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A computer science camp for pre-collegiate students was operated during the summers of 2022 and 2023. The effect the camp had on attitudes was quantitatively assessed using a survey instrument. However, enrollment at the summer camp was small, which meant the well-known Pearson's Chi-Squared to measure the significance of results was not applied. Thus, a quantitative analysis method using a multinomial probability distribution as a model of a multilevel Likert scale survey was used. Exact calculations of a multinomial probability model with likelihood ratio were performed to quantitatively analyze the results of questionnaires administered to participants in two cohort groups (combined N=17). Probabilities per Likert categories were determined from the data itself using Bayes theorem with a Dirichlet prior. Each cohort functioned as part of a homogenous sample, thus allowing cohorts to be pooled. Post-test revealed significant changes in participants' attitudes after camp completion. Using this technique has implications for studies with small sample sizes. Using exact calculation of the multinomial probability model with the use of likelihood ratio as a statistical test of evidence has advantages: a) it is an exact value that can be used on any size sample, although it offers a quantitative analysis option for small sample size studies; b) depends only on what was observed during a study; c) does not require advanced calculation; d) modern spreadsheet and statistical package programs can calculate the analysis; and e) likelihood ratio employed in Bayes theorem can update prior beliefs according to evidence. Utilizing small sample size quantitative analysis can strengthen insights into data trends and showcase the importance of this quantitative technique.

Suicide, which is defined as an individual's intentionally attempting to end his or her life, is considered an important public health problem. In this study, it was aimed to examine the relationship between cognitive distortions and suicide probability in university students who are in age groups at risk for suicide, and to examine the mediating roles of the attachment dimensions of anxiety and avoidance, in this relationship. The study group consisted of 441 university students. In the study, Suicide Probability Scale, Experiences in Close Relationships Inventory, Cognitive Distortions in Relationships Scale and a personal information form were used as data collection tools. In accordance with the purpose of the study, a correlation analysis between variables and regression analyses were applied to examine the mediating roles of avoidance and anxiety in the relationship between cognitive distortions and suicide probability. The findings showed that there was a moderate positive correlational relationship between suicide probability scores and avoidance scores and there was a moderate positive correlational relationship between suicide probability scores and cognitive distortion scores. It was shown that there were low and moderate positive correlations between cognitive distortion scores, and avoidance and anxiety scores. The results of the mediation analyses showed that anxiety and avoidance had a partial mediating role in the relationship between cognitive distortion and suicide probability. The results were discussed in light of the literature.

Grade repetition is an issue with important educational implications. This study analyzes the effect of cognitive variables, socio-economic status, as well as the interaction of socioeconomic status with ethnic origin, on the probability of not repeating. Data were collected to calculate socioeconomic status using the Hollingshead Socioeconomic Index, and the following tests were administered to collect information on cognitive variables: the Primary Mental Aptitude Test (PMA), the Raven's Progressive Matrices Test, and the Wechsler Intelligence for Children Information Scale (WISC IV). The sample consisted of 664 students of Compulsory Secondary Education (ESO), Baccalaureate and intermediate and higher vocational training. The results confirm the predictive power of socioeconomic status. With regard to cognitive variables, significant results were only obtained when the WISC-IV Information Scale was taken as a predictor, this measure being related to crystallized intelligence. The influence of the origin of the students did not yield significant results. There is a clear need for a debate and a rethinking of the issue leading to the identification of new strategies to reduce grade repetition and its negative effects.

This research aims to determine the thinking activity types dominated by a mental process in producing answers characterized by automatic, unconscious, and subjective-empirical processes (system 1) in solving problems so that the default-interventionist interaction occurs. This research novelty is the formulation of the contents and thinking activity arrangement adapted to students' thinking when solving problems. The problem used in this research is a mathematical problem that triggers students to produce answers quickly with confidence that the answers are correct at a high level. Another problem is about probability because the mode of occurrence of students' learning difficulties at the secondary school level occurs when learning the concept of probability. This is qualitative research with a case study approach. The research subjects were students of Mathematics Education in semester 1. The results showed that thinking activity one could condition the occurrence of type 1 default-interventionist interaction. Thinking activity two could condition the occurrence of type 2 default-interventionist interaction. Thinking activity three could condition the occurrence of type 3 default-interventionist interaction. This research concluded that the default-interventionist interaction occurred because the content and arrangement of the thinking activity conditioned the subjects to pay attention to information gradually and change the subjects' beliefs. Lecturers were recommended to produce, develop, and research thinking activities on topics other than probability at various levels of education. The default-interventionist interaction was essential to be conditioned when system one dominated students' thinking, causing difficulties.

