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During the COVID-19 pandemic, people across the globe have been exposed to large amounts of statistical data. Previous studies have shown that individuals' mathematical understanding of health-related information affects their attitudes and behaviours. Here, we investigate the relation between: (1) basic numeracy; (2) COVID-19 health numeracy; and (3) COVID-19 health-related attitudes and behaviours. An online survey measuring these three variables was distributed in Canada, the United States (US) and the United Kingdom (UK) (n = 2032). In line with predictions, basic numeracy was positively related to COVID-19 health numeracy. However, predictions, neither basic numeracy nor COVID-19 health numeracy was related to COVID-19 health related attitudes and behaviours (e.g. follow experts' recommendations on social distancing, wearing masks etc.). Multi-group analysis was used to investigate mean differences and differences in the strength of the correlation across countries. Results indicate there were no between-country differences in the correlations between the main constructs but there were between-country differences in latent means. Overall, results suggest that while basic numeracy is related to one's understanding of data about COVID-19, better numeracy alone is not enough to influence a population's health-related attitudes about disease severity and to increase the likelihood of following public health advice.

Statistics is one of the important branches of mathematics taught in schools, colleges and universities. It is also an important tool in public policy discussions. This paper focuses on the use of statistics in the latter context, rather than its use in adult mathematics education research. I review the key characteristics of the statistical approach to constructing public knowledge, and give a very brief history of key points in its development. I discuss how what I call the "overt crisis of statistics," the apparent disenchantment of large sections of the public with the "expert" statistical methods, outputs and pronouncements, leads to dilemmas both for citizens and for democratic governments. Recently "Big Data" and data analytics seem to many to offer new solutions to problems resulting from the essential lack of certainty surrounding efforts to understand society, and from the need to make quick decisions in a rapidly changing world. These approaches have potential, but also limitations. This leads me to consider a second, "covert" crisis of statistics, resulting from a struggle between proponents of freely available public information and public argument, and those aiming to profit from the appropriation and sequestering of information for private ends. I finish by considering what can be done by ourselves, as citizens, as adult mathematics teachers, and as researchers.

Statistics anxiety is experienced by a large number of psychology students, and previous research has examined a range of potential correlates, including academic performance, mathematical ability and psychological predictors. These varying predictors are often considered separately, although there may be shared variance between them. In the present study a wide range of predictors were measured in a sample of 112 first year undergraduate psychology students. For statistics anxiety, trait anxiety was the clearest predictor, with students who have higher levels of trait anxiety also having higher levels of statistics anxiety. For attitudes towards statistics, students who have better mathematical ability, and greater enjoyment of and confidence in their maths ability, also having more positive attitudes towards statistics. These findings suggest that models of statistics anxiety need to consider a wide range of predictors, which may in turn necessitate the development of a range of different interventions to alleviate statistics anxiety.

Statistics anxiety has often been linked to performance in statistics modules for psychology students, despite this no research to date has examined whether attitudes towards statistics can predict whether or not a student chooses to carry on psychology from pre-tertiary to higher education. In this pilot study 41 second year A-level psychology students completed an online measure of statistics anxiety (Statistics Anxiety Rating Scale, STARS) and answered questions about their current A-levels and whether or not they were applying to study psychology at university. The findings showed that worth of statistics, but no other STARS measures significantly predicted whether or not an individual was planning on studying psychology at university. Findings are discussed primarily in relation to teacher variables that may impact subject choice and statistics anxiety in A-level students.

Statistics anxiety is extremely common in undergraduate psychology students. The Statistics Anxiety Rating Scale (STARS) is at present the most widely used measure to assess statistics anxiety, measuring six distinct scales: test and class anxiety, interpretation anxiety, fear of asking for help, worth of statistics, fear of statistics teachers and computational self-concept. In this paper we first review the existing research that uses the STARS with psychology undergraduates. We then provide an analysis of the factor and reliability analysis of the STARS measure using a sample of undergraduate psychology students (N=315). Factor analysis of the STARS yielded nine factors, rather than the six it is intended to measure, with some items indicating low reliability, as demonstrated by low factor loadings. On the basis of these data, we consider the further development and refinement of measures of statistics anxiety in psychology students. Keywords: STARS, psychology, statistics anxiety.

