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There is a rich literature on students' and teachers' intuitions and misconceptions about probability. However, less attention has been paid to the development of pre-service teachers' probabilistic thinking in teacher education. Based on this, the second author developed a lesson sequence for teaching probability. In particular, it demonstrates how a game context can be used to explore the relationship between experimental and theoretical probabilities in a collaborative learning setting. The lesson sequence integrates concepts and processes related to probability and is grounded in socio-cultural theory. We trialed the sequence with secondary pre-service teachers. This paper focuses on their understanding of the probability concepts embedded in the sequence. Video and audio data indicates that while teachers used a range of strategies and data displays to explain the ideas integrated in the lessons, some reverted to equiprobability bias. The findings also reveal that pre-service teachers can modify their thinking when engaged in rich teaching and learning tasks.

With online learning becoming a more viable option for teachers to develop their expertise, our report shares one such effort focused on improving the teaching of statistics. We share design principles and learning opportunities in an online course developed specifically to serve as a widescale online professional development opportunity for educators, thus deemed as a massive open online course for educators (MOOC-Ed). In this report we focus on a subset of 412 participants who identified themselves as classroom teachers. We use multiple data sources, quantitative and qualitative, to characterize changes in teachers' beliefs and perspectives about statistics and identify triggers in the course that appear to influence teachers' sense making about issues related to teaching statistics. Implications about specific course experiences that served as triggers for critical reflection and change are discussed.

Purpose: The purpose of this manuscript is to provide a summary of Measurement in Physical Education and Exercise Science (MPEES)-related activities in 2021. Manuscripts submitted: In 2021 original submissions (i.e., not counting revised manuscripts) increased by [approximately]20% as compared to 2020. Fifty-eight countries were represented across the 464 original manuscripts submitted to MPEES in 2021. MPEES continues to welcome high-quality submissions from around the world in 2022. Manuscripts submitted by section: The seven sections of MPEES are: (1) exercise science, (2) physical activity, (3) physical education pedagogy, (4) psychology, (5) research methodology and statistics, (6) sport management and administration, and (7) tutorial and teacher's toolbox. More than three-fourths of the manuscripts submitted to MPEES in 2021 were submitted to one of three sections: exercise science or physical activity or research methodology and statistics. MPEES continues to welcome high-quality submissions within each of the seven sections that comprise the journal in 2022. Review process: Each of the original manuscripts submitted to MPEES in 2021 had received an initial decision by April 4, 2022 (i.e., 464 of the 464 manuscripts received). When an immediate decision (e.g., desk-rejection) was rendered by the editor-in-chief it always (i.e., for 369 of 369 manuscripts) occurred within 10 days of receiving the manuscript. When a manuscript was assigned to a section editor by the editor-in-chief it typically (i.e., for 91 of 95 manuscripts) received an initial decision within 90 days of receiving the manuscript. Twenty-four countries were represented across reviewers for the original manuscripts sent out for external review by MPEES in 2021. We gratefully acknowledge, and list in the Appendix, the many scholars (N = 151) from around the world who served as a reviewer for MPEES in 2021. Manuscripts published: Volume 25 (i.e., the volume published in 2021) of MPEES published a total of 37 manuscripts. More than two-thirds of the published manuscripts were submitted to one of two sections: exercise science or research methodology and statistics. MPEES continues to strive for publishing high-quality manuscripts within each of the seven sections that comprise the journal in 2022. Fourteen countries were represented across the manuscripts published in Volume 25 of MPEES. MPEES continues to strive for publishing high-quality manuscripts written by one or more authors from around the world in 2022. Impact factor: The 2020 impact factor for MPEES was 2.30 representing an increase of [approximately]31% compared to 2019 when the journal's impact factor was 1.75. The value of the 2020 impact factor placed MPEES in the second quartile (i.e., ranked #131 out of 265 journals) within the Education & Educational Research category of Clarivate Analytics. The 2021 impact factor for MPEES is expected to be released in [approximately]June 2022.

This paper focuses on the use of home languages as a resource for Pasifika students who are learning about statistical methods. It is acknowledged that there are connections between language use and mathematics in mathematics learning and teaching, and the potential challenges this issue can pose have been investigated by researchers. Yet how the challenges of the use of home language versus teaching language might be overcome in statistics classrooms, where language is even more important as a medium of instruction, has received very little scrutiny. This article reports on research carried out in three New Zealand largely Pasifika dominated Year-12 classes. Data was collected from audio recordings of student group discussions and teacher reflections while students were carrying out an investigation of existing datasets. Findings from the teacher reflection aspect of the study indicate that teachers can struggle with how to use home language and real-life contexts to maximise learning in their classroom. Some strategies to incorporate students home language in their learning worked better than others. However, more in-depth research is needed to explore language issues and the barriers they might present in statistics education.

Statistical investigations, a thread within the statistics strand of the mathematics and statistics learning area (Ministry of Education, 2007), are underpinned by the statistical enquiry cycle. As teachers introduce their students to the statistical enquiry cycle, they are supporting their students to become data detectives, posing and answering investigative questions using data. The statistical enquiry cycle in New Zealand schools is based on the PPDAC model. This article explores the PPDAC model in more detail and emphasises key elements for teaching and learning based on local research.

The first two decades of the 21st century has heralded an unprecedented data revolution increasingly impacting our daily lives. Statistics education must continually update itself to prepare students for this new data-driven world. In this reflection on our research during this time, we discuss how fostering learning from data brought many challenges. We uncovered many gaps in the curriculum and consequently student understanding of the rich network of interconnecting ideas that underpin statistical thinking and reasoning. Teaching statistics in today's world requires focusing on the big ideas that will endure, particularly as we become immersed in an era of data science and artificial intelligence.