This study aims to determine students learning obstacles in probability material based on their probabilistic thinking (PT) level using the theory of didactical situation (TDS) perspective. This is qualitative research with the case study method. The subject consisted of 23 grade 9 students in junior high school who had studied the material and had taken the test. The test results were used to classify students depending on their PT level using the framework developed by Graha A. Jones. Furthermore, interviews were performed with three representative students from each PT level. The interviews indicated that students in each PT level continue to face learning obstacles, which include instrumental ontogenic and epistemological obstacles. The lowest PT level demonstrated a more complex and comprehensive learning obstacle in all constructs of PT. From the TDS perspective, all students who are at various levels of PT have reached an action situation. Only 33% of the students at the subjective level and 83% of the students at the transition level reached the formulation situation. Still, students at that level needed help to reach the other two situations. Unlike the two previous levels, students at the level of quantitative informal thinking can achieve situations of validation and institutionalization.

Education plays a very important role in improving the quality of human resources. In higher education, students need learning that is innovative and not monotonous so that learning goals can be achieved. In this research, what will be discussed further is the development of learning methods by combining 2 methods, namely Cooperative Based Learning (CBL) with Problem-Based Learning (PBL) in the Advanced Financial Management course. This research method uses Pretest - Posttest Design. The data population is 711 students collected from 17 classes taking Advanced Financial Management courses at Putra Indonesia University YPTK Padang. The sampling technique uses probability sampling. The data that will be used as a sample are observations of 117 students collected from 3 classes. The CPBL method is implemented by grouping students into groups of 4-5 people to discuss each case in the material. Data will be analyzed based on the completeness of learning outcomes and calculating N-Gain. From the data processing, the results obtained were that by combining these 2 methods, it was successful in improving student learning outcomes and the students' completeness test scores were also proven to be very successful in being upgraded. The effectiveness of the collaboration between these 2 methods reaches the high category of the N-Gain test. This is a new variation in making learning calculations that use many formulas more challenging, increasing students' enthusiasm for learning and providing satisfactory learning results. This method is worth utilizing and can be used in all courses that involve calculations and case questions.

Mathematical symbols, such as those embodying quantum concepts, are indispensable for conveying complex ideas and relationships in academic writing. However, some education researchers and students keep a distance from anything mathematical: algebraic equations, geometrical reasoning, or statistical symbols. How to lower the access threshold for this type of mathematical narrative and reveal the meanings of a range of quantum conceptions to modern educators thus becomes a real problem. Using the pendulum motion equation as a reference point, I argue in this article for the advantages of academic English or French writing genres that fuse a range of mathematical symbols of quantum concepts and conceptual change. Such writings help demonstrate how incorporating the idea of probability (a) refines the debate among conceptual, verbal, and mathematical academic writing; (b) allows new conceptions that draw on the insights from quantum cognition-supported theories; (c) helps explain students' understanding of mathematical symbols; and (d) offers a new taxonomy for categorizing academic writings.

Teaching and learning undergraduate statistics has been a most challenging task for undergraduate psychology majors (Salkind, 2017). A seasoned statistics instructor consulted with a seasoned instructional designer on a method to improve a particularly demanding course using a performance improvement approach to address learning difficulties she had noted in previous semesters. The Decoding the Disciplines methodology identified the most challenging concepts and provided a methodology to improve student learning performance. The methodology focused on five core concepts in psychological statistics: probability, variability, central limit theorem, independent/dependent variables, and degrees of freedom. The Decoding the Disciplines curriculum was used for three semesters. In these three semesters, performance was compared pre and post on these concepts within the semester. Repeated measures t-tests found a significant change in the percentage of correct answers between the pretest and the final exam on the five core concepts.

Background/purpose: Awareness of the mathematical skills and knowledge children possess in their early years is widely accepted. This includes various common positive aspects, not only for educators but also for researchers and policymakers. This study presents a systematic review conducted to meticulously identify empirical studies published in the Scopus-Index Journal database about the mathematical skills children aged 3 to 8 years old have mastered. Materials/methods: This review followed the PRISMA guidelines and the research database comprised of Scopus-indexed journals. The technique followed used "keywords" and Boolean operators. The screening processes included reviewing abstracts, scanning complete texts of published articles, and rejecting those not meeting preset inclusion criteria. Moreover, systematic reviews, meta-analyses, and papers not written in English were also excluded. Of the 801 studies initially identified, a total of 15 empirical studies were included in the systematic review. Results: Children master various math skills from a very young age, mainly in "numbers and operations", but face difficulties in skills related to "algebra" as well as "geometry and measurement". Additionally, several preschoolers' characteristics help to explain the acquisition of these skills, with "age" being the primary factor. Researchers use various research instruments and mainly conduct individual semi-structured interviews. Children's geometry skills and knowledge appear to have been studied to a small extent. The areas of "measurement" and "data analysis and probability" were found to be under active investigation. Conclusion: It is worth noting that not only does a noticeable research gap exist for the math domains of "measurement," "geometry," and "data analysis and probability". Factors that seem to affect young children's math skills, such as "gender", "parents' educational level", and "attendance to a preparatory preschool" need further investigation. The implications of the current study's results extend beyond academia, providing valuable insights that educators and policymakers can leverage to enhance the quality of mathematics education during the early years period.