Statistics pervades everyone's lives, whether it is through media coverage, reading reports, weighing up internal risks or evaluating decisions. Most managers are swamped by endless targets, dashboards and spreadsheets, but few organisations have enough employees with statistical skills to support the requirement for evidence based decision making. The need to equip today's workforce to deal with the increased amount of data is imperative. The shortage of mathematics and statistics teachers is also likely to increase as the Government aims by 2020 to provide all post 16 students with continued mathematical education until the age of 18. At The Open University we have devised a highly successful first level statistics module which is simultaneously studied by students across a range of different disciplines, many of whom encounter statistics at some point in their qualification. This has been achieved by using topics which are of interest to everyone rather than being discipline specific. The module has produced some impressive results particularly when analysing the progress of different cohorts of students, not just from varying disciplines, but also across a broad spectrum of students with differing backgrounds. It is thought that by adapting these techniques it is possible to produce high quality statistics provision to be widely used as professional career development for employees.

Psychology students often feel anxious about learning statistics, which can impact their performance. However, little research has explored statistics confidence, which may be an important way to reduce the negative connotations of associating statistics with anxiety. We aimed to explore whether modifying an existing measure of statistics anxiety (the STARS scale) and reframing the questions so students rated their confidence instead, would be associated with competence, prior knowledge and experience. A total of 104 undergraduate students completed an online questionnaire comprising these measures. The factor structure of the STARS scale was predominantly maintained when wording was changed to measure confidence instead of anxiety. Confidence was related to experience and competence, but not knowledge. Two aspects of confidence (interpretation of statistics and exam confidence) plus initial experiences were significant predictors of competence. Confidence was a mediator of the relationship between experience and competence. These findings suggest statistics confidence can be measured in a similar way to anxiety, and highlight areas that could be addressed to increase competence. Future research is needed to explore the relationship between statistics anxiety and statistics confidence, as well as to determine their individual impact on performance in assessments.

Preparing students to be critical thinkers and effective communicators is essential in today's multinational and technologically sophisticated environment. New electronic technologies provide opportunities for creating learning environments that extend the possibilities of "old" but still essential technologies: books, blackboards, and linear, one-way communication media. Such technologies contribute to engagement and meaningful learning in the higher education sector. Greater understanding in educational psychology and the effectiveness of educational interventions has motivated the development of various student-centred pedagogies (e.g. Problem-Based Learning [PBL]) addressing perceived shortcomings of traditional didactic instruction. PBL as a pedagogy promotes meaningful learning due largely to its power to stimulate critical, reflective and creative thinking. Can teaching staff, then, adopt technology-based approaches to create multi-disciplinary interactive PBL environments that enhance learning and excite students, inspiring them to take ownership of their own education? This paper presents a cross-case analysis of four cases that explore how classroom-based learning activities have been transferred to online formats in universities to improve critical thinking, problem-solving skills, and other learning attributes across a range of disciplines.

Students often struggle with learning about statistics, which encompass a large proportion of a psychology degree. This pilot study explored how first- and final-year students reflected on their experiences of being taught this topic, in order to identify needs that could be addressed in a project to improve their learning. First-year students reported that they initially found their module challenging but that it became easier towards the end.Third-year students recognised the importance of the topic but were not confident in their abilities. Most students reported anxiety about statistics. Although students were positive about practical classes, many felt that they could not easily remember the materials. The findings suggested three areas of focus to improve student learning. Firstly, diverse needs and levels of ability should be catered for. Secondly, students need help to go beyond surface learning and button clicking. Finally, low levels of engagement should be addressed. This work has informed a project to develop an online resource to address the above identified needs to enhance teaching of this important topic.

Research methods and statistical analysis is typically the least liked and most anxiety provoking aspect of a psychology undergraduate degree, in large part due to the mathematical component of the content. In this first cycle of a piece of action research, students' mathematical ability is examined in relation to their performance across different assessments. A maths test, including only components relevant to psychological research and analysis, was designed and subsequently completed by 427 students. Factor analysis revealed three distinct facets: understanding of mathematical procedures; interpretation of findings; and understanding the semantics of mathematics. Only the procedural and interpretative factors were predictive of overall course performance. Higher scores on both factors predicted better performance on multiple choice questions assessment and an unseen exam, whereas only the interpretation factor predicted performance on a critical thinking assignment and a lab report. The findings are considered with a view to developing another cycle of action research that more actively involves students.

Psychology lecturers are well-qualified to carry out action research which would contribute to the theoretical understanding of learning as well as having practical benefits for students. Pedagogical action research demonstrates how knowledge of psychology can be applied to solve practical problems, providing role models of psychological literacy to students, who can also beneficially be involved as participant researchers. Academics are urged to collect evidence to influence policy where higher education is facing new challenges, whether from changing economic conditions, technological developments, globalisation, student diversity, or greater expectations for personalised, engaging, and flexible learning. Five specific areas within the teaching of psychology are identified as offering rich opportunities for action research: study abroad; study skills for transition to university; engaging students with statistics; gamification; and teaching psychology to students from other disciplines. Readers are invited to join the authors in collaborating on future pedagogic action research in these areas.

