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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.

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.

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.

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.

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.

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.

Probability theory has extensive applications across various domains, such as statistics, computer science, and finance. In probability education, students are introduced to fundamental principles which may include mathematical topics such as combinatorics and symmetric sample spaces. Students pursuing degrees in computer science possess a robust foundation in programming, software engineering, and algorithmic thinking. Despite entering probability courses with a unique perspective and learning potential, these students encounter challenges in grasping combinatorial concepts. In this experiment, we challenged first-year postsecondary computer science students to program a simulation of a practical combinatorics problem. Students commented on whether and how this task helped them internalize the basic concepts of combinatorics. We aim to show how utilizing programming tasks may empower students with a deeper grasp of combinatorics.

Worldwide, childhood sexual abuse (CSA) is widespread with severe consequences. We assessed the influence of CSA on insecure attachment in 488 young women in Botswana with no history of CSA, a history of CSA without re-occurrence in adulthood, and a history of CSA with re-occurrence in adulthood. Binary logistic regression analyses were fitted to study differences in anxious and avoidant attachment dimensions. Young women with a history of CSA only and those with a recurrence of sexual abuse in early adulthood had more than three times (OR, 3.34; 95% CI (1.77-6.28) and more than five times (OR, 5.28; 95% CI [1.84-15.12]) the odds of reporting anxious attachment dimension, respectively. Self-reported CSA is common and a risk to attachment.

Effective undergraduate statistical education requires training using real-world data. Textbook datasets seldom match the complexities and messiness of real-world data and finding these datasets can be challenging for educators. Consulting and industrial datasets often have nondisclosure agreements. Academic datasets often require subject area expertise beyond those of a general education or lack connections to real-world applications. Many governments, including the United States, now require the release of data from projects they directly complete or fund though grants and contracts. We show how statistical educators may find datasets and incorporate them into courses. Specifically, we use two examples from the U.S. Geological Survey (USGS) and one example from the ecology literature. We demonstrate the use of these datasets in an upper-level analysis of variance (ANOVA) class. In addition to describing how we found the datasets, we describe how to include them into course work and the course's student assessments. We have used these datasets over multiple semesters and included student feedback from these courses. Although our examples focus on an ANOVA class, the general methods for finding data shared here could be used for statistical classes ranging from high school to graduate education. Supplementary materials for this article are available online.

This study examined the association between literacy and quality of life among rural seniors in the Republic of Korea. A sample of rural seniors (N = 1,000) was surveyed by the Korea Rural Economic Institute in 2018, which assessed their literacy levels, their lifelong literacy education status and their quality of life. The authors' analyses of the data collected in this survey reveal that higher literacy levels are positively associated with a greater likelihood of social inclusion and better mental health status among rural seniors. Furthermore, seniors with functional literacy demonstrated a higher probability of being included in the rural community compared to those with only basic literacy. Lastly, lifelong literacy education was found to play a crucial role in enhancing the literacy levels of rural seniors. As a policy recommendation, the authors suggest that local governments expand literacy education programmes to more rural areas of South Korea.

Sequence learning is fundamental to a wide range of cognitive functions. Explaining how sequences--and the relations between the elements they comprise--are learned is a fundamental challenge to cognitive science. However, although hundreds of articles addressing this question are published each year, the actual learning mechanisms involved in the learning of sequences are rarely investigated. We present three experiments that seek to examine these mechanisms during a typing task. Experiments 1 and 2 tested learning during typing single letters on each trial. Experiment 3 tested for "chunking" of these letters into "words." The results of these experiments were used to examine the mechanisms that could best account for them, with a focus on two particular proposals: statistical transitional probability learning and discriminative error-driven learning. Experiments 1 and 2 showed that error-driven learning was a better predictor of response latencies than either n-gram frequencies or transitional probabilities. No evidence for chunking was found in Experiment 3, probably due to interspersing visual cues with the motor response. In addition, learning occurred across a greater distance in Experiment 1 than Experiment 2, suggesting that the greater predictability that comes with increased structure leads to greater learnability. These results shed new light on the mechanism responsible for sequence learning. Despite the widely held assumption that transitional probability learning is essential to this process, the present results suggest instead that the sequences are learned through a process of discriminative learning, involving prediction and feedback from prediction error.