As evidence from evaluation and experimental studies continue to influence decision and policymaking, applied researchers and practitioners require tools to derive valid and credible inferences. Over the past several decades, research in causal inference has progressed with the development and application of propensity scores. Since their inception, propensity scores have made an important contribution to the improvement in estimation of causal impacts, particularly in the absence of randomization. When certain core assumptions hold, propensity score-based methods allow for bias-reduced estimation of average treatment effects. In addition to their important role in causal studies, propensity scores have also been integral in improving generalizations from causal studies, specifically when study samples are not randomly selected from a target population of inference. The current study provides an overview of propensity scores, a discussion of the assumptions needed to ensure their validity, and an illustration of the methods both for causal inference and generalization. We highlight the importance of propensity score methods and discuss current applications and directions for ongoing and future research.

Causal inference involves determining whether a treatment (e.g., an education program) causes a change in outcomes (e.g., academic achievement). It is well-known that causal effects are more challenging to estimate than associations. Over the past 50 years, the potential outcomes framework has become one of the most widely used approaches for defining, identifying, and estimating causal effects. In this paper, we review the potential outcomes framework with a focus on potential outcomes notation to define individual and average causal effects. We then show how three canonical assumptions, Unconfoundedness, Positivity, and Consistency, may be used to identify average causal effects. The identification results motivate methods for estimating causal effects in practice, which include model-based estimators, such as regression, inverse probability weighting, and doubly robust estimation, and procedures that target covariate balance, such as matching and stratification. Examples and discussion are grounded in the context of a running example of a study aimed at assessing the causal effect of receipt of special education services on 5th grade mathematics achievement in school-aged children. Practical considerations for education research are discussed.

As colleges and universities grapple with uncertainty around current and future enrollment as well as increasingly vocal questions about the value of postsecondary education, it is critically important that institutions ascertain and invest in the elements of campus learning and engagement that add value to the undergraduate experience. This study examines the relationship between cumulative participation in high-impact practices (HIPs) and the perceived importance of postsecondary experience in preparation for adult life using the Educational Longitudinal Study of 2002 (ELS) dataset. Employing a methodology proposed and tested by Leite et al. (Struct Equ Model Multidiscip J 26(3):448-469, 2019. https://doi.org/10.1080/10705511.2018.1522591), this analysis incorporated the ability to account for self-selection into HIPs using propensity score (PS) analysis with a multiple-group structural equation model (SEM) design to examine differences between students who participated in two or more HIPs and those who did not (n = 3105). Results offered evidence of benefit to participation in two or more HIP experiences with positive and statistically significant differences in the perceived importance of postsecondary education in preparation for adult life across the analytic sample with doubly robust estimation techniques. Interaction effects for female students, students from low SES backgrounds, and students who are members of minoritized racial/ethnic populations were also identified. The findings offered evidence of post-graduation impact of cumulative participation in HIPs that can inform program development and student decision-making as well as the future use of analytic techniques such as PS analysis, doubly robust estimation, and sensitivity analysis to enhance measurement precision.

Missing data are a pervasive problem in data analysis. Three common methods for addressing the problem are (a) complete-case analysis, where only units that are complete on the variables in an analysis are included; (b) weighting, where the complete cases are weighted by the inverse of an estimate of the probability of being complete; and (c) multiple imputation (MI), where missing values of the variables in the analysis are imputed as draws from their predictive distribution under an implicit or explicit statistical model, the imputation process is repeated to create multiple filled-in data sets, and analysis is carried out using simple MI combining rules. This article provides a non-technical discussion of the strengths and weakness of these approaches, and when each of the methods might be adopted over the others. The methods are illustrated on data from the Youth Cohort (Time) Series (YCS) for England, Wales and Scotland, 1984-2002.

The estimation of RxC ecological inference contingency tables from aggregate data is one of the most salient and challenging problems in the field of quantitative social sciences, with major solutions proposed from both the ecological regression and the mathematical programming frameworks. In recent decades, there has been a drive to find solutions stemming from the former, with the latter being less active. From the mathematical programming framework, this paper suggests a new direction for tackling this problem. For the first time in the literature, a procedure based on linear programming is proposed to attain estimates of local contingency tables. Based on this and the homogeneity hypothesis, we suggest two new ecological inference algorithms. These two new algorithms represent an important step forward in the ecological inference mathematical programming literature. In addition to generating estimates for local ecological inference contingency tables and amending the tendency to produce extreme transfer probability estimates previously observed in other mathematical programming procedures, these two new algorithms prove to be quite competitive and more accurate than the current linear programming baseline algorithm. Their accuracy is assessed using a unique dataset with almost 500 elections, where the real transfer matrices are known, and their sensitivity to assumptions and limitations are gauged through an extensive simulation study. The new algorithms place the linear programming approach once again in a prominent position in the ecological inference toolkit. Interested readers can use these new algorithms easily with the aid of the R package lphom.

