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This study investigates the impact of Project-Based Learning (PBL) with an emphasis on statistics on 26 Kinesiology students from a prominent Chilean university. A mixed-methodological approach was employed for the qualitative and quantitative analysis of data collected through surveys, supplementary interviews, and performance evaluations of these students. Furthermore, group grades during the project execution were examined. The correlation between academic performance and the perception of learning through this method was explored. The results indicate a generally favorable assessment of PBL, emphasizing its contribution to the development of statistical and scientific skills, as well as improvement in academic performance, with the option to incorporate additional methods to cater to different student needs. It is concluded that PBL is a potential pedagogical strategy that promotes active engagement in learning and the development of practical skills relevant to health sciences students in Chile.

This paper argues that engaging students in informal statistical reasoning from early school years is essential for the development of statistical understanding. We investigated if and how children aged six-seven years old identified variation in a table of data and made predictions through the design of a teaching experiment. The classroom teaching experiment was comprised of four 45 minutes lessons addressing the understanding and interpretation of data sets. In order to describe students' informal predictive reasoning, we used the framework of "data lenses". More specifically, we analyzed the different types of answers the students produced as they engaged in predictive reasoning during an interview given before and after the teaching experiment. The participation of students in (classroom) and out-of-school (family) communities of practice was also taken into consideration. Our results demonstrate that the students benefited from their learning experience and developed data understanding.

The traditional points system and subsequent Grade Point Average (GPA) in education perpetuates an evaluation of academic performance which reflects arbitrary weighting of assignments and/or assessments. As such, GPAs which are calculated using a traditional points system are not unidimensional in their design. The baseball batting and slugging percentage, which serves as established metrics for performance evaluations among baseball players, better reflects unidimensionality. In essence, this paper puts forth an analysis and discussion which posits that baseball batting average and slugging percentage can serve as an example for how unidimensionality can become more prevalent in educational assessments, especially as it relates to the traditional points system and GPA.

The study compared two survey datasets from higher education students in Germany and Ghana regarding access to digital devices; perceived value of digital media, tools, and services used for learning; gap analysis of the actual and desired use of digital teaching and learning formats; and types of media usage profiles among students. The findings underscored commonalities between the two groups, revealing that students in both contexts are equipped with mobile devices, and are highly utilized for their learning. Similarly, both student groups exhibit a preference for utilizing external media, tools and services not owned nor administered by their respective universities. However, a stark contrast emerged in terms of the provision of, and expressed demand for digital teaching and learning formats, attributable to significant disparities in the underlying internet infrastructure and service provision between the two countries. The high intensity in the use of videos, social networks and messaging applications means majority of the students in both contexts were classified as entertainment users of media by means of a latent class analysis. While students in Germany showed differentiation between non-traditional and traditional students in terms of their media usage patterns, there was little differentiation among Ghanaian students. The study concludes by offering suggestions for enhancing support for non-traditional learning and improving digital education in Ghana and similar contexts.

This article presents the results of applying an educational sequence implemented with technological support on an LMS and focused on peer assessment that was designed specifically to address key concepts in statistics with first-year undergraduate students. Individualized information is available for a total of n=232 students to support the empirical conclusions that are drawn. Based on the comparison of the peer assessments and the academic performance obtained in the two previous academic years in which a different methodology was applied, differential effects are found in the quality of the assignments presented. This, together with the perception of the learning by the students, suggests the incorporation of peer assessment processes in future curricular design.

The present paper investigates one aspect of questionable research practices relating to Arabic L1 learners of foreign languages, namely the use of statistics. The objective of the paper is to argue that reproducible research requires adopting wise practices in linguistics and that the excessive focus on quantification does not seem to serve this purpose. Statistical significance tests in quantitative research are routinely used in linguistic inquiry as well as language teaching and learning studies with a view to supporting the relevant explanatory insights in linguistics. In this article, I will expose the misuse of statistics by doctoral students in English departments of Morocco working on Arabic L1 learners' data, by highlighting some practices that are at odds with international good practices in academic research in linguistics. I will take stock of the current questionable practices in this regard to dispel some of the misunderstanding about the use of statistics which is now gaining grounds lest this becomes an orthodoxy. I will argue that research on Arabic L1 learners' data should be focused more on exploration and discovery, as well as the validation of epistemological insights than on mere descriptive quantification geared to hypothesis verification. These areas of focus constitute the crux of academic research in linguistics, but they seem to be lost in statistics in doctoral students' theses. Recommendations and solutions are provided for enhancing transparency and improving reproducibility of doctoral research outcomes to advance theory building and the delivery of new research lines in linguistics as well as to avoid the risk of research waste, in line with the requirements of open science.

The aim of the present exploratory study was to examine students' situational engagement and motivation in the statistics classroom at Zayed University, in Dubai, United Arab Emirates (UAE). Two instruments were used for this purpose: a) experience sampling method (ESM), and b) the validated Mathematics Motivation Questionnaire (MMQ). This study employed two samples, at undergraduate level (2nd and 4th Semesters). Participants consisted of 100 students enrolled in Statistics I and Statistics II (Probability and Structure of Randomness). The results indicate that, apart from challenge and effort, emotional engagement is not significantly different across different activities. The results also indicate increases in intrinsic value and utility value and decreases in test anxiety. Finally, results indicate higher engagement and effort when social interaction is purposely planned and fostered, such as in small groups. On the contrary, individual class activities seem to generate slightly lower levels of engagement and effort. These findings have significant implications for educators and researchers who seek to enhance students' engagement and motivation in their statistics courses.