In any visual search task in the lab or in the world, observers will make errors. Those errors can be categorized as "deterministic": If you miss this target in this display once, you will definitely miss it again. Alternatively, errors can be "stochastic", occurring randomly with some probability from trial to trial. Researchers and practitioners have sought to reduce errors in visual search, but different types of errors might require different techniques for mitigation. To empirically categorize errors in a simple search task, our observers searched for the letter "T" among "L" distractors, with each display presented twice. When the letters were clearly visible (white letters on a gray background), the errors were almost completely stochastic (Exp 1). An error made on the first appearance of a display did not predict that an error would be made on the second appearance. When the visibility of the letters was manipulated (letters of different gray levels on a noisy background), the errors became a mix of stochastic and deterministic. Unsurprisingly, lower contrast targets produced more deterministic errors. (Exp 2). Using the stimuli of Exp 2, we tested whether errors could be reduced using cues that guided attention around the display but knew nothing about the content of that display (Exp3a, b). This had no effect, but cueing all item locations did succeed in reducing deterministic errors (Exp3c).

We consider the problem of bias arising from conditioning on a post-outcome collider. We illustrate this with reference to Elwert and Winship (2014) but we go beyond their study to investigate the extent to which inverse probability weighting might offer solutions. We use linear models to derive expressions for the bias arising in different kinds of post-outcome confounding, and we show the specific situations in which inverse probability weighting will allow us to obtain estimates that are consistent or, if not consistent, less biased than those obtained via ordinary least squares regression.

Suppose "X" and "Y" are binary exposure and outcome variables, and we have full knowledge of the distribution of "Y," given application of "X." We are interested in assessing whether an outcome in some case is due to the exposure. This "probability of causation" is of interest in comparative historical analysis where scholars use process tracing approaches to learn about causes of outcomes for single units by observing events along a causal path. The probability of causation is typically not identified, but bounds can be placed on it. Here, we provide a full characterization of the bounds that can be achieved in the ideal case that "X" and "Y" are connected by a causal chain of complete mediators, and we know the probabilistic structure of the full chain. Our results are largely negative. We show that, even in these very favorable conditions, the gains from positive evidence on mediators is modest.

Most of the social science research is based on the implied assumption that measurement error is the same across key socio-demographic groups and all differences in key statistics of interest are real. Nevertheless, there is evidence that this is not the case. In this paper, the authors tackle this important topic by investigating if data quality is different in three key groups analysed in social research: the unemployed, the low-income respondents and the elderly respondents. This paper investigates if the assumption of equal data quality across these three key variables in a popular online probability panel in the Netherlands. To do this the authors use multiple types of variables and multiple statistical approaches to evaluate data quality

Using software to teach statistical inference in introductory courses opens the door for methods and practices that are more conceptually appealing to students. With an increasing number of fields requiring competency in statistics including data science, natural and social sciences, public health and more, it is crucial that we as instructors deliver the basic concepts of statistics effectively. In line with guidelines presented in the GAISE College Report, this article demonstrates intuitive approaches to teaching proportion and mean inference that take advantage of statistical software and emphasize conceptual understanding. The article recommends putting aside asymptotic-based methods for proportion inference and using the exact binomial method. Regarding mean inference, we propose a more contextualized and simplified process that uses the distribution of the sample mean directly and avoids standardized statistics such as z or t. In both the proportion and mean inference contexts, we discuss the benefits of the proposed approaches and provide detailed examples that demonstrate the methods using the Rguroo statistical software.

The Miller-Rabin test is a useful probabilistic method for finding large primes. In this paper, we explain the method in detail and give three variations on this test. These variations were originally developed as student projects to supplement a course in error correcting codes and cryptography.

This study employed design-based logistic regression to examine the extent to which attending a science, technology, engineering, and mathematics (STEM) magnet high school, school demographics, and student-level factors explain a student's intent to declare a STEM major in the first semester of college. The results show only student-level factors are statistically significantly associated with a student's likelihood of intending to declare a STEM major.

