Children possess remarkable proportional quantity skills; yet, their proportional estimations are often misguided by absolute quantities. Recent efforts have aimed to both quantify individual differences and identify possible erroneous strategies in proportional reasoning. We examined—across four time points over two years—the strategies pre-K-to-third-grade students used to estimate visually presented proportional quantities on a line and how their initial strategy related to their proportional reasoning growth and math ability. Results showed that individual differences are captured by strategy profiles that vary in the attended proportional or absolute quantity. Children who initially focused on proportional information maintained this strategy throughout the study and had stronger math ability than children who focused on one or two absolute quantities. Importantly, the absolute quantities children focused on were distinctly related to their estimation growth and math ability. These findings underscore the importance of considering quantitative and qualitative descriptions of children's proportional reasoning skills.

Engineering bridge and success programs have been used to support the transition and retention of students in engineering and computing majors at 4-year institutions in the U.S.Many bridge and success programs also aim to broaden participation in engineering and computing by recruiting underserved students such as underrepresented minorities (URMs), women, first-generation students, and low socio-economic status (SES) students.However, their program leaders frequently report difficulties recruiting students from these groups.There is little literature focusing on the recruitment of bridge and success programs.Understanding effective recruitment strategies to reach and convince underserved students to participate in those programs can increase the use of effective practices by program leaders and disseminate best recruitment practices.Our research aims to identify which recruitment strategies are in use, which are most effective, and barriers to communicating with prospective underserved students of the engineering bridge and success programs.The research project includes several stages, investigating perspectives from both program leaders and students.This stage of the study will explore the effectiveness of different communication channels and change agents to reach and persuade underserved students to participate in engineering bridge and success programs from program leaders' perspectives.This is an explanatory sequential mixed method study based on the Diffusion of Innovations (DOI) theory framework.This work-in-progress (WIP) paper will report on instrument development, sampling procedure, planned data analysis, and current progress.This research will also broaden knowledge on applying DOI theory to increase recruitment effectiveness.

Spatial skills are critical for learning in STEM areas and are affected by spatial anxiety and working memory. Prior work also showed that there are interaction effects between spatial anxiety and verbal working memory (WM) on spatial skills, such that the negative relation between spatial anxiety and spatial skills is stronger among higher- than lower-verbal WM children. To date, this interaction effect has not been found for visuospatial WM. However, a recent meta-analysis showed that both verbal WM and visuospatial WM are impaired by anxiety to a similar extent. The current study hypothesized that visuospatial WM interacts with spatial anxiety on spatial skills and that this interaction effect gets stronger as age increases. We investigated spatial anxiety, visuospatial WM, and two spatial skills (mental transformation and mental rotation) in 402 U.S. children in first to fourth grades. We found a significant three-way interaction of spatial anxiety, visuospatial WM, and grade level on mental transformation skill: only fourth-graders with high visuospatial WM showed a significant relation between spatial anxiety and lower mental transformation skills, whereas low-visuospatial WM fourth-graders and children in Grades 1 to 3 did not show this relation. However, this effect was not significant for children's mental rotation skills. We discuss the results in terms of age-related differences in visuospatial WM and strategy use, as well as differences between the mental transformation and mental rotation tasks. Our findings indicate that the interaction effect between spatial anxiety and working memory on spatial skills extends beyond verbal WM to visuospatial WM and becomes more pronounced as children's age increases.

Verbal labels for math concepts influence multiple aspects of math learning. In this study, we examined the influence of point labels (e.g., 0.42 as point four two), decomposed labels (e.g., four tenths and two hun-dredths), and common-unit labels (e.g., forty-two hundredths) on children's processing and representation of decimal magnitudes. We randomly assigned 162 5th-and 6th-graders to briefly learn decomposed, common-unit, or point labels. Children then completed measures of decimal magnitude processing and representation. We found that the place-value labels (i.e., decomposed and common-unit labels) each showed unique advantages in reducing the whole-number bias, and common-unit labels also reduced componential processing. No difference was found in the ratio effect - which served as an index of the precision of decimal magnitude representation -among children from the three conditions. These findings add to our understanding of the role of verbal labels in math learning and have important implications for instructional practices.

Large language models (LLMs) have show great ability in various natural language tasks. However, there are concerns that LLMs are possible to be used improperly or even illegally. To prevent the malicious usage of LLMs, detecting LLM-generated text becomes crucial in the deployment of LLM applications. Watermarking is an effective strategy to detect the LLM-generated content by encoding a pre-defined secret watermark to facilitate the detection process. However, the majority of existing watermark methods leverage the simple hashes of precedent tokens to partition vocabulary. Such watermark can be easily eliminated by paraphrase and correspondingly the detection effectiveness will be greatly compromised. Thus, to enhance the robustness against paraphrase, we propose a semantics-based watermark framework SemaMark. It leverages the semantics as an alternative to simple hashes of tokens since the paraphrase will likely preserve the semantic meaning of the sentences. Comprehensive experiments are conducted to demonstrate the effectiveness and robustness of SemaMark under different paraphrases.

Recently, there has been increasing evidence showing that males estimate whole numbers more accurately than females on the number line. However, relatively little is known about what factors contribute to this gender gap. The current study explored potential mediators of the gender difference in number line estimation, including spatial skills and spatial anxiety. In the Fall (time-point 1 [T1]), 490 children from kindergarten through fourth grade (274 girls) completed age-appropriate measures of number line estimation, spatial skills (including proportional reasoning, mental rotation, mental transformation, and visuospatial working memory), and spatial anxiety. About 5 month later in the Spring (time-point 2 [T2]), children completed the same measure of number line estimation again. Boys were more accurate on number line estimation, proportional reasoning, and mental rotation than girls, whereas girls showed higher levels of spatial anxiety. Critically, spatial skills (a latent variable constructed from proportional reasoning, mental rotation, mental transformation, and visuospatial working memory) at T1 mediated the gender difference in T2 number line estimation whereas spatial anxiety was not a significant mediator. These relationships held even after controlling for T1 number line estimation, reading achievement, and reading anxiety. Among the four spatial skills, proportional reasoning and mental rotation (but not mental transformation or visuospatial working memory) were mediators of the gender difference in T2 number line estimation. These findings constitute, to our knowledge, the first evidence regarding factors contributing to the gender difference in whole number line estimation.

