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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 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.

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.

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.

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.

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.

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.

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).

There is a need for public health undergraduates to acquire skills in data collection, statistical programming, and infectious diseases modeling. Public health officials and accreditation bodies underline the importance of a cumulative, "real-world" experience as part of a student's education. The Watermelon Meow Meow (WMM) outbreak is a cumulative experience that teaches upper-level undergraduate/graduate students about infectious disease dynamics by asking students to: participate in a fictitious outbreak; collect and analyze outbreak data. Innovative to our approach is the use of DataCamp as a technology to support learning statistical programming and framing WMM under principles of Universal Design Learning (UDL). We evaluated 27/32 student responses using a mixed-methods approach. We found WMM: augmented traditional lecture-style instruction and increased student awareness of heterogeneous risks associated with infectious diseases. We identified three student typologies: students who learn best from: (i) integrating traditional lecture plus WMM; (ii) participating in WMM data collection but not coding; and (iii) from lecture and classroom-based learning from peers. WMM is an example of a more general approach - which we call Slate, Operate, Translate - that instructors can follow to combine technology and a hands-on experiment to satisfy both UDL principles and increasing demands of public health education in a mathematics/statistics class.

Teaching statistics to undergraduate business students is an enduring challenge, often due to student apprehension and low understanding of relevance. The Data to Decision Project is an approach designed to address this challenge. At the onset of an introductory statistics course, fifty-two students received instruction on the Define, Collect, Organize, Visualize and Analyze (DCOVA) framework to integrate data with business-related decision-making. Concurrent with this instruction, students selected and completed individual projects, using the DCOVA framework to explore their individual decisions. Quantitative and qualitative methods indicated that this approach positively impacted the students' ability to apply statistics, as well as their attitudes regarding their statistics abilities.

Statistics has been a content domain in the mathematics curriculum for decades. However, statistics is a distinct discipline from mathematics and there are important differences in how one should teach the two disciplines. In this article, the authors consider how these differences can inform an adaptation to the 5 Practices for Orchestrating Productive Mathematics Discussions framework to engage students and teachers in meaningful statistical investigations and the ensuing class discussions. In this article, the authors aim to show how the 5 Practices for orchestrating mathematical discussions can be translated to teaching statistical investigations.

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.

Previous work has demonstrated similarities and differences between aerial and terrestrial image viewing. Aerial scene categorization, a pivotal visual processing task for gathering geoinformation, heavily depends on rotation-invariant information. Aerial image-centered research has revealed effects of low-level features on performance of various aerial image interpretation tasks. However, there are fewer studies of viewing behavior for aerial scene categorization and of higher-level factors that might influence that categorization. In this paper, experienced subjects' eye movements were recorded while they were asked to categorize aerial scenes. A typical viewing center bias was observed. Eye movement patterns varied among categories. We explored the relationship of nine image statistics to observers' eye movements. Results showed that if the images were less homogeneous, and/or if they contained fewer or no salient diagnostic objects, viewing behavior became more exploratory. Higher- and object-level image statistics were predictive at both the image and scene category levels. Scanpaths were generally organized and small differences in scanpath randomness could be roughly captured by critical object saliency. Participants tended to fixate on critical objects. Image statistics included in this study showed rotational invariance. The results supported our hypothesis that the availability of diagnostic objects strongly influences eye movements in this task. In addition, this study provides supporting evidence for Loschky et al.'s (Journal of Vision, 15(6), 11, 2015) speculation that aerial scenes are categorized on the basis of image parts and individual objects. The findings were discussed in relation to theories of scene perception and their implications for automation development.

The introductory statistics course has gotten better over the years, but there are many content areas in STAT 101 that should be reconsidered.

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.