Studies of non-linguistic statistical learning (SL) have often linked performance in SL tasks with differences in language outcomes. Most of these studies have focused on Western and high-income educational contexts, but children worldwide learn in radically different educational systems and communities, and often in a second language. In the west African nation of Côte d'Ivoire, children enter fifth grade (CM-1) with widely varying ages and literacy skills. Across three iteratively-developed experiments, 157 children, age 8-15 years, in rural communities in the greater-Adzópe region of Côte d'Ivoire watched sequences of cartoon images with embedded triplet patterns on touchscreen tablets, while performing a target-detection task. We assessed these tablet-based adaptations of non-linguistic visual SL and asked whether the children's individual differences in performance on the SL tasks were related to their first and second language and literacy skills. We found group-level evidence that children used the statistical regularities in the image sequence to gradually decrease their response times, but their responses on post-test discrimination did not reflect this learning. When evaluating the correlation between SL and language skills, individual differences related to other task demands predicted oral language skills shared by first and second languages, while SL better predicted second language print skills. These findings suggest that non-linguistic SL paradigms can measure similar skills in Ivorian children as previous samples, but they also echo recent calls for further cross-cultural validation, greater internal reliability, and tests for confounding variables (such as processing speed) in studies of individual differences in statistical learning.

The sample mean in statistics is a concept of great importance, with its properties being extensively utilized in other areas, such as computer science. This research centers on the concept of the sample mean and its characteristics in a cohort of computer engineering students undertaking a required course in statistics at a university in the Netherlands. The objective of this study was to analyze students' comprehension of the fundamental structure, properties, and applications of the sample mean. A digital mini-course on sample mean was developed and employed with 97 students, who had the option to apply the concepts at their own pace. The action-process-object-schema (APOS) theoretical framework was utilized to analyze the interview responses of seven participants. The majority of participants were able to demonstrate an understanding of the Process conception of the sample mean, with only a minority demonstrating an understanding of the Object conception. The lack of comprehension of the sample mean hindered students' capacity to effectively utilize the associated applications and properties. These findings imply that educators should strive to ensure that students have a sound comprehension of the sample mean so that they are better equipped to work with related applications. Suggestions of this study and further research ideas are indicated.

To estimate the distribution of the number of acquaintances of the members of a society, the network scale-up method asks survey respondents about the number of people they know with features for which national statistics are available. While many features have been used for this purpose, first names have been suggested to produce particularly low levels of transmission error and recall bias. For this method to be precise, a set of names needs to be selected for the survey that jointly represents the population in relevant variables such as gender or age. This article provides a solution approach to finding the optimal set of names. This can be applied to any population for which a joint distribution of first names and relevant variables is available. We show that our approach successfully provides sets of names closely mirroring the population distributions for six countries with different name statistics.

This article describes an activity and resource from The New York Times that can be used to help learners cultivate critical statistical literacy. Critical statistical literacy involves understanding, interpreting, and questioning statistical information to make informed decisions (Casey et al., 2023; Franklin et al., 2015; Weiland, 2017). It is a vital skill that needs to be learned and reinforced with students early and often. The authors find What's Going On in This Graph? (WGOITGraph?), a collaboration between the American Statistical Association (ASA) and The New York Times Learning Network (NYT LN), to be a useful, accessible, effective online resource and share an example implementation.

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.

Statistical literacy is critical for all sociology students because it facilitates academic and professional success, high-paying jobs, and informed citizenship. Most students, however, lack adequate statistical literacy to engage with sociological research. Within that general deficit, there are gender, racial, and social-class differences, with students from historically marginalized groups starting and staying behind. In this conversation, we argue that to deepen statistical literacy and reduce inequalities, instructors must be willing to sacrifice breadth of content to attend to students' psychosocial needs throughout sociology curricula, especially in courses where quantitative methodology is not the core focus. We synthesize prior literature into a holistic psychosocial approach for teaching quantitative sociology content at all course levels: build interest and motivation, foster a growth mindset, develop statistical efficacy, encourage belonging, and challenge stereotypes.

As the key to STEM education, teachers' level of STEM literacy plays a crucial role in teaching and learning. The purpose of this study is to assess the current STEM literacy of science teachers in China. This is a survey study using a questionnaire instrument to gain both quantitative and qualitative data. The quantitative data were analyzed by Statistical Package for the Social Science (SPSS) to evaluate the status of STEM literacy among China's school science teachers. Interpretive methods were applied for qualitative data analysis to support the quantitative data. The researcher found that current science teachers generally have a poor understanding of STEM education, lack STEM knowledge and teaching skills, but have the awareness to improve their own literacy. It is hoped that by investigating the STEM literacy of science teachers, the research will have a positive impact on improving science education and is expected to contribute to the development of science education in China.