In China, the prevalence of academic dishonesty has attracted considerable negative attention. One explanation for observed differences is found in cultural norms around the acceptability of individual unethical academic behaviors. The establishment of international cooperative universities in China presents a unique challenge for educators and administrators due to cultural differences in practices around academic integrity. This is especially relevant in the context of Sino-American universities due to increased tolerance and decreased training concerning plagiarism in Chinese education relative to the USA. The unique academic experience of bilingual Chinese students enrolled in Sino-American universities presents an opportunity to investigate whether academic experience in English influences attitudes and behaviors around academic integrity. Drawing from research on the foreign language effect, the present study tested the hypothesis that knowledge, and by extension behavior, associated with academic integrity is bound to the English language. Mandarin-English bilingual university students (n = 106) completed both objective and self-report assessments of language experience and responded to two dilemmas designed to mirror commonly experienced academic scenarios presented in either Mandarin or English. We identified a modulatory role of English proficiency with higher levels associated with a lower likelihood of academically dishonest behavior. Additional findings support that separable dimensions of English experience interact to modulate responses to academic dilemmas. Findings suggest that higher levels of English proficiency may reflect higher access to Western norms around academic integrity.

This study investigates a range of non-normative ideas that pre-service teachers (PSTs) employ in reasoning about sampling variability. This issue was studied in the context of a content course on statistics and probability for pre-service middle grade teachers at a Midwestern American university. Analysis of seven PSTs' video and screen records of task-based interviews has articulated fundamental facets of sampling variability that have not yet been fully explicated in the literature, especially with middle grade PSTs. With the content expectation of sampling variability for middle grade students as suggested by policy reports in the United States of America, this study is particularly fertile ground for designing curricula that can support middle grade PSTs' development of critical specialized content knowledge on sampling variability.

Diabetes mellitus is a challenging chronic health condition at the forefront of attention of the healthcare system. Important estimates quantifying how diabetes prevalence varies by age are available for the general population, but these estimates are poorly characterized among autistic adults. Improved diabetes prevalence and likelihood estimates are needed to understand the impact of diabetes on this population. We analyzed IBM MarketScan health claims data from 2019 to 2020 to estimate diabetes prevalence among privately insured autistic (N = 54,500) and non-autistic adults (N = 109,000) and estimate autistic adults' likelihood of diabetes relative to non-autistic adults at 5-year age intervals (e.g. 18-22 to 23-27) when controlling for demographic factors. Diabetes prevalence was 5.15% for autistic adults and 3.07% for non-autistic adults. Autistic adults had a higher likelihood of diabetes than non-autistic adults at most 5-year age intervals, with the greatest difference at ages 23-37 (odds ratio = 2.67; 95% confidence interval = 2.33-3.06). Our findings suggest that autistic adults may be more likely than non-autistic adults to experience diabetes. Thus, development of diabetes support services and programs that accommodate autistic adults' individualized needs are important for future study to promote optimal diabetes outcomes for this population.

The objective of this meta-epidemiological study was to explore the impact of attrition rates on treatment effect estimates in randomised trials of chronic inflammatory diseases (CID) treated with biological and targeted synthetic disease-modifying drugs. We sampled trials from Cochrane reviews. Attrition rates and primary endpoint results were retrieved from trial publications; Odds ratios (ORs) were calculated from the odds of withdrawing in the experimental intervention compared to the control comparison groups (i.e., differential attrition), as well as the odds of achieving a clinical response (i.e., the trial outcome). Trials were combined using random effects restricted maximum likelihood meta-regression models and associations between estimates of treatment effects and attrition rates were analysed. From 37 meta-analyses, 179 trials were included, and 163 were analysed (301 randomised comparisons; n = 62,220 patients). Overall, the odds of withdrawal were lower in the experimental compared to control groups (random effects summary OR = 0.45, 95% CI, 0.41-0.50). The corresponding overall treatment effects were large (random effects summary OR = 4.43, 95% CI 3.92-4.99) with considerable heterogeneity across interventions and clinical specialties (I2 = 85.7%). The ORs estimating treatment effect showed larger treatment benefits when the differential attrition was more prominent with more attrition in the control group (OR = 0.73, 95% CI 0.55-0.96). Higher attrition rates from the control arm are associated with larger estimated benefits of treatments with biological or targeted synthetic disease-modifying drugs in CID trials; differential attrition may affect estimates of treatment benefit in randomised trials.

This article describes a hands-on geometric tiling art activity used in two third-grade classes and four fifth-grade classes in a rural public elementary school with class sizes of around 20 students each. The lesson investigates concepts in geometry, number sense, and probability. Examples of student work and takeaways for other teachers interested in implementing the tasks in their own classrooms are also shared.