Understanding randomness is essential for modern life, as it underpins decisions under uncertainty. It is also an essential part of both the mathematics and science curricula in schools. Yet, research has shown that many people consider randomness difficult to perceive and argue about, with a number of different and contradictory views on the nature of randomness prevailing. This study explores beginning mathematics and science teachers' understanding of randomness. A questionnaire was used with student teachers in an initial teacher-education course to explore their understanding of and reasoning about randomness and random events. Results suggest that mathematics and science student teachers conceptualize and argue about randomness in a variety of ways. Furthermore, these different conceptualizations affect how they respond to both common classroom tasks and everyday contexts involving randomness. This raises important implications for the education of teachers who will themselves be teaching probability and statistical inference.

First-year seminars (FYS) comprise one of 11 researched interventions in postsecondary education known as High-Impact Practices, but few rigorous studies report significantly high impacts. This study examined a FYS employing propensity score matching to link cases and controls in a quasi-experimental design. One semester later cumulative grade point average (GPA), cumulative hours attempted, and 1-year later indicators (hours earned, hours attempted, and term GPA) were statistically different between the two groups. Three freshman survey items were also statistically significant and differences were observed within the same semester of the program. Quantitative differences did not appear immediately but appeared one term and 1 year later. Mean differences did not appear to diminish between groups over time. This analysis helps to fill a void in the paucity of studies clarifying the relationship between FYS participation and outcomes using comparison groups.

External visualization (i.e., physically embodied visualization) is central to the teaching and learning of mathematics. As external visualization is an important part of mathematics at all levels of education, it is diverse, and research on external visualization has become a wide and complex field. The aim of this scoping review is to characterize external visualizations in recent mathematics education research in order to develop a common ground and guide future research. A qualitative content analysis of the full texts of 130 studies published between 2018 and 2022 applied a deductive-inductive coding procedure to assess four dimensions: visualization product or process, type of visualization, media, and purpose. The analysis revealed different types of external visualizations including visualizations with physical resemblance ranging from pictorial to abstract visualizations as well as three types of visualizations with structural resemblance: length, area, and relational visualizations. Future research should include measures of visualization products or processes to help explain the demands and affordances that different types of visualizations present to learners and teachers.

Drug repurposing refers to the process of discovering new therapeutic uses for existing medicines. Compared to traditional drug discovery, drug repurposing is attractive for its speed, cost, and reduced risk of failure. However, existing approaches for drug repurposing involve complex, computationally-intensive analytical methods that are not widely used in practice. Instead, repurposing decisions are often based on subjective judgments from limited empirical evidence. In this article, we develop a novel Bayesian network meta-analysis (NMA) framework that can predict the efficacy of an approved treatment in a new indication and thereby identify candidate treatments for repurposing. We obtain predictions using two main steps: first, we use standard NMA modeling to estimate average relative effects from a network comprised of treatments studied in both indications in addition to one treatment studied in only one indication. Then, we model the correlation between relative effects using various strategies that differ in how they model treatments across indications and within the same drug class. We evaluate the predictive performance of each model using a simulation study and find that the model minimizing root mean squared error of the posterior median for the candidate treatment depends on the amount of available data, the level of correlation between indications, and whether treatment effects differ, on average, by drug class. We conclude by discussing an illustrative example in psoriasis and psoriatic arthritis and find that the candidate treatment has a high probability of success in a future trial.

The Torrance Test of Creative Thinking (TTCT) is the most widely used norm-referenced creativity test used in gifted identification. Although commonly used for identifying talent, little is known about how creativity tests, like the TTCT-Figural, contribute to the probability of being identified as gifted especially with underrepresented populations. Using nominated students (n = 1,191) from a diverse midsized urban school district, this study examined the differential predictive validity among student demographics (i.e., race/ethnicity, free/reduced price lunch status, English learning status, sex) and the TTCT-Figural to the probability of being identified as gifted. Results of a multilevel hierarchical generalized linear regression indicated underrepresented groups showed no difference in the probability of being identified after controlling for cognitive ability and academic achievement; the same was true when the TTCT-Figural was included within the model. The inclusion of the TTCT-Figural does contribute to the probability of identification; however, the disproportionality of underrepresented student groups remains in this school district. Gifted administrators looking to enhance equity may not find the solution with the mere inclusion of a creativity assessment. Implications for practice and future directions are discussed.