Students from many different subject areas are required to study statistics as part of their qualification. The Open University developed a statistics module which could simultaneously be studied by students from a variety of different disciplines, by engaging them with topics which are of interest to everyone, namely money, education and health, rather than being based in the student's own discipline. The module attracts students from a wide variety of backgrounds and has one of the highest retention and pass rates of any OU module at level one. In addition, it has succeeded in successfully teaching a highly visual subject, which includes a wide range of online resources, to all students, including widening participation priority groups. It is hoped this can provide a model for other large service teaching courses, together with providing career and professional development for professional bodies.

This paper compares the use of confidence intervals (CIs) and a sensitivity analysis called the number needed to disturb (NNTD), in the analysis of research findings expressed as 'effect' sizes. Using 1,000 simulations of randomised trials with up to 1,000 cases in each, the paper shows that both approaches are very similar in outcomes, and each one is highly predictable from the other. CIs are supposed to be a measure of likelihood or uncertainty in the results, showing a range of possible effect sizes that could have been produced by random sampling variation alone. NNTD is supposed to be a measure of the robustness of the effect size to any variation, including that produced by missing data. Given that they are largely equivalent and interchangeable under the conditions tested here, the paper suggests that both are really measures of robustness. It concludes that NNTD is to be preferred because it requires many fewer assumptions, is more tolerant of missing data, is easier to explain, and directly addresses the key question of whether the underlying effect size is zero or not.

As a component of the ongoing development of the mathematics curriculum in China, we compare the country's high school mathematics textbooks with those of several other countries. We base our analysis on the assumption that textbooks, as primary printed teaching resources, are key tools for interpreting educational policy. In this paper, we compare what content is selected and how that content is presented in series of high school textbooks from China, France, Germany, Japan, Russia, the United Kingdom, and the United States according to four core domains: algebra, geometry, statistics and probability, and calculus. We then discuss the implications of the analysis for the reform of the high school mathematics curriculum in China, particularly as it applies to the development of textbooks within that process of reform. The comparative results provide us with the opportunity to recognise the distinguishing features of the content and presentation of the Chinese mathematics curriculum and lead to some suggestions for future curriculum development.

Some psychology students achieve high grades in all classes except for research methods (RM). Previous research has usually treated low levels of achievement in RM as a unitary phenomenon, without reference to the grades the student is achieving in other subjects. The present internet survey explored preferences for learning RM in 140 psychology students. Students were categorised as: those who achieved higher grades for RM than other subjects in psychology; those whose grades for RM were equal to their grades for other subjects; and those who had lower grades for RM than other subjects. An interesting finding was that whereas wanting to see more humour in RM teaching was significantly associated with lower RM grades, wanting more visual aids in teaching RM was significantly associated with low grades only for RM. Implications of these findings are discussed in relation to explaining low achievement specific to RM. (Contains 4 tables.)

The purpose of this annual report is to provide a summary of measurement in physical education and exercise science-related activities in 2017. A recent trend for an annual increase in manuscript submissions to measurement in physical education and exercise science continued in 2017. Twenty-nine countries were represented (i.e., corresponding author) with the United States of America, Canada, the United Kingdom, Brazil, Spain, and Australia collectively accounting for slightly more than two-thirds of the submissions. Measurement in physical education and exercise science continues to welcome high-quality submissions from around the world in 2018. More than three-quarters of the manuscripts that were submitted to measurement in physical education and exercise science in 2017 were submitted to the exercise science section or the physical activity section or the research methodology and statistics section. Measurement in physical education and exercise science continues to welcome high-quality submissions within each of the seven sections that comprise the journal in 2018. We also gratefully acknowledge the many scholars from around the world who served as a reviewer for measurement in physical education and exercise science in 2017. Twenty-two countries were represented with the United States, Australia, Hong Kong, Spain, the United Kingdom, Canada, and Germany collectively accounting for more than 85% of the total number of reviewers. Measurement in physical education and exercise science continues to welcome high-quality manuscript reviews from around the world in 2018. Volume 21 (i.e., the volume published in 2017) of measurement in physical education and exercise science published a total of 26 manuscripts. More than three-quarters of the published manuscripts were submitted to the research methodology and statistics section or the physical education pedagogy section or the exercise science section or the physical activity section. Twelve countries were represented with the United States of America, the United Kingdom, Canada, and Australia collectively accounting for approximately three-fourths of the publications. Measurement in physical education and exercise science continues to strive for publishing high-quality manuscripts from around the world in 2018.