Most higher education institutions in the UK now offer some form of additional individual support for mathematics and statistics. Whilst numerous studies have shown mathematics support can improve grades and reduce failure rates, there is a lack of research on other outcomes of interest such as anxiety or confidence, and very little research relating specifically to statistics support. This study uses quantitative and qualitative results from student questionnaires to evaluate the effectiveness of support in reducing anxiety and increasing confidence immediately after the first statistics support session and in the longer term. Comparisons of and preferences for online or face-to-face sessions and other aspects relating to anxiety were also explored. Key quantitative findings include a significant reduction in statistics anxiety after only one session of statistics support and a long-term increase in confidence with statistics. When asked how support impacts on anxiety or confidence, key themes emerging included feeling comfortable asking questions in statistics support, tailoring to individual needs and confirmation of understanding. The majority of students preferred face-to-face sessions over online particularly those with higher levels of statistics anxiety. Although differences were generally not significant, higher levels of anxiety were observed before online sessions and greater changes in anxiety occurred during face-to-face sessions.

Statistical learning (SL), the ability to detect and extract regularities from inputs, is considered a domain-general building block for typical language development. We compared 55 verbal children with autism (ASD, 6-12 years) and 50 typically-developing children in four SL tasks. The ASD group exhibited reduced learning in the linguistic SL tasks (syllable and letter), but showed intact learning for the nonlinguistic SL tasks (tone and image). In the ASD group, better linguistic SL was associated with higher language skills measured by parental report and sentence recall. Therefore, the atypicality of SL in autism is not domain-general but tied to specific processing constraints related to verbal stimuli. Our findings provide a novel perspective for understanding language heterogeneity in autism.

The current study presents a systematic review of teachers' data literacy, arising from a synthesis of 83 empirical studies published between 1990 to 2021. Our review identified 95 distinct indicators across five dimensions: (a) knowledge about data, (b) skills in using data, (c) dispositions towards data use, (d) data application for various purposes, and (e) data-related behaviors. Our findings indicate that teachers' data literacy goes beyond addressing the needs of supporting student learning and includes elements such as teacher reflection, collaboration, communication, and participation in professional development. Considering these findings, future policies should acknowledge the significance of teacher dispositions and behaviors in relation to data, recognizing that they are as important as knowledge and skills acquisition. Additionally, prioritizing the provision of system-level support to foster teacher collaboration within in-school professional development programs may prove useful in enhancing teachers' data literacy.

Generative artificial intelligence (AI) has shown the potential to reshape the world and redefine daily workflows. One specific instance of generative AI, ChatGPT, specializes in understanding natural language and generating human-like conversational text. Its free access, user-friendly interface, and instant feedback have propelled its popularity within and beyond education. Given its extensive knowledge of traditional statistics and contemporary data science, it can be considered for integration into modern statistics education. However, there have been ongoing questions and serious concerns regarding the accuracy and accountability of the responses generated by ChatGPT. This study explores ChatGPT's capabilities in addressing conceptual problems, implementing analytical techniques, and facilitating teaching while considering its disadvantages and ongoing development. With continued practice and deeper insights into this novel technology, its benefits can be cautiously leveraged in teaching and learning activities.

In this new era drenched with data, statistical literacy becomes more essential for individuals to be able to read, communicate, and make informed decisions. Moreover, statistical literacy is highly essential for education policy makers who are highly accountable for all policy outcomes including school improvement, resource allocation, curriculum planning and intervention. Hence, there is a need to understand their perceptions and beliefs. The aim of this study is to explore whether attitude towards statistics and statistical anxiety are related to the education policy makers' statistical literacy. Considering that statistics coursework is the basis and major contributor to a statistically literate society, real problems with statistics are likely due to non-cognitive factors, which include attitudes or beliefs towards statistics. There is a global increase in literature exploring beliefs and attitudes of teachers towards statistics, indicating that studies on attitudes towards statistics do not stop at the students' level but should also be extended to education personnel who uses statistics in their workplace. While pre-service teachers in college claimed that statistics anxiety is the main obstacle to get their teaching degree. This is alarming as they are the future teachers and education policy makers with anxiety may develop avoidance to read educational diagnoses containing statistical information. Participants self-reported their statistical literacy with 20 multiple choice items tailor made to the work of education policy makers. Data were drawn from a survey elicited using a cross-sectional method on 328 education personnel working at different levels in Ministry of Education. The findings show that attitude towards statistics is not significantly related to statistical literacy while statistics anxiety has a significant negative relationship with statistical literacy. Statistical anxiety also has a negative significant relationship with attitudes towards statistics. These findings help strengthen Model of Statistical Literacy, where dispositional element including beliefs and attitude was addressed while confirming Anxiety Expectation Model. Future studies to explore other potential predictors of statistical literacy and suggested to investigate possible difference in attitude towards statistics between adult workers and students.