There is growing consensus that selection history strongly guides spatial attention and is distinct from current goals and physical salience. Here, we focused on target-location probability cueing: when the target is more likely to appear in one region, search performance gradually improves for targets appearing in that region. Probability cueing is thought to reflect a long-lasting, inflexible and implicit attentional bias. However, strong evidence for these claims is lacking. We re-examined them in four experiments. The target was more likely to appear in one than in the other regions during the learning phase, whereas all regions were equiprobable during the extinction phase. We manipulated set size in all experiments. Probability cueing reduced search slopes during learning and extinction, suggesting that the bias is attentional and long-lasting. Although intertrial priming from several previous trials had an influence, it did not account for all the effects. We also found the bias to be largely inflexible: informing participants that the probability imbalance during learning would be discontinued during extinction did not reduce the bias. Moreover, the acquired bias remained the default determinant of attentional priority when goal-directed guidance failed (i.e., when a cue instructing participants to start their search in a given region during the extinction phase was omitted or invalid). Finally, many more participants than predicted by chance showed awareness of the probability manipulation, although we could not establish whether awareness was associated with the bias. We conclude that probability cueing is a long-lasting and inflexible attentional bias, distinct from intertrial priming.

In the present study, we used a modeling approach for measuring task conflict in task switching, assessing the probability of selecting the correct task via multinomial processing tree (MPT) modeling. With this method, task conflict and response conflict can be independently assessed as the probability of selecting the correct task and the probability of selecting the correct response within a given task, respectively. These probabilities can be estimated on the basis of response accuracy in the different experimental conditions. In two task-switching experiments, we used bivalent stimuli and manipulated irrelevant-task difficulty by varying the saliency of the stimulus feature belonging to the irrelevant task. The more salient the task-irrelevant stimulus feature, the more salient the irrelevant task, leading to more task conflict. Consistent with this assumption, we observed that task conflict, but not response conflict, was larger when the task-irrelevant stimulus feature was made more salient. Furthermore, both task conflict and response conflict were larger when the task switched than when the task was repeated. On a methodological level, the present results demonstrate that MPT modeling is a useful approach for measuring task conflict in task switching and for dissociating it from within-task response conflict. Furthermore, the present results inform theories of task switching by showing that the task-irrelevant feature tends to activate the irrelevant task set rather than being associated with a specific response option via a direct stimulus--response route.

Evidence of processing costs for unexpected words presented in place of a more expected completion remains elusive in the eye-movement literature. The current study investigated whether such prediction error costs depend on the source of constraint violation provided by the prior context. Participants' eye movements were recorded as they read predictable words and unpredictable alternatives that were either semantically related or unrelated in three-sentence passages. The passages differed in whether the source of constraint originated solely from the global context provided by the first two semantically rich sentences of the passage, from the local context provided by the final sentence of the passage, from both the global and local context, or from none of the three sentences of the passage. The results revealed the expected processing advantage for predictable completions in any constraining context, although the relative contributions of the different sources of constraint varied across the time course of word processing. Unpredictable completions, however, did not yield any processing costs when the context constrained toward a different word, instead producing immediate processing benefits in the presence of any constraining context. Moreover, the initial processing of related unpredictable completions was enhanced further by the provision of a supportive global context. Predictability effects therefore do not appear to be determined by cloze probability alone but also by the nature of the prior contextual constraint especially when they encourage the construction of higher-level discourse representations. The implications of these findings for understanding existing theoretical models of predictive processing are discussed.

In a range of settings, human operators make decisions with the assistance of automation, the reliability of which can vary depending upon context. Currently, the processes by which humans track the level of reliability of automation are unclear. In the current study, we test cognitive models of learning that could potentially explain how humans track automation reliability. We fitted several alternative cognitive models to a series of participants' judgements of automation reliability observed in a maritime classification task in which participants were provided with automated advice. We examined three experiments including eight between-subjects conditions and 240 participants in total. Our results favoured a two-kernel delta-rule model of learning, which specifies that humans learn by prediction error, and respond according to a learning rate that is sensitive to environmental volatility. However, we found substantial heterogeneity in learning processes across participants. These outcomes speak to the learning processes underlying how humans estimate automation reliability and thus have implications for practice.