This article seeks to present some of the key challenges in facilitating autonomous learning and effective engagement in the teaching of statistics to undergraduate medical students involved in short-term research projects. With a view to addressing these challenges, recommendations for good practice are presented in the form of ten tips for teachers of medical statistics. The ten tips are justified by appeal to the more general educational literature on self-directed learning and engagement. Practical suggestions for the implementation of these tips are provided on the basis of the author's own experience of teaching statistics to medical students who have embarked on 14-week clinical research projects within the 4th year of their undergraduate curriculum. (Contains 1 figure and 2 endnotes.)

Within undergraduate psychology courses, students often have significant levels of anxiety and negative attitudes toward the statistical element. This has been attributed to poor interaction with teachers, fears about mathematical abilities, and simply being unaware of that portion of the course or its relevance to psychology. To address this, 196 undergraduate psychology students completed a survey on statistics anxiety and attitudes. Additionally, 27 different students in similar situations took part in focus group to share their experiences of introductory statistics courses. Survey results showed that fewer than half were aware of the statistics portion of their course and that the expectation was a key factor in their experiences. Qualitative feedback from the focus groups revealed much about how the teaching may or may not improve attitudes nor decrease anxiety. Findings support various broad strategies (i.e. increase awareness of statistics in psychology and confidence in success in the course) as opposed to skill-specific (better ways of teaching probability or using games to increase participation, for example) classroom interventions to improve statistics education. (Contains 2 tables and 1 figure.)

In this exploratory study, we investigated the personal epistemologies of statisticians in academia with the aim of offering some insight into what might be an availing epistemology for learning statistics. Findings from in-depth, semi-structured interviews with six academics in the UK currently researching within the field of statistics showed that their statistical personal epistemologies were consistent with constructivist theories of learning. Based on these findings, we proposed an integrated model to represent participants' beliefs about knowledge and knowing in statistics. Furthermore, we found differences between participants' mathematical and statistical personal epistemologies, and we offered an argument for domain-specificity of personal epistemologies. The implications of our findings for research in statistics education and statistical misconceptions are discussed.

There is continuing concern about the paucity of social science graduates who have the quantitative skills required by academia and industry. Not only do students often lack the confidence to explore, and use, statistical techniques, the dominance of qualitative research in many disciplines has also often constrained programme-level integration of more quantitative material. However, whilst the topic of statistical literacy is relatively well researched within the more general educational literature, the evidence-base with respect to the effectiveness of teaching and learning of quantitative research methods in the social science remains somewhat limited. This paper describes the development, integration and evaluation of a series of student-led inquiry-based quantitative workbooks within a sociology/social policy undergraduate degree. It outlines how the workbooks were constructively aligned within a "methods spine" and offers some insight into quantitative teaching and learning generally. The paper also discusses some of the opportunities and challenges of taking both an aligned and IBL approach to the teaching of quantitative methods. In doing so it adds to growing evidence that 'problem-based pedagogies' tend to increase educational gain over and above more didactic approaches to learning and teaching. It highlights three key findings: programme-level approaches to curriculum design can be crucial in improving quantitative skills, particularly where they are tailored to student needs; a general indifference to quantitative methods is likely to be due to a process of disenfranchisement that happens before and during students' engagement with university; and, meaningfully engaging students as partners in the process of designing, integrating and evaluating curricula can help to overcome some of the barriers associated with the learning and teaching of quantitative skills.

Although our health professional students have some experience of simple charts, such as pie and bar, and some intuition of histograms, they do not appear to have much knowledge or understanding about box and whisker plots and their relation to the data they are describing or compared to histograms. The boxplot is a versatile charting tool, useful for presenting data from surveys and any other projects, where a reasonable quantity of data has been collected. An opportunity arose to create a reusable learning object (RLO) to describe, explore, and interpret boxplots, especially in relation to their data and summary statistics. Examples included interprofessional learning, as this was the main remit of the Centre for Excellence in Teaching and Learning, from which funding was obtained. The RLO is aimed at both undergraduate and post-graduate HP students, who would be able to use the resource flexibly, to augment their limited exposure to statistical techniques, and add to their appreciation of IP learning and working. The RLO includes animation and opportunities for students to interact with the resource. Existing, available "real" data, collected as part of research projects concerning (IP) learning, as well as generated data, is used as illustrative material. This paper explores some of the issues raised during the creation of the RLO, and presents limited feedback from users. Issues raised include the working of the project team, delivery platform, copyright and intellectual property rights and software incompatibilities. To date, feedback from colleagues and students has been very positive and has encouraged further improvements. The creation of this RLO has been a longer and more time-consuming experience than anticipated, and has highlighted the importance of a team approach, with constant reviewing. It will be interesting to see how the RLO will be used, and usage will be evaluated in the future.