This research examines the role of Supplemental Instruction in assisting students at a small Hispanic-Serving Institution (HSI) in the Southwest United States to improve their final grades in a required statistics course for criminal justice majors. Data collected over three semesters were analyzed using multivariate regression to test if participation in Supplemental Instruction moderates the relationship between race, ethnicity, and final grades earned, with Latinx students and students from other historically underrepresented racial and ethnic groups especially benefitting from SI participation. We find positive interactions for race, ethnicity, and final grades; however, the interaction term is only statistically significant for students from other, non-Latinx underrepresented racial and ethnic groups. These students attended SI most frequently, derived the most benefits from their participation, and were also notably the most underrepresented in the institution and the course. We go on to discuss evidence-based recommendations that SI and other collaborative learning programs may consider if their goal is to move toward servingness by improving equity in performance and academic success outcomes across students from diverse backgrounds.

Statistical significance and averages are two pieces of statistical information that are often presented as evidence in support of researchers' conclusions and teaching recommendations. In this article, I consider interpretation of this information as research evidence for ELT. In simple terms that will be accessible even to readers without any knowledge of statistics, I explain the basic nature of this information with the aim of elucidating what it can and cannot tell us about ELT findings and the implications for our teaching. I discuss what additional information crucially must be considered for adequate interpretation, and specifically how interpretation depends on this information. I urge producers of ELT research to present and interpret this important information and consumers of ELT research to consider it in assessing the implications of ELT findings for their teaching.

The COVID-19 pandemic has posed one of the most challenging situations for the academicians as well as the students all around the world. Students being the biggest stake holders of the education process, their challenges during this pandemic become even more pivotal. These challenges vary in intensity and type depending on multiple items. In this paper, we analyse and document the challenges particular to the courses of mathematics and statistics in higher education. A survey was carried out for students, who have taken mathematics/statistics courses at universities mainly in UAE, to analyse various items affecting the learning process during the COVID-19 pandemic. The results of the survey showed that a significant portion of students are satisfied with distance education.

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.

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.

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.

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.

Mixed methods approaches are increasing advocated for researching complex problems in the social sciences, but they are not widely used by postgraduate students of public management. This article describes a study where qualitative and quantitative methods lecturers worked collaboratively to design and teach both methodology courses in an integrated way to encourage public management master's students to see the two methods as complementary, and thus possibly be more open to consider using the mixed methods approach in their research. A multi-method research design was used in this study. Students' prior studies of qualitative and quantitative research methodology were not found to predict their summative course marks significantly on qualitative and quantitative components, respectively, but initial cognitive competence in the study of statistics correlates with summative performance in the quantitative component. Qualitative and quantitative summative scores correlate strongly, with those students with higher qualitative and higher quantitative summative scores tending to score higher on a task where they reflect on the value of both approaches to their own proposed research. However, students with lower scores, who comprise the majority of the sample, are not able to demonstrate appreciation of the possibilities or status of applying both methodologies to their own research. They tend to misunderstand foundational concepts when applied to their research design and/or show limited ability to apply their understanding to design their own work accurately or in a workable way. This study suggests that, where postgraduate students have prior limited exposure to research methods, improving the quality of student research and their engagement with mixed methods may require more mastery of both methods and methodologies than the scope and pacing of taught master's programmes usually allow.

Social desirability bias (SDB) has been a major concern in educational and psychological assessments when measuring latent variables because it has the potential to introduce measurement error and bias in assessments. Person-fit indices can detect bias in the form of misfitted response vectors. The objective of this study was to compare the performance of 14 person-fit indices to identify SDB in simulated responses. The area under the curve (AUC) of receiver operating characteristic (ROC) curve analysis was computed to evaluate the predictive power of these statistics. The findings showed that the agreement statistic (A) outperformed all other person-fit indices, while the disagreement statistic (D), dependability statistic (E), and the number of Guttman errors (G) also demonstrated high AUCs to detect SDB. Recommendations for practitioners to use these fit indices are provided.