This study aimed to identify whether appetitive traits predict exclusive breastfeeding (EBF) duration for the first 6 months of life and to assess other predictors of its duration. 186 six- month-old term infants were included. Appetitive traits were assessed at 3-4 months of age. EBF duration, feeding practices, sex, maternal age and education, socioeconomic level, mode of delivery and gestational age were also evaluated. Risk ratios (RR) and 95% confidence intervals (CI) were estimated through generalized linear regression models to identify predictors of EBF for the first 6 months of life. Only 32.9% of infants achieved 6-month EBF. Vaginal birth, not using formula the first 3 days, maternal education [greater than or equal to] university and slowness in eating significantly increased the probability of EBF for 6 months. Slowness in eating was the only appetitive trait related to EBF for the first 6 months and was the most significant predictor in the multivariate model.

This study aimed to identify the prevalence of current smoking and examine the association between meeting combinations of the 24-h movement guidelines and current smoking in autistic adults. This cross-sectional study administered an electronic survey to a national sample of autistic adults in the United States. The study outcome was current smoking. Independent variables included the 24-h movement behaviors. Multivariable statistical modeling was used to assess the study aims. The study sample (n = 259) had a mean age of 31.05 years (standard deviation = 7.70), 58.7% were male, 11.2% were fully independent, and 35.5% were current smokers. Current smokers met significantly fewer 24-h movement guidelines than non-smokers (mean = 1.52 (standard deviation = 0.73) vs mean= 1.93 (standard deviation = 0.88), respectively, t = 3.77, p < 0.01). Autistic adults with high levels of sedentary behavior were almost three times more likely (odds ratio = 2.784, 95% confidence interval = 1.490, 5.237) to be a current smoker than those who did not meet these guidelines. Autistic adults not meeting sleep and sedentary behavior recommendations had a 1.581 increased odds (odds ratio = 1.581 95% confidence interval = 1.25, 2.001) of being a smoker as compared to those meeting these recommendations. Current smoking was highly prevalent in this sample. Improving sleep health and reducing sedentary time may be viable intervention targets to help promote smoking cessation in autistic adults.

In order to ensure content validity by covering a broad range of content domains, the testing times of some educational large-scale assessments last up to a total of two hours or more. Performance decline over the course of taking the test has been extensively documented in the literature. It can occur due to increases in the numbers of: (a) incorrect responses or (b) missing responses. Both reasons can be regarded as the result of decreasing effort. We investigated the roles of self-reported effort and omission propensity for performance decline over the course of taking a comprehensive educational large-scale assessment in Germany. Latent change score models showed that the effects of initial effort and change in effort on decline in performance remained almost unchanged when we added omission propensity and change in omission propensity as predictors of performance decline. This indicates that self-reported effort and omission propensity capture different aspects of performance decline. This finding held in both proficiency domains we investigated: math and science. When developing strategies for mitigating threats to test score validity, the two constructs (i.e., effort and omission propensity) may be considered separately.

Extreme response style (ERS), the tendency of participants to select extreme item categories regardless of the item content, has frequently been found to decrease the validity of Likert-type questionnaire results. For this reason, various item response theory (IRT) models have been proposed to model ERS and correct for it. Comparisons of these models are however rare in the literature, especially in the context of cross-cultural comparisons, where ERS is even more relevant due to cultural differences between groups. To remedy this issue, the current article examines two frequently used IRT models that can be estimated using standard software: a multidimensional nominal response model (MNRM) and a IRTree model. Studying conceptual differences between these models reveals that they differ substantially in their conceptualization of ERS. These differences result in different category probabilities between the models. To evaluate the impact of these differences in a multigroup context, a simulation study is conducted. Our results show that when the groups differ in their average ERS, the IRTree model and MNRM can drastically differ in their conclusions about the size and presence of differences in the substantive trait between these groups. An empirical example is given and implications for the future use of both models and the conceptualization of ERS are discussed.