Following the success of last year's teaching and career development workshop, this year's DART-P sponsored workshop at the Psychology Postgraduate Affairs Group (PsyPAG) Annual Conference held at Lancaster University focused on postgraduate's experiences of teaching research methods. This article provides a review of the invited speakers presentation, Dr. Emma McDonald, the Higher Education Academy (HEA) Psychology Technician of the year.

The issue of poor statistical literacy amongst undergraduates in the United Kingdom is well documented. At university level, where poor statistics skills impact particularly on social science programmes, embedding is often used as a remedy. However, embedding represents a surface approach to the problem. It ignores the barriers to learning that students bring to class, which may not always be addressed solely through embedding, such as, mathematics anxiety. Instead, embedding can only work within a much deeper pedagogic model that places students at its heart, as active participants in learning. This paper examines the development of such a model within a large sociology programme, where there was an implementation of a range of pedagogic strategies to support the development of students' statistical literacy.

Full Fact is an independent, non-partisan fact-checking charity. A particular focus is the analysis of factual claims in political debate in the UK; for example, fact-checking claims and counterclaims made during Prime Minister's questions. Facts do not appear in a vacuum as they are often used as key elements in an effort to make a coherent argument. This paper describes a number of case histories where facts are disputed, drawn from our election work, to give an overview of the contemporary state of statistical literacy among politicians and the media. Common pitfalls in politicians' claims are set out, along with descriptions of our attempts to close the communication gap between different communities.

Statistical literacy involves engagement with the data one encounters. New forms of data and new ways to engage with data--notably via interactive data visualisations--are emerging. Some of the skills required to work effectively with these new visualisation tools are described. We argue that interactive data visualisations will have as profound an effect on statistical literacy as the introduction of statistics packages had on statistics in social science in the 1960s. Current conceptualisations of statistical literacy are too passive, lacking the exploration part in data analysis. Statistical literacy should be conceived of as empowerment to engage effectively with evidence, and educators should seek to move students along a pathway from using interactive data visualisations to building them and interpreting what they see.

Recent concerns about a shortage of capacity for statistical and numerical analysis skills among social science students and researchers have prompted a range of initiatives aiming to improve teaching in this area. However, these projects have rarely re-evaluated the content of what is taught to students and have instead focussed primarily on delivery. The emphasis has generally been on increased use of complex techniques, specialist software and, most importantly in the context of this paper, a continued focus on inferential statistical tests, often at the expense of other types of analysis. We argue that this "business as usual" approach to the content of statistics teaching is problematic for several reasons. First, the assumptions underlying inferential statistical tests are rarely met, meaning that students are being taught analyses that should only be used very rarely. Secondly, all of the most common outputs of inferential statistical tests--p-values, standard errors and confidence intervals--suffer from a similar logical problem that renders them at best useless and at worst misleading. Eliminating inferential statistical tests from statistics teaching (and practice) would avoid the creation of another generation of researchers who either do not understand, or knowingly misuse, these techniques. It would also have the benefit of removing one of the key barriers to students' understanding of statistical analysis. [For a response to this article, "A Response to White and Gorard: against Inferential Statistics: How and Why Current Statistics Teaching Gets It Wrong," see EJ1152509. For the rejoinder, "Still against Inferential Statistics: Rejoinder to Nicholson and Ridgway," see EJ1152510.]

This article reports an analysis of the relationship between women's increased participation in higher education and other recent social changes over the last four decades. To date, women's increased involvement in higher education has been studied as either a force for or a consequence of other sociocultural changes. Drawing on data from key international data sets and with a focus on a range of Organisation for Economic Co-Operation and Development (OECD) countries, this article details an exploratory factor analysis of women's higher education participation and a range of other variables identified as indicators of or mediators for social change. This analysis reveals the existence of four underlying factors showing the structural interrelationship between the variables.

The CASE project (Case-based Approaches to Statistics Education; see www.mas.ncl.ac.uk/~nlf8/innovation) was established to investigate how the use of real-life, discipline-specific case study material in Statistics service courses could improve student engagement, motivation, and confidence. Ultimately, the project aims to promote deep learning of course material, with students from other disciplines being equipped with the skills to undertake independent quantitative analyses (for example, in their final year dissertations). In this article, I describe the case-based materials and associated activities, developed as part of this project, for first year Business undergraduates taking a compulsory course in quantitative methods. I also attempt to evaluate the success of the CASE project through a trial in which a randomly selected subgroup of students was exposed to case-based learning and teaching activities. After adjusting for nuisance factors, I found that students in this subgroup outperformed their peers who were not selected for case-based learning and teaching, in terms of their grades in both routine algorithmic homework exercises and more open-ended projects requiring problem-solving and interpretative skills.

