student performance and sense-making because it requires students to reason explicitly about the context described in the problem. Middle school students (N = 229) were randomly assigned to one of three conditions. In the standard textbook condition, students solved a set of six word problems taken from current textbooks. In the modified yes/no condition, students solved the same six problems rewritten so the solution helped answer a "yes" or "no" question. In the disfluency control condition, students solved the standard problems each rewritten in a variety of fonts to make them look unusual. After solving the six problems in their assigned condition, all students solved the same three "problematic" problems designed to assess sense-making. Contrary to predictions, results showed that students in the modified yes/no condition solved the fewest problems correctly in their assigned condition problem set. However, consistent with predictions, they subsequently demonstrated more sense-making on the three problematic problems. Results suggest that standard textbook word problems may be able to be rewritten in ways that mitigate a "senseless" mindset.

Partial knowledge in the development of number word understanding.

A common measure of number word understanding is the give-N task. Traditionally, to receive credit for understanding a number, N, children must understand that N does not apply to other set sizes (e.g. a child who gives three when asked for 'three' but also when asked for 'four' would not be credited with knowing 'three'). However, it is possible that children who correctly provide the set size directly above their knower level but also provide that number for other number words ('N + 1 givers') may be in a partial, transitional knowledge state. In an integrative analysis including 191 preschoolers, subset knowers who correctly gave N + 1 at pretest performed better at posttest than did those who did not correctly give N + 1. This performance was not reflective of 'full' knowledge of N + 1, as N + 1 givers performed worse than traditionally coded knowers of that set size on separate measures of number word understanding within a given timepoint. Results support the idea of graded representations (Munakata, Trends in Cognitive Sciences, 5, 309-315, 2001.) in number word development and suggest traditional approaches to coding the give-N task may not completely capture children's knowledge.

Improved set-size labeling mediates the effect of a counting intervention on children's understanding of cardinality.

How does improving children's ability to label set sizes without counting affect the development of understanding of the cardinality principle? It may accelerate development by facilitating subsequent alignment and comparison of the cardinal label for a given set and the last word counted when counting that set (Mix et al., 2012). Alternatively, it may delay development by decreasing the need for a comprehensive abstract principle to understand and label exact numerosities (Piantadosi et al., 2012). In this study, preschoolers (N = 106, Mage  = 4;8) were randomly assigned to one of three conditions: (a) count-and-label, wherein children spent 6 weeks both counting and labeling sets arranged in canonical patterns like pips on a die; (b) label-first,wherein children spent the first 3 weeks learning to label the set sizes without counting before spending 3 weeks identical to the count-and-label condition; (c) print referencing control. Both counting conditions improved understanding of cardinality through increases in children's ability to label set sizes without counting. In addition to this indirect effect, there was a direct effect of the count-and-label condition on progress toward understanding of cardinality. Results highlight the roles of set labeling and equifinality in the development of children's understanding of number concepts.

Consequences of Individual Differences in Children's Formal Understanding of Mathematical Equivalence.

Experts claim that individual differences in children's formal understanding of mathematical equivalence have consequences for mathematics achievement; however, evidence is lacking. A prospective, longitudinal study was conducted with a diverse sample of 112 children from a midsized city in the Midwestern United States (Mage [second grade] = 8:1). As hypothesized, understanding of mathematical equivalence in second grade predicted mathematics achievement in third grade, even after controlling for second-grade mathematics achievement, IQ, gender, and socioeconomic status. Most children exhibited poor understanding of mathematical equivalence, but results provide clues about which children are on the path to constructing an understanding and which may need extra support to overcome their misconceptions. Findings suggest that mathematical equivalence may deserve more attention from educators.

Comparing Meta-analysis and Individual Person Data Analysis Using Raw Data on Children's Understanding of Equivalence.

A prevailing theory of mathematical problem solving predicts that children will be less accurate solving a + b = c + __ problems versus a + b = __ + c. However, this has never been tested directly. Because of low base rates, information combined from multiple studies can help improve estimation accuracy and precision. This study compared meta-analysis and individual person data (IPD) analysis using raw data from 14 studies (N = 1,414; ns = 30-232; Mage reported = 8;7). Substantive results challenge the prevailing theory. Methodological results demonstrate the advantages of using meta-analysis and IPD over single-study analysis. Moreover, IPD can be more powerful than meta-regression for detecting between-study moderation effects.

Perceptual support promotes strategy generation: Evidence from equation solving.

Over time, children shift from using less optimal strategies for solving mathematics problems to using better ones. But why do children generate new strategies? We argue that they do so when they begin to encode problems more accurately; therefore, we hypothesized that perceptual support for correct encoding would foster strategy generation. Fourth-grade students solved mathematical equivalence problems (e.g., 3 + 4 + 5 = 3 + __) in a pre-test. They were then randomly assigned to one of three perceptual support conditions or to a Control condition. Participants in all conditions completed three mathematical equivalence problems with feedback about correctness. Participants in the experimental conditions received perceptual support (i.e., highlighting in red ink) for accurately encoding the equal sign, the right side of the equation, or the numbers that could be added to obtain the correct solution. Following this intervention, participants completed a problem-solving post-test. Among participants who solved the problems incorrectly at pre-test, those who received perceptual support for correctly encoding the equal sign were more likely to generate new, correct strategies for solving the problems than were those who received feedback only. Thus, perceptual support for accurate encoding of a key problem feature promoted generation of new, correct strategies. Statement of Contribution What is already known on this subject? With age and experience, children shift to using more effective strategies for solving math problems. Problem encoding also improves with age and experience. What the present study adds? Support for encoding the equal sign led children to generate correct strategies for solving equations. Improvements in problem encoding are one source of new strategies.