In Italy, parents are free to choose the primary school for their children without restrictions imposed by catchment areas. This freedom of choice, inspired by quasi-market mechanisms, aims to foster competition between schools and raise educational standards. Analysing the case of Milan using regression models and administrative data for the 2015-16 school year, we study the factors associated with the probability that parents choose a school different from the one closest to where they live. We focus on both push factors (the characteristics of local schools) and pull factors (the features of chosen schools). The findings indicate that parents select schools which have a lower proportion of immigrant pupils and higher socio-economic status of the student body. On the other hand, school performance in standardised tests is not statistically associated with parents' decisions to opt out of local schools, nor does it emerge as a feature of the schools most likely to attract non-local students after accounting for the socio-economic composition of school intake. The resulting picture shows that affluent Italian parents implement avoidance strategies to avoid schools attended by a high proportion of immigrant or lower-class students--with the potential of fostering segregation and concentrations of disadvantaged groups.

A modified and improved inductive inferential approach to evaluate item discriminations in a conditional maximum likelihood and Rasch modeling framework is suggested. The new approach involves the derivation of four hypothesis tests. It implies a linear restriction of the assumed set of probability distributions in the classical approach that represents scenarios of different item discriminations in a straightforward and efficient manner. Its improvement is discussed, compared to classical procedures (tests and information criteria), and illustrated in Monte Carlo experiments as well as real data examples from educational research. The results show an improvement of power of the modified tests of up to 0.3.

Multiple factors influence a student's success in high school graduation. Individual factors such as disability, racial or ethnic identity, and gender may result in inequity in the school environment, interfering with learning and possibly leading to poorer educational outcomes. This secondary analysis of student educational records (N = 3,782) from 2008-2018 tested the associations among the disability, racial or ethnic identity, gender, and 5th grade attendance on high school attendance and graduation. Linear and logistic regression analysis identified students without a disability had a 40% greater chance of graduation (AOR = 1.4 [95% CI = 1.15, 1.71]) than those with a disability. Students identifying as Black, Hispanic, or Native American had half the odds of graduating compared to White students. When controlling for 9th grade attendance, these disparities decreased. Attendance in 5th grade, disability, and racial and ethnic identity influenced attendance, being on track to graduate, and high school graduation.

There is a growing awareness of the importance of financial management skills. However, few studies have systematically examined this topic in China's current higher education (HE) system. In this study, we examine whether enrolling in a finance-related program, either as a degree program or as an elective, improves students' financial literacy and habits. We conducted a mixed-method study with a sample of 1334 students from seven universities in central China. Multivariate regression, matching methods, and the inverse-probability-weighting methods were used for quantitative analysis. The results indicate that college students are generally dissatisfied with their financial situation. Enrolling in finance-related majors has little effect on improving students' financial habits, despite a substantial improvement in their financial literacy. In the current HE system, there is a significant lack of personal finance management training. Therefore, curriculum design and field practices regarding students' personal finance management skills should be introduced to enhance their financial habits.

Purpose: Children with developmental language disorder (DLD) tend to interpret noncanonical sentences like passives using event probability (EP) information regardless of structure (e.g., by interpreting "The dog was chased by the squirrel" as "The dog chased the squirrel"). Verbs are a major source of EP information in adults and children with typical development (TD), who know that "chase" implies an unequal relationship among participants. Individuals with DLD have poor verb knowledge and verb-based sentence processing. Yet, they also appear to rely more on EP information than their peers. This paradox raises two questions: (a) How do children with DLD use verb-based EP information alongside other information in online passive sentence interpretation? (b) How does verb vocabulary knowledge support EP information use? Method: We created novel EP biases by showing animations of agents with consistent action tendencies (e.g., clumsy vs. helpful actions). We then used eye tracking to examine how this EP information was used during online passive sentence processing. Participants were 4- to 5-year-old children with DLD (n = 20) and same-age peers with TD (n = 20). Results: In Experiment 1, children with DLD quickly integrated verb-based EP information with morphosyntax close to the verb but failed to do so with distant morphosyntax. In Experiment 2, the quality of children's sentence-specific verb vocabulary knowledge was positively associated with the use of EP information in both groups. Conclusion: Depending on the morphosyntactic context, children with DLD and TD used EP information differently, but verb vocabulary knowledge aided its use.

Publication selection bias undermines the systematic accumulation of evidence. To assess the extent of this problem, we survey over 68,000 meta-analyses containing over 700,000 effect size estimates from medicine (67,386/597,699), environmental sciences (199/12,707), psychology (605/23,563), and economics (327/91,421). Our results indicate that meta-analyses in economics are the most severely contaminated by publication selection bias, closely followed by meta-analyses in environmental sciences and psychology, whereas meta-analyses in medicine are contaminated the least. After adjusting for publication selection bias, the median probability of the presence of an effect decreased from 99.9% to 29.7% in economics, from 98.9% to 55.7% in psychology, from 99.8% to 70.7% in environmental sciences, and from 38.0% to 29.7% in medicine. The median absolute effect sizes (in terms of standardized mean differences) decreased from d = 0.20 to d = 0.07 in economics, from d = 0.37 to d = 0.26 in psychology, from d = 0.62 to d = 0.43 in environmental sciences, and from d = 0.24 to d = 0.13 in medicine.