This introductory article to the special issue of "Comparative Education" on measuring the unmeasurable in education considers measurement as reflecting facts and uncertainties. The notion of negative capability is used metaphorically to depict some limits of what is measurable, and portray aspects of the process of education, associated with uncertainty and public scrutiny of complexity. Four overarching questions--what, when, why and how--have guided the reflections of the authors who have contributed to the special issue. "What" are we measuring when we try to measure the unmeasurable in education and what are we not measuring? "When" have attempts been made to measure the unmeasurable in education, what metrics have been adopted in which contexts, and with what outcomes? "Why" have measures been adopted as indicators of the unmeasurable, such as human rights? "How" have particular historically located organisations approached the problem of measuring the apparently unmeasurable in education, with what epistemological, normative and conceptual resources, and consequences? The introductory article looks at measurement as a form of negative capability in some discussions of history of social statistics in education, the current debate over indicators for the Sustainable Development Goals, and how to measure gender equality in education.

This article reviews a flexible model for engaging students in statistical enquiry. Data from a student survey are first used to stimulate interest and introduce statistical concepts, while easing the transition to working with larger "real world" secondary data.

This study investigates students' perceptions of computer-based learning environments, their attitude towards business statistics, and their academic achievement in higher education. Guided by learning environments concepts and attitudinal theory, a theoretical model was proposed with two instruments, one for measuring the learning environment and the other for measuring student attitude. Data were collected from 453 postgraduate business students in a UK university. Factor analyses were carried out to validate the instruments, whilst structural equation modelling was employed to validate the proposed model. The results demonstrate the importance of students' perceptions of subject integration within the learning environment and the relationship between their perceptions of cohesiveness, task orientation, and anxiety. The findings show that attitude towards statistics is significantly related to achievement, explaining almost 40% of variation, whilst perception of the learning environment (indirectly) explains about 29% of the achievement. Implications for teaching business statistics in higher education are discussed.

This article reports the results of research concerned with students' statistical anxiety and confidence to both complete and learn to complete statistical tasks. Data were collected at the beginning and end of a quantitative method statistics module. Students recognised the value of numeracy skills but felt they were not necessarily relevant for graduate employability and preferred to study with words rather than numbers. A significant reduction in anxiety and increase in confidence to complete statistical tasks were found. Students seemed to feel more confident about doing and learning less complex procedures. Results reinforce the need to provide students with additional mathematical and statistical support outside of quantitative method courses as well as that numeric learning materials and study tasks need to be embedded across the curriculum within substantive disciplinary modules. The design of numeric study tasks needs to be carefully considered to ease the transition for students from simple to more complex statistical procedures while simultaneously reinforcing the importance of numeracy skills for examining substantive disciplinary topics and promoting graduate employability.

Graduates with well-developed capabilities in finance are invaluable to our society and in increasing demand. Universities face the challenge of designing finance programmes to develop these capabilities and the essential knowledge that underpins them. Our research responds to this challenge by identifying threshold concepts that are central to the mastery of finance and by exploring their potential for informing curriculum design and pedagogical practices to improve student outcomes. In this paper, we report the results of an online survey of finance academics at multiple institutions in Australia, Canada, New Zealand, South Africa and the United Kingdom. The outcomes of our research are recommendations for threshold concepts in finance endorsed by quantitative evidence, as well as a model of the finance curriculum incorporating finance, modelling and statistics threshold concepts. In addition, we draw conclusions about the application of threshold concept theory supported by both quantitative and qualitative evidence. Our methodology and findings have general relevance to the application of threshold concept theory as a means to investigate and inform curriculum design and delivery in higher education.

Learning to talk about motion in a second language is very difficult because it involves restructuring deeply entrenched patterns from the first language. In this paper we argue that statistical learning can explain why L2 learners are only partially successful in restructuring their second language grammars. We explore to what extent L2 learners make use of two mechanisms of statistical learning, entrenchment and pre-emption to acquire target-like expressions of motion and retreat from overgeneralisation in this domain. Paying attention to the frequency of existing patterns in the input can help learners to adjust the frequency with which they use path and manner verbs in French but is insufficient to acquire the boundary crossing constraint and learn what not to say. We also look at the role of language proficiency and exposure to French in explaining the findings.

This paper summarizes the evaluation of a project that involved undergraduate mathematics students in the development of teaching and learning resources for statistics modules taught in various departments of a university. This evaluation regards students' participation in the project and its impact on their learning of statistics, as characterized in terms of statistical reasoning, statistical thinking, and skills for statistical consultancy. The participation of students is evaluated from the viewpoint of communities of practice. The evaluation resulted in a characterization of the benefits of such a project and suggestions for implementations of future projects, and in addition brought to light new theoretical elements both as regards the learning of statistics and as regards communities of practice. In particular, the analysis highlighted contributions of the students involved to resource development practice in the community of university statistics teachers, as well as contributions to students' learning as a result of participation in this community.