Parents provide motivational and cognitive support within the same interaction, yet researchers have investigated these separately. We examined two key aspects of parental support, praise (motivational support) and spatial language (cognitive support), from fathers and mothers during three tasks with their first-grade children (6-7-year-olds; N = 107; 56 girls; 72.0% White, 23.4% Black). Parents' praise and spatial language varied by task but not child sex: Both parents produced more praise in the Etch-a-Sketch and block tasks than the card game and produced more spatial language in the Etch-a-Sketch task than other tasks. We further examined whether praise and spatial language in the two spatial tasks (Etch-a-Sketch and block construction) were related to children's later math and spatial skills. We found neither additive nor multiplicative effects of parents' praise or spatial language. We also did not see additive or multiplicative effects of fathers' and mothers' support. However, fathers' greater spatial language at first grade was negatively associated with boys' (but not girls') math achievement in third grade, with greater father spatial tokens related to their sons' lower math achievement. This suggests that boys may perceive fathers' support more negatively than girls do or that fathers may offer additional support for boys with lower abilities. Taken together, this study emphasizes the importance of considering contexts in examining parental support. The correlational nature of the study warrants future research to establish causal relations and to enhance our understanding of multifaceted parent-child interactions.

When students start learning decimals, they may incorrectly apply features of their prior numerical knowledge (e.g., whole-number or fraction rules). However, because whole numbers, fractions, and decimals all have their own unique features, these whole-number and fraction strategies do not always lead to correct solutions. We examined whether receiving immediate accuracy feedback while comparing decimal pairs that were either congruent with whole-number rules (e.g., decimals with more digits were larger in magnitude) or incongruent with whole-number rules (e.g., decimals with fewer digits were larger in magnitude) would lead students to change their decimal comparison strategies. We also examined whether students' potential improvement after feedback would generalize to decimal comparisons involving different numbers of digits. We found that sixthto eighth-grade students' use of the whole-number strategy declined and their use of the normative decimal strategy increased over the course of receiving feedback, whereas no significant strategy change was observed among students who did not receive any feedback. Students who received feedback were also less likely to use a whole-number strategy and more likely to use a decimal strategy in different decimal comparisons in an immediate posttest and a 2-week delayed posttest. Our exploratory analyses found that students' improvement on decimal comparisons did not transfer to decimal arithmetic. Moreover, students' inhibitory control also predicted strategy use in immediate and delayed posttests. Our study provides insights into the mechanisms of rapid strategy change and has implications for designing interventions to improve children's understanding of decimal magnitudes. (C) 2020 Elsevier Inc. All rights reserved.

Decades of research have established that spatial skills correlate with numerical skills. However, because both spatial and numerical skills are multidimensional, we sought to determine how specific spatial skills relate to specific numeracy skills. We used a cohort-sequential design, assessing a large diverse sample of students (N = 612, initially in pre-kindergarten [pre-K]-3rd grade, 4-9 years of age) at four time points spanning 2 years. We examined how initial levels of five spatial skills (visuospatial working memory [VSWM], mental transformation, mental rotation, proportional reasoning, and analog magnitude system [AMS] acuity) related to initial levels and growth rates in exact and approximate calculation skills, and we further investigated number line estimation as a potential mediator. We found unique patterns of relations between spatial skills and numeracy. Initial levels of mental rotation, proportional reasoning, and AMS acuity related to initial levels of exact calculation skill; initial levels of AMS acuity related to initial levels of approximate calculation; and initial levels of proportional reasoning related to initial levels of number line estimation. VSWM and mental transformation did not relate to numeracy skills after controlling for other spatial skills. Initial levels of number line estimation related to both exact and approximate calculation after controlling for spatial skills. Notably, neither spatial skills nor number line estimation predicted growth in exact or approximate calculation skills. These results indicate that there is specificity in the time-invariant relations between spatial skills and numeracy, and they suggest that researchers and educators should treat spatial skills and numeracy as multidimensional constructs with complex and unique interrelations. (c) 2021 Elsevier Inc. All rights reserved.

Young children are sensitive to both numerical and spatial magnitude cues early in development, but many questions remain about how children's attention to magnitudes relates to their early math achievement. In two studies, we tested three hypotheses related to the flexible attention to magnitudes (FAM) account, which suggests that young children's flexible attention to both numerical and spatial magnitudes is an important predictor of early math success. In Study 1, we recruited 318 preschool-age children (51.5% female; M-age = 54.7 months, SDage = 4.24 months) and assessed them at two time points on a battery of math, executive function, and language measures, including a novel assessment of FAM ability developed for this study. Consistent with our hypotheses, we found that young children had specific difficulty flexibly shifting between numerical and spatial magnitudes, that their FAM ability was related to both their executive function and math skills controlling for covariates, and finally that their FAM ability at the first time point was predictive of their math achievement growth over time controlling for executive function skills and covariates. In Study 2, we recruited 157 preschool-age children (47.4% female; M-age = 53.36 months, SDage = 7.17 months). We replicated the findings of Study 1 and extended them to account for children's non-symbolic numerical magnitude discrimination skills. Implications of the results of these studies for early math activities development are discussed.