The purpose of this meta-analytic review is to investigate the relation between statistical learning (SL) and language-related outcomes, and between SL and reading-related outcomes. A comprehensive search of peer-reviewed published research resulted in 42 articles with 53 independent samples and 201 reported effect sizes (Pearson's r). Results of our robust variance estimation correlated effects model revealed a significant, moderate relation between SL and language-related outcomes, r = 0.236, p < 0.001, and a significant, moderate relation between SL and reading-related outcomes, r = 0.239, p < 0.001. Moreover, age, the writing system of the language, and SL paradigm moderate the strength of the association between SL and reading. Age is the only significant moderator on the strength of the association between SL and language. The findings from this meta-analysis shed light on the contribution of multiple factors that impact how SL relates to language and reading outcomes, with important implications for developing effective instructional practices that emphasize statistical regularities of oral and written materials in the classroom. Theoretical implications of these findings for language and reading development are discussed.

Learning to interpret data in context is an important educational outcome. To assess students' attainment of this outcome, it is necessary to examine the interplay between their contextual and statistical reasoning. We describe a research method designed to do so. The method draws upon Toulmin's (1958, 2003) model of argumentation for the first stage of qualitative data analysis and the Structure of the Observed Learning Outcome (SOLO) (Biggs & Collis, 1991) model for the second stage. Toulmin analyses help identify the justifications and expressions of uncertainty students provide in their interpretive arguments. Subsequent analyses based on the multi-modal conceptualization of SOLO help characterize the quality of student arguments relative to one another. Existing literature and an empirical example are drawn upon to explain how the Toulmin and SOLO models can be used in tandem to analyze students' interpretations of contextualized data. We also explain how pairing Toulmin and SOLO can address theoretical and practical limitations that arise when using just one of the two models on its own.

This study aims to investigate the advantages of implementing multimedia resources in the teaching and learning environment of mathematics and statistics. It examines the use of tablet PCs to create video learning resources. Such practices allow lecturers to provide additional learning support to students via the learning platform Moodle. This paper discusses the experiences of three lecturers in developing a technology-based, interactive teaching method to support student learning. The results found that "solved examples" in the video resources are useful in demonstrating topics about statistics. Furthermore, the paper encourages lecturers to learn from their experiences and develop learning resources to enable students to better engage in the learning process.

Business Statistics is a required course for undergraduate business majors and presents significant challenges for students with weak quantitative and critical thinking skills. This paper shows that changing the pre-requisite for the Business Statistics course from Business Calculus to Probability and Statistics makes a significant positive impact, despite the increase in course content, on student performance for business students at a comprehensive regional university in the southeast. It is recommended business schools that experience difficulties with students successfully completing business statistics to carefully consider curriculum changes, particularly the chosen pre-requisite courses.

This study investigates whether statistical learning ability, conceptualized as a cognitive ability to learn regularities implicitly, is a good predictor for L2 learners' online language processing performance. Native-English-speaking adults, as a control group, and native-Korean-speaking adult L2 learners of English participated. They completed: (1) an artificial grammar learning task containing nonadjacent dependencies in sequences of non-words, to test statistical learning ability; and (2) a self-paced English reading task containing relative clauses (RC) in which the "filler" and the "gap" formed a long-distance dependency, to test language processing. Both tasks' stimuli were presented element-by-element to mimic the incremental nature of online language processing. The results for the L1 group show that higher accuracy scores on the artificial grammar learning task did not predict higher sentence comprehension scores. The results for the L2 group, however, show a marginally significant correlation between accuracy scores on the artificial grammar learning task and sentence comprehension scores. For both groups, the reading time difference between grammatical and ungrammatical items in the artificial grammar learning task did predict the speed of reading times for items with RCs with a long-distance dependency in the sentence processing task: Larger differences in RTs in the artificial grammar task correlated with slower reading at the critical region of English RCs. These findings suggest a similar mechanism for online first and second language processing of core syntactic phenomena and for statistical learning ability that involves implicitly tracking distributional relations across elements.

Adults with learning disabilities (LD) face educational and employment challenges and may also have other disabilities and health conditions. Little is known about these adults' numeracy skills and how they use numeracy at work or home. The article's objective was to investigate numeracy skills and skill use for U.S. adults with LD. The author conducted descriptive and regression analyses of the data from the 2012/2014/2017 U.S. Program for the International Assessment of Adult Competencies (PIAAC). Findings are presented on assessed numeracy skills and skill use, relationships of use and skills, and skill use among seven groups of adults with LD. Compared with the general population, adults with LD have lower mean numeracy scores. Skill use at home adds to the variance explained in numeracy skills, which suggests that using numeracy skills matters in gaining skills. Knowing the relationships of assessed numeracy skills with skill use helps educators implement strategies to support adult program completion. Implications of findings are discussed for adult educators and policymakers.