This study utilises an integrated conceptual model of academic performance which captures a series of psychological factors: cognitive style; self-theories such as self-esteem and self-efficacy; achievement goals such as mastery, performance, performance avoidance and work avoidance; study-processing strategies such as deep and surface learning; and effort. We investigate a group of first-year university undergraduates taking a course in business statistics at a British university. The results show a significant causal path of the form: "self-esteem"? "self-efficacy"? "mastery"? "effort"? "performance." We conclude that the strengthening of any of the elements in this path would have beneficial effects on students' academic performance and discuss various approaches to pedagogy, primarily assessment and feedback, to achieve this goal.

Background: The equiprobability bias is a tendency for individuals to think of probabilistic events as "equiprobable" by nature, and to judge outcomes that occur with different probabilities as equally likely. The equiprobability bias has been repeatedly found to be related to formal education in statistics, and it is claimed to be based on a misunderstanding of the concept of randomness. Aims: The aim of the present study was to examine whether experimenting with random generators would decrease the equiprobability bias. Sample: The participants were 108 psychology students whose performance was measured either immediately after taking part in a training session ("n" = 55), or without doing any training exercises ("n" = 53). Method: The training session consisted of four activities. These included generating random sequences of events, and learning about the law of large numbers. Subsequently, the participants were tested on a series of equiprobability problems, and a number of other problems with similar structure and content. Results: The results indicated that the training successfully decreased the equiprobability bias. However, this effect was moderated by participants' cognitive ability (i.e., higher ability participants benefitted from the training more than participants with lower cognitive ability). Finally, the training session had the unexpected side effect of increasing students' susceptibility to the representativeness heuristic. Conclusions: Experimenting with random generators has a positive effect on students' general understanding of probability, but the same time it might increase their susceptibility to certain biases (especially, to the representativeness heuristic). These findings have important implications for using training methods to improve probabilistic reasoning performance. (Contains 6 tables and 2 figures.)

This article illustrates how statistical arguments can be used to influence public policy... for better or for worse. Road safety has improved in a signi?cant way since the 1970s in developed countries. If road casualties and number of killed have decreased, there are many reasons for this, including improvement in roads, building of motorways, better active security in vehicles (crumple zone, seat belts, airbags, improved brake systems etc.), reduced speed limits, anti-- drinking campaigns, and, maybe, an increasing awareness of drivers about the risks of driving. The European Commission (EC) has launched a program for improving road safety over the years 2011-2020 (EC 2010). It takes all these points into account but does not mention speed cameras. (Contains 7 figures.)

This study examined the relationships among statistics achievement and four components of attitudes toward statistics (Cognitive Competence, Affect, Value, and Difficulty) as assessed by the SATS. Meta-analysis results revealed that the size of relationships differed by the geographical region in which the studies were conducted as well as by the component of statistics attitudes being examined. Medium effect sizes were found between statistics achievement and scores on the Affect and Cognitive Competence components for studies conducted in the United States whereas those conducted in other countries yielded small effect sizes. The Value and Difficulty components exhibited small effect sizes for both regions. In every case, the U.S. effect sizes were about double in size in comparison to those from non-U.S. countries. (Contains 2 tables.)

Over the past few decades there has been a large amount of research dedicated to the teaching of statistics. The impact of this research has started to change course content and structure, in both introductory and advanced courses for statisticians and those from other disciplines. In the light of these changes future directions in the teaching and learning of statistics must take into account new innovative pedagogical instructions, educational technologies and the abundance of Web resources that are now available. This article examines different aspects of currently identified challenges in the teaching and learning of statistics and gives an overview of useful strategies and innovations for developing research-based statistics courses in the context of recommendations for reforms, outlining the place of information technology within this framework. The article presents a review of the literature on the topic of statistics education and gives instructors a set of guidelines for generating new and effective teaching material. The summarised recommendations incorporate many innovations employed in a variety of successful statistics classes today. The review is complemented by a collection of statistics related online resources currently available on the Web. (Contains 3 tables.)

With rapid and continuing growth of learning support initiatives in mathematics and statistics found in many parts of the world, and with the likelihood that this trend will continue, there is a need to ensure that robust and coherent measures are in place to evaluate the effectiveness of these initiatives. The nature of learning support brings challenges for measurement and analysis of its effects. After briefly reviewing the purpose, rationale for, and extent of current provision, this article provides a framework for those working in learning support to think about how their efforts can be evaluated. It provides references and specific examples of how workers in this field are collecting, analysing and reporting their findings. The framework is used to structure evaluation in terms of usage of facilities, resources and services provided, and also in terms of improvements in performance of the students and staff who engage with them. Very recent developments have started to address the effects of learning support on the development of deeper approaches to learning, the affective domain and the development of communities of practice of both learners and teachers. This article intends to be a stimulus to those who work in mathematics and statistics support to gather even richer, more valuable, forms of data. It provides a "toolkit" for those interested in evaluation of learning support and closes by referring to an on-line resource being developed to archive the growing body of evidence. (Contains 1 note, 3 tables, and 1 figure.)