Literature screening is the process of identifying all relevant records from a pool of candidate paper records in systematic review, meta-analysis, and other research synthesis tasks. This process is time consuming, expensive, and prone to human error. Screening prioritization methods attempt to help reviewers identify most relevant records while only screening a proportion of candidate records with high priority. In previous studies, screening prioritization is often referred to as automatic literature screening or automatic literature identification. Numerous screening prioritization methods have been proposed in recent years. However, there is a lack of screening prioritization methods with reliable performance. Our objective is to develop a screening prioritization algorithm with reliable performance for practical use, for example, an algorithm that guarantees an 80% chance of identifying at least 80% of the relevant records. Based on a target-based method proposed in Cormack and Grossman, we propose a screening prioritization algorithm using sampling with replacement. The algorithm is a wrapper algorithm that can work with any current screening prioritization algorithm to guarantee the performance. We prove, with mathematics and probability theory, that the algorithm guarantees the performance. We also run numeric experiments to test the performance of our algorithm when applied in practice. The numeric experiment results show this algorithm achieve reliable performance under different circumstances. The proposed screening prioritization algorithm can be reliably used in real world research synthesis tasks.

Faced the vast amount of information, choosing the appropriate materials is a prerequisite for effective self-directed learning. The recommendation algorithm is a kind of intelligent technology that can accurately locate the required information which the users care about most. However, many recommendation techniques experience can not be trained adequately in scenarios with small sample data and extremely sparse ratings. Moreover, DLRAs (Deep learning based Recommendation Algorithms) require high hardware support. The probabilistic graph (PG) can effectively represent the implicit complex relations among nodes, but it still has the problem of sparse data sensitivity. Therefore, we propose a Matrix-Factorization-based Probabilistic Graph Model for Recommendation Algorithm (MF-PGMRA): By matrix-factorizing the sparse rating matrix, the users and items are mapped to the user/item spaces, respectively; We employ the inner product to data-enhance and overcome the problems of sparse data and cold start; Then, we build Probabilistic Graph to construct the "user-item" latent spaces and estimate the probability distribution based on expectation maximization (EM), so as to predict the ratings; Finally, we built a library management system with the recommendation module to highlight the benefits of MF-PGMRA for students' subject learning. According to a questionnaire, we confirmed that the students are satisfied with the system from four aspects of speed, accuracy, usability and convenience, which can confirm that the library management system based on MF-PGMRA can efficiently and accurately recommend suitable materials for students from the huge amount of learning materials to improve students' self-directed learning efficiency.

In countries with a school-entry cutoff date, individuals born right after the cutoff are almost 1 year older than individuals in the same school cohort born right before that date. Abundant research has documented that, as a result of that extra year of maturation and skill accumulation, older students in a cohort outperform their younger peers. It is also well-established that this effect peaks at the initial stages of the educational career and wanes as students grow. However, it remains unclear whether or not the age at school entry affects final educational attainment. In this work, we use Spanish census data to assess whether individuals born right after the school-entry cutoff (January 1) are more likely to complete post-compulsory education, a university degree and post-graduate education. We also assess if the age at school entry affects the probability of completing education in a STEM field of study. Our findings indicate that males born after the cutoff accumulate more years of education than males born before that date, but are less likely to complete their education in a STEM field of study. Interestingly, the effect concentrates among the youngest and oldest students in each cohort, is less intense for higher levels of education and disappears among females.

The purpose of this study was to investigate the effects of the anonymity of the internet and gender differences in online trolling and cybervictimization. A sample of 151 college students attending a southeastern university completed a survey to assess their internet activities and online trolling and cybervictimization. Multivariate analyses of logistic regression and ordinary least squares regression were used to analyze online trolling and cybervictimization. The results indicated that the anonymity measure was not a significant predictor of online trolling and cybervictimization. Female students were less likely than male students to engage in online trolling, but there was no gender difference in cybervictimization. In addition, the total hours spent on the internet increased the likelihood of the decision of college students to participate in online trolling, but not cybervictimization. Further implications for research related to online trolling and risk factors are discussed.

During the last two years, the COVID-19 pandemic had a secondary effect of increased media content loaded with mathematical, often probabilistic information (and misinformation). Our exploratory study investigates the probabilistic intuitions, misconceptions, biases, and fallacies in conditional probability reasoning of mathematics teacher candidates in the context of the pandemic. The pre-service mathematics teachers who participated in our study were given a questionnaire with five contextual conditional probability problems, all formulated similarly to media statements often encountered when discussing the COVID-19 pandemic. Our findings confirm the previous findings on biases and fallacies related to conditional probability problems with a social context. They were also indicative of several types of errors (both numerical and logical) as more common than expected. Our results also reveal that pre-service mathematics teachers apparently separate the content learned in the classroom from the application of the knowledge in critical examination of the information to which they are daily exposed by the media.