Structure-Activity Relationships of Potent, Targeted Covalent Inhibitors That Abolish Both the Transamidation and GTP Binding Activities of Human Tissue Transglutaminase.

Human tissue transglutaminase (hTG2) is a multifunctional enzyme. It is primarily known for its calcium-dependent transamidation activity that leads to formation of an isopeptide bond between glutamine and lysine residues found on the surface of proteins, but it is also a GTP binding protein. Overexpression and unregulated hTG2 activity have been associated with numerous human diseases, including cancer stem cell survival and metastatic phenotype. Herein, we present a series of targeted covalent inhibitors (TCIs) based on our previously reported Cbz-Lys scaffold. From this structure-activity relationship (SAR) study, novel irreversible inhibitors were identified that block the transamidation activity of hTG2 and allosterically abolish its GTP binding ability with a high degree of selectivity and efficiency (kinact/KI > 105 M-1 min-1). One optimized inhibitor (VA4) was also shown to inhibit epidermal cancer stem cell invasion with an EC50 of 3.9 µM, representing a significant improvement over our previously reported "hit" NC9.

An integrative data analysis of gender differences in children's understanding of mathematical equivalence.

This study examined gender as a potential source of variation in children's formal understanding of mathematical equivalence. The hypothesis was that girls would perform more poorly than boys. An integrative data analysis was conducted with 960 second and third graders across 14 previously conducted studies of children's understanding of mathematical equivalence. Measures included problem solving, problem encoding, and equal sign definition. Overall, children performed poorly on all measures. As predicted, girls were less likely than boys to solve mathematical equivalence problems correctly, even though there were no gender differences in calculation accuracy. In addition, girls were more likely than boys to use the "add-all" strategy, an incorrect strategy that has been shown to be more resistant to change than other incorrect strategies. There were not statistically significant differences for encoding or defining the equal sign, suggesting that deficits may reflect girls' tendency to follow taught algorithms.

Enhanced Glutathione Peroxidase Activity of Water-Soluble and Polyethylene Glycol-Supported Selenides, Related Spirodioxyselenuranes, and Pincer Selenuranes.

Diaryl selenides containing o-hydroxymethylene substituents function as peroxide-destroying mimetics of the antioxidant selenoenzyme glutathione peroxidase (GPx), via oxidation to the corresponding spirodioxyselenuranes with hydrogen peroxide and subsequent reduction back to the original selenides with glutathione. Parent selenides with 3-hydroxypropyl or 2,3-dihydroxypropyl groups produced the novel compounds 10 and 11, respectively, with greatly improved aqueous solubility and catalytic activity. The phenolic derivative 28 displayed similarly ameliorated properties and also modest radical-inhibiting antioxidant activity, as evidenced by an assay based on phenolic hydrogen atom transfer to the stable free radical DPPH. In contrast, several selenides that afford pincer selenuranes (e.g., 20 and 21) instead of spiroselenuranes upon oxidation showed inferior catalytic activity. Several selenide analogues were attached to polyethylene glycol (PEG) oligomers, as PEG substituents can improve water solubility and bioavailability, while retarding clearance. Again, the PEG derivatives afforded remarkable activity when oxidation generated spirodioxyselenuranes and diminished activity when pincer compounds were produced. Several such compounds proved to be ca. 10- to 100-fold catalytically superior to the diaryl selenides and their spirodioxyselenurane counterparts investigated previously. Finally, an NMR-based assay employing glutathione in D2O was designed to accommodate the faster reacting water-soluble mimetics and to more closely duplicate in vivo conditions.

Specific early number skills mediate the association between executive functioning skills and mathematics achievement.

A growing literature reports significant associations between children's executive functioning skills and their mathematics achievement. The purpose of this study was to examine if specific early number skills, such as quantity discrimination, number line estimation, number sets identification, fast counting, and number word comprehension, mediate this association. In 141 kindergarteners, cross-sectional analyses controlling for IQ revealed that number sets identification (but not the other early number skills) mediated the association between executive functioning skills and mathematics achievement. A longitudinal analysis showed that higher executive functioning skills predicted higher number sets identification in kindergarten, which in turn predicted growth in mathematics achievement from kindergarten to second grade. Results suggest that executive functioning skills may help children quickly and accurately identify number sets as wholes instead of getting distracted by the individual components of the sets, and this focus on sets, in turn, may help children learn more advanced mathematics concepts in the early elementary grades. (PsycINFO Database Record

Oxidation of Disulfides to Thiolsulfinates with Hydrogen Peroxide and a Cyclic Seleninate Ester Catalyst.