Much has been done on assessment literacy (AL) components and job demand-resources (JD-R). However, an interdisciplinary look at AL components as the predictors of JD-R and its possible consequences for the engagement and burnout of teachers' assessment performance has been neglected. To fill this gap, the present study explored this issue in the context of Iran. To this end, through convenience sampling, 146 Iranian EFL teachers were selected to answer questionnaires on AL, JD-R, burnout, and engagement. A series of multiple regression analyses were run to analyze the collected data. The results showed that some components of AL such as 'test construction', 'administering, rating, and interpreting test', 'psychometric properties of a test', 'using and interpreting statistics', and 'authenticity' were significant predictors of job demand. Moreover, the results revealed that alternative and digital-based assessment, recognizing test type, distinction and function, and authenticity were significant predictors of job resources. Furthermore, test construction, administering, rating, and interpreting test, psychometric properties of a test, and using and interpreting statistics could significantly predict teachers' burnout. In addition, alternative and digital-based assessment, giving feedback in assessment, and ethical and cultural considerations in assessment turned out to significantly predict teachers' engagement. These findings can have theoretical and practical implications for stakeholders.

This study investigates the correlates of statistics anxiety. Considering that statistics anxiety and spatial anxiety have been separately correlated with related constructs (e.g., mathematics anxiety, academic performance, etc.), the possibility that spatial anxiety plays a role in statistics anxiety is explored. When facing statistics or mathematics operations, people may imagine or visualize the task operations they must do to obtain the result. To examine this hypothesis, 778 students in a Social or Health Sciences program, enrolled in a--often mandatory--statistics course from Canadian, French and Belgian universities completed an online survey. The results show moderate to strong positive correlations between all three types of anxiety (spatial, mathematics, and statistics). In addition, a mediation analysis reveals the intermediate role played by mathematics anxiety in the relationship between spatial and statistics anxieties. Nonetheless, the direct link from spatial anxiety to statistics anxiety is non-negligible in the model. Finally, the results also indicate that women report higher levels of statistics anxiety, which may be partly explained by their higher level of spatial anxiety.

The goal of this research was to provide a general assessment framework of students' statistical reasoning in medicine, then build three scales to assess students' statistical reasoning ability in solving practical medical problems, including Description, Interpretation and Prediction. On that basis, the study designed a set of tools to assess students' statistical reasoning ability in solving practical medical problems. Through the analysis of the students' performance, assessments of the students' statistical reasoning in medicine were done. These research results were suitable for student assessment in medical statistics courses, useful for faculty and students in teaching and learning medical statistics.

J.D. Brown (JD) served as the author of an instructional column titled "Statistics Corner" in the "Shiken": JALT "Testing & Evaluation SIG Newsletter" for an extensive period spanning over two decades, from 1997 to 2019. This publication was under the auspices of the Testing and Evaluation Special Interest Group, a subdivision of the Japanese Association of Language Teaching. The audience for the columns was diverse, and included language teachers, graduate students, and language practitioners encountering real-world issues with language assessment. Throughout his tenure, JD addressed over 40 reader-submitted inquiries related to testing and quantitative research. The subjects explored in these columns can be broadly classified into two thematic areas: Second Language Testing and Second Language Research. This present article aims to provide an exhaustive examination of the diverse range of topics covered within each of these thematic categories and to trace the evolution of these subjects over the course of JD's twenty-year involvement with the newsletter. Its goal is to help situate JD's abiding concern with connecting theory and practice.

Statistics education is increasingly important to our society with enrolment increases of 16% in introductory statistics courses and 85% in upper-level statistics courses. Research has demonstrated many factors related to students' behaviors and outcomes in statistics courses such as past achievement, attitudes, and effort. We sought to model these factors together to better understand how introductory statistics students' attitudes were related to students' achievement behaviors and what student characteristics mediated such relationships. Structural equation modeling with data from N=301 students in an introductory statistics course for psychology majors revealed that majors with higher GPAs had more interest, enjoyment as well as utility value for statistics, and these variables were in turn related to expectations for success or achievement behaviors. Females had lower interest in statistics, and this was related to lower expectations of success. The findings highlight the need to increase interest and enjoyment and utility value for non-majors studying statistics. Recommendations for how to adapt the statistics classroom to that end are discussed.

Real-world applications of statistics are rarely 'off the top of your head'; however, statistics and research methods courses default to closed-book exams that only test rote learning. Trending research supports open-book exams testing the application of student knowledge rather than memory, however statistics courses in psychology are lagging amidst fears of cheating in online open-book multiple-choice exams. The aim of this study was twofold; first, to develop an online open-book multiple-choice exam that tests the application of psychology statistics and research methods knowledge, and second, to demonstrate that it is just as reliable a source of final grades as traditional closed-book exams. We compared results from a new Applied Exam (N = 104 undergraduate third-year psychology statistics students) with the previous year's Traditional Exam (N = 81), correlating these with Research Report grades (the best course-assessment indicator of real-world performance). Similarly strong positive correlations were observed between the written assessments and the Traditional Exam (0.59**) or Applied Exam (0.54**), and both exams display comparable bell curves for grade differentiation, suggesting we can depend on the new Applied Exam for final course grade data. It also reflects a better alignment with course objectives and graduate qualities for effective problem solving in novel situations. Automated assessment of applied knowledge benefits psychology instructors and organisations in reducing administration, and psychology students by alleviating the anxiety in closed-book invigilated exams. Together this presents an opportunity to improve student outcomes by encouraging the development of real-world skills, preparing them for competitive job markets that value critical thinking.