This paper reports on an exploratory study about probabilistic intuition in learning mathematics for decision-making. The analysis was carried out on a group of high school students in relation to their probabilistic intuition in problem-solving, after performing playful learning activities on a simulation platform specifically designed for this study. The analysis used a mixed qualitative-quantitative method. The results showed that the simulation activities facilitated the students' probabilistic intuition and boosted their performance in solving problems, particularly avoiding decisions based on previous results (when unnecessary) and identifying situations, where binomial distribution can be used.

Problem-based learning (PBL) has been widely applied as an alternative to improve learning outcomes, but it is still little studied in the context of the probability theory course. This study described how implementing the PBL model improves students' problem-solving and critical thinking skills in probability theory course and evaluates its quality. This design research involved 58 undergraduate students and two probability theory course lecturers from two universities in Indonesia as participants. Data collection used observation to describe PBL implementation, then questionnaire and pretest-posttest to evaluate the quality of the model. This study produced a PBL model for the probability theory course which is implemented through five steps: i) Orienting students on problems; ii) Organizing students to study; iii) Assisting individual and group investigations; iv) Developing and presenting work or solutions; and v) Analyzing and evaluating problem solving processes. Lecturers and students consider that the implementation of PBL is practical. PBL implementation can also improve students' problem-solving skills and critical thinking in the probability theory course. Thus, implementing PBL can be used as a solution to optimize learning outcomes in the probability theory course.

The aim of this study is to classify the subjects and skills of middle school mathematics course in the context of MATH Taxonomy and to determine their relations. For this purpose, the questions and answers related to the mathematics subtest of a national exam were analyzed over the answers of 20154 students. The study continued with the analysis of the data set containing the answer patterns of the students according to the rules of association of data mining methods by using RapidMiner program and FP-Growth algorithm. The results show that students with any level of skill in MATH taxonomy related to mathematical skills could perform skills in subcategories at a high rate. Students who have attainment in the learning areas provided later in the mathematics program had a high rate of knowledge in the previously provided learning areas. However, this result is not valid for Probability of Simple Events.

Mixed Membership Models (MMMs) are a popular family of latent structure models for complex multivariate data. Instead of forcing each subject to belong to a single cluster, MMMs incorporate a vector of subject-specific weights characterizing partial membership across clusters. With this flexibility come challenges in uniquely identifying, estimating, and interpreting the parameters. In this article, we propose a new class of "Dimension-Grouped" MMMs (Gro-M[superscript 3]s) for multivariate categorical data, which improve parsimony and interpretability. In Gro-M[superscript 3]s, observed variables are partitioned into groups such that the latent membership is constant for variables within a group but can differ across groups. Traditional latent class models are obtained when all variables are in one group, while traditional MMMs are obtained when each variable is in its own group. The new model corresponds to a novel decomposition of probability tensors. Theoretically, we derive transparent identifiability conditions for both the unknown grouping structure and model parameters in general settings. Methodologically, we propose a Bayesian approach for Dirichlet Gro-M[superscript 3]s to inferring the variable grouping structure and estimating model parameters. Simulation results demonstrate good computational performance and empirically confirm the identifiability results. We illustrate the new methodology through applications to a functional disability survey dataset and a personality test dataset.

Multiple representations can enhance students' understanding of mathematical concepts and complex information but can also pose well-documented challenges for students. Whereas instructional designs have been optimized to support students' "learning" with multiple representations, little is known about supportive "teaching" practices for dealing with multiple representations in whole-class discussions. In this article, we qualitatively investigate two cases of teacher-student interaction in whole-class discussions in grades 10-12 (about the mathematical topic of complex conditional probability information). The analysis aims at decomposing the teaching practices into those actions that can support or hinder students' understanding. The comparison of cases reveals that teaching practices can vary greatly: simply translating compacted concepts of a given text into other representations (visual area model, symbolic representation of fractions, and three language varieties) seems to be sufficient for students with advanced understanding. Other students need teachers' supportive actions for unfolding the highly compacted concepts (such as part-of-part) into several concept elements (part, whole, and part-whole relationship) and explicitly connecting (rather than only translating) the concept elements in multiple representations for the different concept elements. The findings can inform both theory building on teaching practices with multiple representations and professional development.