Cyclic seleninate esters function as mimetics of the antioxidant selenoenzyme glutathione peroxidase. They catalyze the reduction of harmful peroxides with thiols, which are converted to disulfides in the process. The possibility that the seleninate esters could also catalyze the further oxidation of disulfides to thiolsulfinates and other overoxidation products under these conditions was investigated. This has ramifications in potential medicinal applications of seleninate esters because of the possibility of catalyzing the unwanted oxidation of disulfide-containing spectator peptides and proteins. A variety of aryl and alkyl disulfides underwent facile oxidation with hydrogen peroxide in the presence of catalytic benzo-1,2-oxaselenolane Se-oxide affording the corresponding thiolsulfinates as the principal products. Unsymmetrical disulfides typically afforded mixtures of regioisomers. Lipoic acid and N,N'-dibenzoylcystine dimethyl ester were oxidized readily under similar conditions. Although isolated yields of the product thiolsulfinates were generally modest, these experiments demonstrate that the method nevertheless has preparative value because of its mild conditions. The results also confirm the possibility that cyclic seleninate esters could catalyze the further undesired oxidation of disulfides in vivo.

Easy as ABCABC: Abstract Language Facilitates Performance on a Concrete Patterning Task.

The labels used to describe patterns and relations can influence children's relational reasoning. In this study, 62 preschoolers (Mage  = 4.4 years) solved and described eight pattern abstraction problems (i.e., recreated the relation in a model pattern using novel materials). Some children were exposed to concrete labels (e.g., blue-red-blue-red) and others were exposed to abstract labels (e.g., A-B-A-B). Children exposed to abstract labels solved more problems correctly than children exposed to concrete labels. Children's correct adoption of the abstract language into their own descriptions was particularly beneficial. Thus, using concrete learning materials in combination with abstract representations can enhance their utility for children's performance. Furthermore, abstract language may play a key role in the development of relational thinking.

Effects of methoxy substituents on the glutathione peroxidase-like activity of cyclic seleninate esters.

Cyclic seleninate esters function as mimetics of the antioxidant enzyme glutathione peroxidase and catalyze the reduction of hydrogen peroxide with a stoichiometric thiol. While a single electron-donating methoxy substituent para to the selenium atom enhances the catalytic activity, m-methoxy groups have little effect and o-methoxy substituents suppress activity. The effects of multiple methoxy groups are not cumulative. This behavior can be rationalized by opposing mesomeric and steric effects. Oxidation of the product disulfide via its thiolsulfinate was also observed.

Fluxional cyclic seleninate ester: NMR and computational studies, glutathione peroxidase-like behavior, and unexpected rearrangement.

The oxidation of allyl selenide 12 with hydrogen peroxide produced the corresponding allyl selenurane 14, the cyclic seleninate ester 4, or the rearranged O-allyl seleninate ester 18, dependng on the conditions. Crossover experiments with selenide 12 and its deuterated crotyl analogue 27 indicated an intramolecular rearrangement that proceeds by an intramolecular pathway where the allyl or crotyl group is translocated via its distal carbon atom to the hydroxymethyl functionality. Variable-temperature NMR experiments with cyclic seleninate ester 4 revealed fluxional behavior at room temperature that was catalyzed by trifluoroacetic acid. Computational studies indicated an activation energy of 12.3 kcal mol(-1) for hydroxyl interchange at selenium, comparable to the value of 15.5 kcal mol(-1) derived from the NMR experiments. The glutathione peroxidase-like activity of 4 was measured in an assay where the catalysis of the reduction of hydrogen peroxide with benzyl thiol was monitored by the appearance of dibenzyl disulfide. The catalytic activity of 4 was double that observed with the unsubstituted seleninate ester 2 but was limited by the competing accumulation of the relatively inert selenenyl sulfide 32, resulting in a deactivation pathway that competes with the primary catalytic cycle.

An eye for relations: eye-tracking indicates long-term negative effects of operational thinking on understanding of math equivalence.

Prior knowledge in the domain of mathematics can sometimes interfere with learning and performance in that domain. One of the best examples of this phenomenon is in students' difficulties solving equations with operations on both sides of the equal sign. Elementary school children in the U.S. typically acquire incorrect, operational schemata rather than correct, relational schemata for interpreting equations. Researchers have argued that these operational schemata are never unlearned and can continue to affect performance for years to come, even after relational schemata are learned. In the present study, we investigated whether and how operational schemata negatively affect undergraduates' performance on equations. We monitored the eye movements of 64 undergraduate students while they solved a set of equations that are typically used to assess children's adherence to operational schemata (e.g., 3 + 4 + 5 = 3 + __). Participants did not perform at ceiling on these equations, particularly when under time pressure. Converging evidence from performance and eye movements showed that operational schemata are sometimes activated instead of relational schemata. Eye movement patterns reflective of the activation of relational schemata were specifically lacking when participants solved equations by adding up all the numbers or adding the numbers before the equal sign, but not when they used other types of incorrect strategies. These findings demonstrate that the negative effects of acquiring operational schemata extend far beyond elementary school.