It is important to note that the development of pre-service teachers' noticing abilities does not happen spontaneously; hence, assistance programs are crucial. This qualitative study aimed to examine pre-service teachers' noticing of student thinking within the context of lesson study. Three pre-service teachers conducted three lesson study cycles. Lesson plans, voice and video recordings of lesson study meetings and implementations, observations, field notes, and reflective writings are used as data collection techniques. The findings indicated that the pre-service teachers' early levels of noticing were constrained. Their noticing levels increased as the lesson study progressed. Hence, the improvement of pre-service teachers' noticing abilities can be assisted by lesson study. Activities such as planning, reflection and implementation helped pre-service teachers develop their noticing levels. To enhance the development of noticing skills, it can be proposed that lesson study should be integrated into teacher training programs.

Curriculum change and the ready access to school level appropriate statistical software has seen the focus of statistical practice for novice statisticians move from primarily constructing graphs and calculating statistics to describing and reasoning from distributions. Many multi-faceted concepts and statistical ideas underpin distributions, which students find difficult to navigate and cognitively coordinate. Limited research, however, exists on how to enhance students' communication when describing distributions. This paper explores the actions of a teacher as she supported 14-15-year-old students to develop notions of distribution and to describe distributions. The findings indicated that the teacher, through knowing, modelling, and listening, supported the development of student statistical language and communication. Students, through engaging in specifically designed instructional activities to engineer learning around the concept of distribution, seem to be able to transition from using their own language to using statistical language to describe distributions that communicated the concepts and features that were identified in the distribution description framework.

The teaching and learning of statistical thinking begins at a young age in Australia, with a focus on data representation and interpretation from Foundation Year (age 5), and the collection, sorting and categorising of items from the natural environment starting even earlier. The intangible concept of "data," as part of statistical literacy, can be complex for children to grasp, especially when applying the notion of data to the everyday world or when data are explored in isolation to an investigation process. Authentic data modelling experiences present meaningful opportunities to apply statistical thinking although expert STEM knowledge is not always accessible to primary classroom teachers, nor is it always obvious how to implement such authentic problems within a classroom context. In this exploratory case study, we present data from a Year 4 classroom (age 9) statistical investigation addressing, 'How big is a leaf?' linking data to the real-life STEM context they represented. The authors were interested in how the teacher's communication processes supported her students' emerging understandings about data. Wit's (2018) cognitive tuning framework offered a way to capture how the communication processes in a group build to a commonly shared frame of reference. Findings revealed a pattern of communication between the teacher and students, supporting students' changing conceptions of data and related statistical thinking processes, throughout the investigation.

The introduction of statistical concepts into school curricula in Australia and New Zealand in the early 1990s initiated an ongoing research program into the learning and teaching of statistics and probability in both countries. This paper reviews the contribution of Australian and New Zealand researchers to building statistical literacy at school, alongside international developments. From recognising how students develop understanding of specific statistical and probabilistic concepts, through teacher knowledge and beliefs for teaching statistics, to intervention studies and targeted teaching, the field of statistics education has grown and changed. Statistics and probability are now well established as part of the mathematics curriculum. The importance of linking statistical literacy and statistical understanding across the curriculum, as well as in STEM, has also begun to receive attention as other subjects have recognised the importance of data in their fields. Following a comprehensive review of the field in Australia and New Zealand, this paper then considers emerging areas of interest, such as new approaches to data visualisation, and suggests future research.

The capacity to interrogate data with critical thinking is a strong predictor of statistical literacy (SL). This data interrogation, from the data consumers' perspective, incorporates four complex response skills: "interpreting," "communicating," "evaluating," and "decision-making," and those skills are strongly supported by students' appreciation of three interrelated knowledge components ("text and context," "representation," and "statistical-mathematical knowledge"). Due to the need to be critical data-information readers, students' SL should develop during their formal schooling. The aim of this paper was to investigate differences in SL between Indonesian year 9 and year 12 students and between female and male students. The same test was administered to 48 year 9 students (50% females) and 48 year 12 students (50% females) from 16 different schools in Indonesia. Findings revealed that the highest percentage of year 9 and 12 students demonstrated evidence of "consistent but non-critical thinking" (level 4), suggesting that they exhibited their statistical knowledge but not in critical ways. There were 42% of year 9 students showing limited statistical thinking (levels 1 to 3) compared to 17% of year 12 students. Furthermore, while there were no significant gender differences in students' SL and its all skills, the study shows significant grade level differences in overall SL as well as in its skills except "interpreting." Implications of this study include the development of a framework that provides a coherent assessment of students' SL from a data consumers' perspective, along with suggestions for classroom teaching.

Identifying wordlike units in language is typically done by applying a battery of criteria, though how to weight these criteria with respect to one another is currently unknown. We address this question by investigating whether certain criteria are also used as cues for learning an artificial language--if they are, then perhaps they can be relied on more as trustworthy top-down diagnostics. The two criteria for grammatical wordhood that we consider are a unit's free mobility and its internal immutability. These criteria also map to two cognitive mechanisms that could underlie successful statistical learning: learners might orient themselves around the low transitional probabilities at unit boundaries, or they might seek chunks with high internal transitional probabilities. We find that each criterion has its own facilitatory effect, and learning is best where they both align. This supports the battery-of-criteria approach to diagnosing wordhood, and also suggests that the mechanism behind statistical learning may not be a question of either/or; perhaps the two mechanisms do not compete, but mutually reinforce one another.