Purpose: Course evaluations are formative and are used to evaluate learnings of the students for a course. Anomalies in the evaluation process can lead to a faulty educational outcome. Learning analytics and educational data mining provide a set of techniques that can be conveniently applied to extensive data collected as part of the evaluation process to ensure remedial actions. This study aims to conduct an experimental research to detect anomalies in the evaluation methods. Design/methodology/approach: Experimental research is conducted with scientific approach and design. The researchers categorized anomaly into three categories, namely, an anomaly in criteria assessment, subject anomaly and anomaly in subject marks allocation. The different anomaly detection algorithms are used to educate data through the software R, and the results are summarized in the tables. Findings: The data points occurring in all algorithms are finally detected as an anomaly. The anomaly identifies the data points that deviate from the data set's normal behavior. The subject which is consistently identified as anomalous by the different techniques is marked as an anomaly in evaluation. After identification, one can drill down to more details into the title of anomalies in the evaluation criteria. Originality/value: This paper proposes an analytical model for the course evaluation process and demonstrates the use of actionable analytics to detect anomalies in the evaluation process.

In this paper, we develop a personal synthesis of the most outstanding research on the teaching and learning of probability in the past years. We conducted a systematic search to examine publications on this topic in mathematics education, statistics education, education, and psychology journals. This exploration was complemented by additional studies published in conference proceedings or books. We classified these papers to highlight the main recent research tendencies in the field, according to the theme studied and considering the research objectives. Epistemological analyses suggest that informal inference based on simulation diminishes the topic abstraction but reduces probability to its frequentist view. Topics receiving particular attention include children's probabilistic knowledge, the effect of visualizations on solving conditional probability problems, teachers' education and probability modelling. In the final section, we recommend relevant points in which more investigation is needed to complete our knowledge about teaching and learning. In particular, we miss research on teachers' mathematical knowledge of many probability concepts and on their didactic knowledge.

We tested two accounts of the cognitive process underlying the N400 event-related potential component: one that it reflects meaning-based processing and one that it reflects the processing of specific words. The experimental design utilized separable Persian phrasal verbs, which form a strongly probabilistic, long-distance dependency, ideal for the study of probabilistic processing. In sentences strongly constraining for a particular continuation, we show evidence that between two low-probability words, only the word that changed the expected meaning of the sentence increased N400 amplitude, while a synonym of the most probable target word did not. The findings support an account of the N400 in which its underlying process is driven by the processing of meaning rather than of specific words.

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.

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.

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.

When constructed-response items are administered for a second time, it is necessary to evaluate whether the current Time B administration's raters have drifted from the scoring of the original administration at Time A. To study this, Time A papers are sampled and rescored by Time B scorers. Commonly the scores are compared using the proportion of exact agreement across times and/or t-statistics comparing Time A means to Time B means. It is common to treat these rescores with procedures that assume a multinomial sampling model, which is incorrect. The correct, product-multinomial model reflects the stratification of Time A scores. Using direct computation, the research report demonstrates that both proportion of exact agreement and the t-statistic can deviate substantially from expected behavior, providing misleading results. Reweighting the rescore table gives each statistic the correct expected value but does not guarantee that the usual sampling distributions hold. It is also noted that the results apply to a wider class of situations in which a set of papers is scored by one group of raters or scoring engine and then a sample is selected to be evaluated by a different group of raters or scoring engine.

Logistic regression (LoR) is a foundational supervised machine learning algorithm and yet, unlike linear regression, appears rarely taught early on, where analogy and proximity to linear regression would be an advantage. A random sample of 50 syllabi from undergraduate business statistics courses shows only two percent of the courses included LoR. Conceivable reasons for this dearth of LoR content is likely related to topic complexity, time constraints, and varying degrees of tool ease of use and support. We propose that these constraints can be countered by: [1] introducing logistic regression early, [2] informed tool selection prioritizing ease of use with comprehensive output, and [3] using/developing innovative, accessible, and easy to understand concept learning aids. This approach would leverage the proximity to linear regression and probability readily embed distributed practice for student understanding of a foundational technique.