Technology is increasingly used to aid the teaching of statistics. Personal Response Systems (PRS) involve equipping students with a handset allowing them to send responses to questions put to them by a lecturer. PRS allows lectures to be more interactive and can help reinforce material. It can also allow the lecturer to monitor students' understanding of course content. PRS is most commonly used in large lectures where interaction from the students is particularly difficult. However, we consider its use in a small group (around 15 students) of MSc in Statistics students. Recommendations based on this experience are discussed, in particular the importance of good question design. We consider possible diagnostics for the appropriateness of questions based on response data. (Contains 1 figure and 3 tables.)

The UK higher education sector is facing a significant reduction in the level of public funding over the next few years. In August 2010 the Cabinet Secretary informed groups of vice-chancellors that they should prepare for cuts of 35% over the four years 2011-2015, the period covered by the next Comprehensive Spending Review. It is inevitable that, faced with this level of diminution, careful attention will need to be paid to the level of expenditure on administrative services. In this review the author looks at expenditure on the processes and activities that underpin the institutional mission and organisation, and not at the total of non-academic expenditure, only part of which should be classified as administrative. It is important to give a health warning about higher education statistics. Institutions can vary in their interpretation of the requirements, and the definitions can alter over time. The way particular services and activities are undertaken will vary and this will affect the way in which the costs are reported. It can be very misleading to take returns made by individual institutions and attempt to construct comparative cost league tables. Nevertheless, when taken as an aggregate these data should give a clear indication of the direction of expenditure. Leslie and Rhoades (1995) list a range of possible reasons why USA's expenditure on administration was growing at a faster rate than expenditure on academic activity. In this article, the author discusses the parallel trend in the UK. (Contains 5 tables.)

Drawing on the traditions of critical race theory, the paper is presented as a chronicle--a narrative--featuring two invented characters with different histories and expertise. Together they explore the strengths and weaknesses of quantitative approaches to race equality in education. In societies that are structured in racial domination, such as the USA and the UK, quantitative approaches often encode particular assumptions about the nature of social processes and the generation of educational inequality that reflect a generally superficial understanding of racism. Statistical methods can obscure the material reality of racism and the more that statisticians manipulate their data, the more it is likely that majoritarian assumptions will be introduced as part of the fabric of the calculations themselves and the conclusions that are drawn. Focusing on the case of recent national data on the secondary education of minoritized children in England, the paper highlights statisticians' ability to define what counts as a "real" inequality without public challenge or scrutiny; reflects on the dangers of statistical "explanations" in the realm of public debate and policy outcomes; and questions quantitative assumptions about the intersectional relationships between different forms of oppression, including gender, class and race. (Contains 19 notes and 2 tables.)

Courses for non-statistics majors (service courses) play an integral role in teaching statistics and pose some unique challenges. In these courses, students are often undermotivated on the one hand while on the other hand the syllabus frequently is overly crowded. In this manuscript we target the issues arising from the latter problem by making use of technology. The use of screen capture, a fast and easy way of recording lectures, is discussed through an example of an introductory statistics course for first year biology students at Lancaster University. Student feedback on the use of these recordings is discussed. (Contains 1 table and 5 figures.)

In this paper we report the results from a major UK government-funded project, started in 2005, to review statistics and handling data within the school mathematics curriculum for students up to age 16. As a result of a survey of teachers we developed new teaching materials that explicitly use a problem-solving approach for the teaching and learning of statistics through real contexts. We also report the development of a corresponding assessment regime and how this works in the classroom. Controversially, in September 2006 the UK government announced that coursework was to be dropped for mathematics exams sat by 16-year-olds. A consequence of this decision is that areas of the curriculum previously only assessed via this method will no longer be assessed. These include the stages of design, collection of data, analysis and reporting which are essential components of a statistical investigation. The mechanism outlined here could provide some new and useful ways of coupling new teaching methods with learning and doing assessment--in short, they could go some way towards making up for the educational loss of "not" doing coursework. Also, our findings have implications for teaching, learning and assessing statistics for students of the subject at all ages. (Contains 4 tables and 15 figures.)

Evidence-based policy requires sophisticated modelling and reasoning about complex social data. The current UK statistics curricula do not equip tomorrow's citizens to understand such reasoning. We advocate radical curriculum reform, designed to require students to reason from complex data.