In recent years, numeracy has had an increasing focus in the Australian educational system, with policies and assessments in place for both students and teachers. In order to address the requirements of their careers, teachers need to have sufficient numeracy capabilities. In our study, we explored the numeracy capabilities of post-graduate pre-service teachers enrolled in a numeracy unit at an Australian university. Specifically, we investigated participants' statistical literacy capabilities by examining responses to a multi-part question involving the analysis of Australian National Assessment Program--Literacy and Numeracy (NAPLAN) data presented graphically. Participants' multiple-choice answers were analysed quantitatively. To assess the depth of participants' statistical literacy reasoning, the explanations for their responses were analysed qualitatively using an adaptation of the Structure of Learning Outcomes (SOLO) taxonomy levels. Although the vast majority of participants exhibited strong basic statistical literacy skills, few participants demonstrated high-level statistical reasoning. Surprisingly, there were few differences in the response patterns of participants who had or had not studied university mathematics in their undergraduate studies.

There is widespread misuse of statistics in research, particularly in the life sciences, which is one of the contributing factors to reproducibility concerns in research. However, the formal quantitative training that life sciences research trainees receive is often quite limited. Our survey of statistics requirements in undergraduate life sciences programmes offered by the top research-intensive universities in Canada, the U15 Group of Canadian Research Universities, confirmed that training in statistics tends to be limited and more general in nature. To help raise awareness and address these limitations, this paper shares findings of this statistics requirements survey and describes the evidence-based framework for a second-year undergraduate course at the University of Toronto, which was introduced to integrate statistics instruction with the life sciences research process. We hope these insights will inform future quantitative course offerings, and ultimately, better prepare students to effectively engage with statistics in life sciences research.

Online education, while not a new phenomenon, underwent a monumental shift during the COVID-19 pandemic, pushing educators and students alike into the uncharted waters of full-time digital learning. With this shift came renewed concerns about the integrity of online assessments. Amidst a landscape rapidly being reshaped by online exam/homework assistance platforms, which witnessed soaring stocks as students availed its questionable exam assistance, and the emergence of sophisticated artificial intelligence tools like ChatGPT, the traditional methods of assessment faced unprecedented challenges. This paper presents the results of an observational study, using data from an introductory statistics course taught every semester by the author, and delves into the proliferation of cheating methods. Analyzing exam score results from the pre and post introduction of ChatGPT periods, the research unpacks the extent of cheating and provides strategies to counteract this trend. The findings starkly illustrate significant increases in exam scores from when exams of similar difficulty were administered in person (pre-COVID) versus online. The format, difficulty, and grading of the exams was the same throughout. Although randomized controlled experiments are generally more effective than observational studies, we will indicate when we present the data why experiments would not be feasible for this research. In addition to presenting experimental findings, the paper offers some insights, based on the author's extensive experience, to guide educators in crafting more secure online assessments in this new era, both for courses at the introductory level and more advances courses The results and findings are relevant to introductory courses that can use multiple choice exams in any subject but the recommendations for upper-level courses will be relevant primarily to STEM subjects. The research underscores the pressing need for reinventing assessment techniques to uphold the sanctity of online education.

Making connections within and between different aspects of mathematics is recognised as fundamental to learning mathematics with understanding. However, exactly what these connections are and how they serve the goal of learning mathematics is rarely made explicit in curriculum documents with the result that mathematics tends to be presented as a set of discrete, disconnected topics. Interest in establishing a more coherent approach to the teaching and learning of school mathematics has led to a focus on big ideas. That is, networks of related concepts, skills and ways of thinking that facilitate learning mathematics with understanding. Research on learning progressions has helped identify what these big ideas are and how they serve to build connections within and between different aspects of mathematics. This paper draws on research that provides an evidenced-based learning progression for multiplicative reasoning to illustrate the connective role of multiplicative thinking in the development of algebraic, geometrical, and statistical reasoning.

We explore ways in which statistics can be used to understand disease spread and support decision-making by governments. "Past performance does not guarantee future results"--we hope. We discuss and show examples from the National Science Foundation (NSF)-funded COVID-Inspired Data Science Education through Epidemiology (CIDSEE) project. Throughout, the emphasis is on the relationships between evidence, modeling and theorizing, and appropriate action. Statistics should be an essential element in all these aspects. We point to some "big statistical ideas" that underpin the whole process of modeling, which can be illustrated vividly in the context of pandemics. We argue that statistics education should emphasize the application of statistics in practical situations, and that many curricula do not equip students to use their understandings of statistics outside the classroom. We offer a framework for curriculum analysis and point to some rich teaching resources.

During the last two decades, universities around the world have increased the adoption of English-medium instruction (EMI) as a way to enhance internationalisation and global competitiveness. EMI adoption presents a wide range of opportunities, but it also presents some challenges, being one of them the potential impact on students' academic performance. This paper analyses the impact of EMI on the academic performance of the students in a Spanish university. The objective is to extend previous research, that shows contradictory conclusions. In the first part of the paper, using a multiple linear regression model to control key covariates, we have compared the performance of 229 EMI vs 635 Non-EMI students, corresponding to cohorts 2013-2014 to 2017-2018, considering the average grade in the 10 subjects of the first course. In the second part, we focus on the 2017-2018 cohort (49 EMI vs 116 Non-EMI students), carrying out a longitudinal study of its behaviour during two academic years in four different subjects. The results show that there are no statistically significant differences in academic performance between EMI and non-EMI students, ie language of instruction does not play a relevant role in academic performance.