How to make own advantages when submitting applications and increase the probability of getting a job early? The target of this study is to analyse the determinants of unemployment duration and the probability of seeking a job after graduation. It is carried out by using survival analysis along with the Cox model and Kaplan-Meier estimator and based on the dataset integrated from survey data and academic data. The empirical results show that taking part-time jobs related to training majors and setting goals as well as planning to go internship early have a positive influence on the ability of students to get a job early. The results also reveal that the mother's occupation, the type of internment enterprise, the type of work contract, and the refusal of job opportunities offered previously have a negative impact on students' chances of escaping unemployment. The findings are the basis for students to properly assess their advantages and disadvantages. Thereby, they can determine the goal of a job that suits their capacity and have a reasonable plan combined with their efforts to achieve it. They also support companies to identify groups of potential students and build their suitable evaluation criteria in recruitment.

Talent identification and development systems (TIDS) adopt a deterministic perspective (i.e. athletes' future state/performances can be predicted by observations of their initial state/performance), which encourages early identification and specialisation in sport. In this framework, the main aim of sport systems is to enhance predictability and reduce uncertainty, by investigating the causal relationship between entering a talent pathway and becoming an expert performer. Generally, athletes who display ideal body proportions and attain certain performance standards in early developmental stages are labelled as talented (i.e. they display the potential to succeed) and are selected by TIDS, which afford them a superior developmental opportunity (i.e. better training facilities, certified coaching staff, and higher competition levels), to realise their potential. A deterministic approach, thus, (a) sees talent as a fixed capacity, whereby future successful athletes can be identified early (i.e. early identification); and (b) considers entering at an earlier age in a talent pathway a pre-requisite for sporting success (i.e. early specialisation). Contrary to deterministic expectations, recent research has highlighted how being considered talented from the early stages does not guarantee a better likelihood of successfully achieve senior sporting success. In this paper, taking ideas from ecological anthropology, a new probabilistic approach is proposed which considers TIDS as a process (i.e. being talented is about remaining responsive to what you could become), dialogical (i.e. athlete selection and development are not done in isolation, but both influenced by sociocultural constraints), and open-ended (i.e. unpredictability related to future outcomes). If sport systems embrace the uncertainty of developmental pathways opportunities arise to participate in conversations across and within TIDS to support systemic change. We conclude by proposing four key foundations of any probabilistic TIDS: give sport back to kids, ethos of amateurism, delaying selection processes, and early diversification.

In statistics classes, the central limit theorem has been demonstrated using simulation-based illustrations. Known population distributions such as a uniform or exponential distribution are often used to consider the behavior of the sample mean in simulated samples. Unlike such simulations, a number of real-data-based simulations are here implemented in which the populations are empirical distributions of data selected from Japanese firms. The dataset chosen contains 38 variables familiar to business students, such as sales and assets. The maximum population size of the variables is 2243. One thousand samples with replacement are selected for specific variable--sample size combinations. Hypothesis testing results indicate that the normality hypothesis for the sample mean is rejected for 31 variables at the 0.1% level even with a sample size of 500. It is emphasized that the data for these variables indicate that this should not be a surprise, and emphasize the importance of looking at data.

This article introduces an innovative sampling scheme, the median sampling (MS), utilizing individual observations over time to efficiently estimate the mean of a process characterized by a symmetric (non-uniform) probability distribution. The mean estimator based on MS is not only unbiased but also boasts enhanced precision compared to its simple random sampling-based counterpart. Moreover, a new EWMA chart based on the mean estimator within the MS scheme is proposed. The performance of the EWMA charts, derived from both simple random sampling (SRS) and MS schemes, is evaluated using the metrics of steady-state average run-length and average number of items-to-signal. The findings underscore the superiority of the EWMA-MS chart over the EWMA-SRS chart. Additionally, as the magnitude of ranking errors escalates, the behavior of the EWMA-MS chart converges toward that of the EWMA-SRS chart. The practical implementation of the newly introduced EWMA chart is demonstrated through an illustrative example.

A growing body of research has provided evidence for the foreign language effect on thinking, notably decision-making. Our prior work found reduction of recency effect following positive feedback in a foreign language as compared to the native tongue during even-probability gambling. However, the fundamental mechanisms underlying this effect remain unclear. The present study, therefore, aims to probe into this by engaging Chinese-English bilinguals in a functional magnetic resonance imaging version of our gambling task, which required participants to make decisions between playing and leaving equal-odds bets whilst manipulating language and valence of feedback. Results showed fewer 'play' choices following positive feedback presented in English relative to Chinese while no cross-language differences were observed after negative feedback. This valence-dependent language effect on risk-taking behaviour was supported by a language-emotion-decision neural circuit involving interplay between the right lingual gyrus, left fusiform gyrus, and right inferior frontal gyrus. Overall, our findings suggest valence-differential mechanisms of the foreign language effect in the risky decision. That is, the use of a foreign language in feedback presentation attenuates emotional reaction to positive feedback and thus diminishes subsequent risk-taking behaviour. Differently, negative counterparts seem to trigger detachment from negative emotion, leading to dissociation between feedback-encoding and decision-making.