In 1908, Felix Klein suggested that to mend the discontinuity that prospective secondary teachers face, university instruction must account for teachers' needs. More than a century later, problems of discontinuity remain. Our project addresses the dilemma of discontinuity in university mathematics courses through simulating core teaching practices in mathematically intensive ways. In other words, we interpret teachers' needs to include integrating content and pedagogy. We argue that doing so has the potential to impact teachers' competence. To make this argument, we report findings from the Mathematics of Doing, Understanding, Learning, and Educating for Secondary Schools (MODULE(S2)) project. The results are based on data from 324 prospective secondary mathematics teachers (PSMTs) enrolled in courses using curricular materials developed by the project in four content areas (algebra, geometry, modeling, and statistics). We operationalized competence in terms of PSMTs' content knowledge for teaching and their motivation for enacting core teaching practices. We examined pre- and post-term data addressing these constructs. We found mean increases in PSMTs' outcomes in content knowledge for teaching and aspects of motivation.

As data are 'numbers with context' (Cobb & Moore, 1997), contextual knowledge plays a prominent role in dealing with statistics. While insights about a specific context can further the depth of interpreting and evaluating outcomes of data analysis, research shows how it can also hinder relying on data especially if results differ from expectations. In this article, the aim is to investigate how young students informally deal with empirical evidence, which differs from their initial expectations in a specific context. We present a case study with three pairs of students at the age of 9 to 10 who compare groups in survey datasets. The interpretative analysis shows how conjectures of varying degrees of confidence shape the students' statistical expectations and can play different roles in interpreting results from data analysis.

We describe an innovative, semester-long course in biology and communication skills for master's degree students in biostatistics. The primary goal of the course is to make the connection between biological science and statistics more explicit. The secondary goals are to teach oral and written communication skills in an appropriate context for applied biostatisticians, and to teach a structured approach to thinking that enables students to become lifelong learners in biology, study design, and the application of statistics to biomedical research. Critical evaluation of medical literature is the method used to teach biology and communication. Exercises are constructivist in nature, designed to be hands-on and encourage reflection through writing and oral communication. A single disease area (cancer) provides a motivating example to: (1) introduce students to the most commonly used study designs in medical and public health research, (2) illustrate how study design is used to address questions about human biology and disease, (3) teach basic biological concepts necessary for a successful career in biostatistics, and (4) train students to read and critically evaluate publications in peer-reviewed journals. We describe the design and features of the course, the intended audience, and provide detailed examples for instructors interested in designing similar courses.

Pedagogical methods for graduate-level statistics courses have rarely focused on the pursuit of conditional knowledge or the ability to choose which concepts/procedures are relevant given a specific research situation. However, utilization of an innovative approach called decision-based learning (DBL) not only provides students with the conceptual, declarative, and procedural knowledge of traditional statistics courses, it also demystifies the process of gaining conditional knowledge; thus decreasing "statistics anxiety." This study examined the impact of a DBL course on students' ability to select appropriate statistical methods based on the wording of story problems, and specifically looked at pre-post differences. Participants were graduate students enrolled in an introductory statistics course who completed a combination of a pre, and post, and follow-up interviews. Interviews were coded and scored based on students' ability to correctly identify statistical methods, run and interpret statistical output. Results indicated that students' conditional knowledge increased significantly from pre- to post- to follow-up (effect sizes of 0.63 to 0.64). This compares favorably with the range of effect size increase from published studies of other innovative approaches (0.21 to 0.52). Results also showed nominal conditional knowledge decay, suggesting that DBL can be an effective and efficient means of teaching introductory graduate-level statistics. Implications for other disciplines are noted.