We explore how students' course concerns at the outset of their introductory statistics course predict their later perceived course challenges and future interest in statistics via a function of achievement motivation. Data were collected from undergraduate students (N = 524; 70% female; 37.8% students from racially marginalized groups) during the COVID-19 pandemic, using both open-ended (concerns and challenges) and closed-ended (achievement motivation and future interest) questions. Overall, incoming course concerns positively predicted perceived costs during the course and challenges at the end of the course and negatively predicted success expectancy and utility value during the course and future interest in statistics at the end of the course. Patterns varied by individual concerns/challenges, gender, and race/ethnicity. Cost played an important mediating role for female students and students from racially marginalized groups (e.g., Black, Latinx, or Native American/Indigenous students) between course concerns and future interest in statistics. Our findings (a) add to the increasing body of research reporting differences in how female and male students as well as students from racially marginalized backgrounds and racial majority students experience STEM courses and help explain different levels of interest in pursuing STEM careers, and (b) suggest that increasing future interest in statistics might require different interventions.

Two novel proofs show that the sum of a specific pair of normal random variables is not normal are established in this note. This is one of the most often misunderstood facts by first-year students in probability theory and statistics. The first proof is concise using the moment generating function. The second proof checks whether the moments of the sum have the property of normal distribution.

For the last decade or more, circulation numbers of physical materials have declined in academic libraries across the United States. In the spring of 2020, the COVID-19 pandemic drastically altered society and daily life, not to mention library functions. In particular, fears of contagion via physical surfaces and transmission by contact led many libraries to shutter their in-person services or temporarily close altogether. The circulation of physical materials was hit particularly hard, as the ability to browse shelves, check out items, access interlibrary loan, and a host of other similar services were curtailed. This article will examine the statistical markers of physical material handling (checkouts, renewals, item browses, etc.) for two years before and after the pandemic, to reach conclusions about how COVID-19 impacted usage, what we can tell about general patterns in circulation before and due to these changes, and ultimately what these numbers tell us about the future of traditional material use.

Introductory undergraduate statistics courses widely focus on statistical concepts or software-based data analysis. Despite the fact that the analysis of real data has shown to enhance students' engagement, the step of data collection is often neglected. Once students know the challenges of data collection, they are more aware of potential imperfections, such as a lack of representativeness, during data analysis. In this paper, we present a course that closes the gap allowing Business and Economics students to conduct a full survey under realistic conditions including questionnaire design, sampling, and data analysis. It entangles theory and application by combining course-based research experiences with cooperative learning and a flipped classroom approach. Students do not only obtain competences in the field of statistics, they also gain experiences and self-confidence for future research projects because the lecturer acts as a mentor guiding the students throughout the project. Although statistics is usually an unpopular field for Business and Economics students, their motivation was high throughout the semester as they acted as researchers who analysed a specific research question. This is in agreement with student feedback, which highlights the promotion of research-related competences and self-efficacy within the course.

Despite the growing interest in mindfulness in higher education, the literature on its relation to decision-making under risk (i.e. academic misconduct) and statistics anxiety is scarce. The present research shall fill this gap. Based on the prospect theory, we assessed the mediating effect of mindfulness on the relationship between statistics anxiety and academic dishonesty moderated by risk aversion. Data were collected from 791 undergraduate students in six Israeli academic institutions studying for bachelor's degrees in social sciences. Questionnaires included the following measures: risk behaviour according to the prospect theory framework, Mindful Attention Awareness Scale, Statistics Anxiety Rating Scale, Academic Misconduct Scale and sociodemographic variables. Correlations among these variables were explored. The data was analysed using Structural Equation Modelling (SEM). The results indicate that the variance in academic dishonesty is explained by students' statistics anxiety with a mediation of Mindfulness moderated by Risk Aversion. Mindfulness negatively affects Academic Dishonesty, while Risk Aversion has a significant positive effect on Mindfulness. Finally, among individuals with high statistics anxiety, Risk Averse individuals show significantly higher Mindfulness than Risk Seekers. We conclude that mindfulness-based interventions might be a constructive tool to reduce risk-taking and promote ethical decision-making among individuals who experience high levels of statistics anxiety. Furthermore, developing mindful skills may help individuals with higher anxiety levels neutralize these unwanted feelings and get along with their learning tasks. Hence, avoid academic unethical behaviours.

It is important for young people to be aware of job profiles and activities in the professional world. Bringing the education system closer to the professional world is vital for them to make decisions about their academic and professional futures. Programs developed to connect 15-year-old students who in Spain are in year 4 of their Compulsory Secondary Education, and Research Support Units within the Health Research Institutes of the Hospitals and the Clinical Research Support Platforms of the Carlos III Institute of Health are a good opportunity to highlight the role of biostatistics in clinical trials. The aim of this article is to share the outcomes of and learnings from an interactive workshop for 15-year-old students on biostatistics and clinical trials conducted within the 4°ESO + Empresa program and directed by the Scientific Support Unit of the Health Research Institute of Hospital 12 de Octubre in Madrid, Spain.

Statistical software is commonly used in undergraduate social sciences statistics courses. Due to the increase in online/hybrid courses and the cost of SPSS, instructors may wish to switch to another statistical software. We cover seven programs: Excel, Google Sheets, jamovi, JASP, PSPP, R, and SOFA. We compare programs using the following criteria: ease of download, quality of online instructions, availability of instructor resources, sophistication of analyses available, ease of use, operating system requirements, whether it uses point-and-click or code, and whether a VPAT is available. Adopting new course materials is a valuable part of instruction but time-consuming. Therefore, this review provides information about commonly available or free open-source programs so instructors can choose based on the needs of their students and/or institutions.

Multi-site randomized controlled trials (RCTs) provide unbiased estimates of the average impact in the study sample. However, their ability to accurately predict the impact for individual sites outside the study sample, to inform local policy decisions, is largely unknown. To extend prior research on this question, we analyzed six multi-site RCTs and tested modern prediction methods--lasso regression and Bayesian Additive Regression Trees (BART)--using a wide range of moderator variables. The main study findings are that: (1) all of the methods yielded accurate impact predictions when the variation in impacts across sites was close to zero (as expected); (2) none of the methods yielded accurate impact predictions when the variation in impacts across sites was substantial; and (3) BART typically produced "less inaccurate" predictions than lasso regression or than the Sample Average Treatment Effect. These results raise concerns that when the impact of an intervention varies considerably across sites, statistical modeling using the data commonly collected by multi-site RCTs will be insufficient to explain the variation in impacts across sites and accurately predict impacts for individual sites.

The rapidly increasing capacity of technology to collect, organize, and manage data has spurred changes in the practice of statistics: new methods of collecting data, large data sets, new forms of data, different ways to visualize and represent data, and recognition of the importance of being able to understand and to communicate data-based arguments and findings from the perspective of data consumers and data producers. Using a narrative review based on Delphi methods, we asked leading members of the statistics education community to describe trends they have observed in the field and to identify interesting and relevant papers related to those trends. We received 24 responses and over 200 suggestions for papers. Our analysis included papers published in journals, book chapters, conference proceedings, handbooks, and curricular documents. We focused on future directions for statistics education research, and thus included articles based on opinion or principles if the arguments made a strong case supported by evidence as to why the idea was needed. From our analysis of 50 papers in this review, we suggest four emerging themes in statistics education research, challenging what should be taught and suggesting new ways of thinking about the teaching and learning of statistics: Data Science, Visibilizing Statistical Concepts, Social Statistics, and New Contexts for Learning. The review focuses on articles from 2017-mid 2022 and highlights the relevance and importance of each theme. Our choice of a particularly important paper for each theme is annotated in the references.

In recent years, the discipline of statistics has begun reckoning with its difficult history. Institutions are reconsidering names that have honored key historical figures in statistics who have deep ties to eugenics movements and racial and class prejudice. These names, however, continue to appear in our classrooms, where we teach the methods created by these individuals, raising the question of how instructors should address their legacies. Three examples of famous statisticians and their work - Francis Galton's use of conditional probabilities to demonstrate "hereditary talent," Karl Pearson's attempt to quantify the intelligence of Jewish immigrant students, and Ronald A. Fisher's creation of the analysis of variance to de-emphasize environment in human development - highlight the intimate ties between statistics and eugenics. These examples, along with a discussion of the context of these men, eugenics movements, and the statisticians and scientists who opposed their eugenic programs, can humanize the field for students, teach them about the challenges in accurate and unbiased data collection and analysis, and connect historical mistakes to contemporary ethical issues. Confronting this history in the classroom can both improve the teaching of the statistical methodologies themselves and begin a broader conversation about the role of statistics in the world. Supplementary materials for this article are available online.

Teachers' knowledge of the subject matter is considered an important component of their expertise in teaching mathematics. Yet how teachers' understanding of one content area is related to other content areas has not been investigated in depth. We explored this question by investigating teachers' knowledge of two theoretically related areas: (1) fractions and (2) ratios and proportional relationships. We also investigated the extent to which teachers' educational backgrounds are related to their understanding of these concepts. Based on the results obtained from structural equation modeling and path analysis, we found that teachers' knowledge of these two concepts is highly interdependent, forming a single construct. Furthermore, holding a credential in teaching mathematics, the route teachers took to enter teaching, and their undergraduate majors were associated with their knowledge of these concepts. This study illustrates the importance of attending to the theoretical relationships among different content areas when assessing teachers' subject matter knowledge and provides initial evidence that teachers' subject matter knowledge may be unidimensional for theoretically related domains.

The COVID-19 pandemic altered course delivery in higher education at many universities. This article evaluates the differences between student experiences in the fall 2019 semester (pre-pandemic) and those during the fall 2020 semester (pandemic) within a multidisciplinary, project-based introductory statistics course. Results indicated that there were minimal differences in student experiences of this course based on delivery mode (in person vs. online).