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.

The project team for the National Monitoring Study of Student Achievement (NMSSA) has recently begun writing reports focussed on how insights generated by the study can be used to promote learning and teaching. The reports are written primarily for teachers. This short article introduces the reports with a special emphasis on the mathematics and statistics report that was released in February this year.

This paper examines the pedagogical and organisational changes three lead teachers made to their statistics teaching and learning programs. The lead teachers posed the research question: What would the effect of contextually integrating statistical investigations and literacies into other curriculum areas be on student achievement? By finding the significance of statistics nested within mathematics and other curriculum learning areas, the teachers increased their own value of statistical content and contexts and this impacted positively on the statistical achievement outcomes of their students. (Contains 6 tables and 2 figures.)

This paper describes a qualitative survey of professional statisticians carried out in New Zealand in 2014. The aim of the study was to find out if the issues this group faced were consistent with those identified in the literature. The issues identified were integrity, legitimacy, isolation, workforce shortage, communication, and marginalisation. They represent points of frustration for statisticians that may impact on the future of the profession as it responds to increasing demands and higher expectations. We found that these issues resonated for many of the statisticians included in our study and we have discussed a number of strategies to address them. They include raising our profile, attracting a broader range of people to the profession, increasing our communication skills, raising the statistical literacy of the people we work with, and a commitment to making it easy to engage with our colleagues.

This paper focuses on the curriculum links between statistics and science that teachers need to understand and apply in order to be effective teachers of the two fields of study. Meaningful statistics does not exist without context and science is the context for this paper. Although curriculum documents differ from country to country, this paper uses extracts from three countries: Australia, New Zealand and the USA. The statistical ideas from the "Australian Curriculum: Mathematics," the "New Zealand Mathematics and Statistics" Curriculum and the US "Common Core State Standards for Mathematics" are linked to the relevant parts of the "Australian Curriculum: Science," the New Zealand "Science" Curriculum and the US "Next Generation Science Standards for States, by States." Teachers of mathematics need to be aware of the potential of science to provide meaningful contexts within which to set statistical investigations. Similarly, teachers of science, who are developing methods for implementing investigations and experiments in their classrooms, need to be aware of the close ties to statistical tools for decision-making.

In this paper, we report on the results of a series of e-mail interviews with statistics educators around the world, focusing on their views of the nature of teaching statistics as a "service" subject. What do they think are the important aspects of statistics to focus on in such servicing teaching? What do they think are the characteristics of good teachers? And how do they go about developing themselves as statistics teachers? We analyse their responses to these and other questions using a phenomenographic approach to identify an outcome space for their conceptions of teaching service statistics. We examine the centralities and tensions that emerged from their responses and discuss the implications--insights on agency and reflective practice. The study contributes to a research framework for understanding the nature of pedagogical awareness in contexts beyond the setting for this study and aims to stimulate discussion about teaching service courses.

Statistical literacy is complex and multifaceted. In every country, education and numeracy are a function of a multitude of factors including culture, history, and societal norms. Nevertheless, since the launch of the International Statistical Poster Competition (ISLP) in 1994, a number of patterns have emerged to suggest there are some common or universal success factors in running statistical literacy competitions involving schools, universities, statistical offices, and many other institutions. This paper outlines some of those factors, such as institutional cooperation, celebrating participation and success, improvement of statistical literacy in the local schools, support for teachers, the involvement of national statistics institutes, and use of technology. These factors have been identified from our own experience running the competition and from articles submitted to the ISLP newsletters. Statistical literacy is a complex phenomenon, and so this is neither an exhaustive list of key factors nor a formula for success, but rather an overview of recurring themes across countries participating in the competition around the world.

Statistical information pervades everyday life in the twenty-first century. Research shows, however, that the skills needed to be able to understand and critically evaluate statistical information must be specifically taught. In 2013, an externally assessed National Certificate in Educational Achievement standard in statistical literacy was introduced for the first time in New Zealand. A small exploratory study investigated a possible teaching approach designed to enable Year- 13 students (aged 17-18) to critically evaluate media reports. Findings suggest that the learning trajectory required several key components including media reports as both a motivational and conceptual development tool. In addition, computer visualizations and procedural scaffolds appeared valuable tools for facilitating conceptual understanding of the margin of error.

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.

A number of trends are converging to drive the need for more informed teacher data use. These include advocacy for formative assessment and the need for teachers to account for student learning. In this context, assessment literacy and data literacy have emerged as a focus in research and professional development. Problematically, research signals that developing assessment/data literacy is challenging with evidence that teachers may not have mastered relevant aspects of mathematics and statistics. This paper reports lecturer, student teacher and school leader views of the role and requirements of data literacy using data from a larger study into how to foster student teacher mathematical thinking for the breadth of teacher professional work. Data were generated via interviews, surveys and document analysis. Findings suggest a concern and opportunity to develop assessment/data literacy as this calls on mathematical and statistical understanding.

There exists considerable and rich literature on students' misconceptions about probability; less attention has been paid to the development of students' probabilistic thinking in the classroom. Grounded in an analysis of the literature, this article offers a lesson sequence for developing students' probabilistic understanding. In particular, a context familiar to teachers--exploring compound events that occur in a game of chance--is presented, and it is demonstrated how the context can be used to explore the relationship between experimental and theoretical probabilities in a classroom setting. The approach integrates both the content and the language of probability and is grounded in socio-cultural theory.

Because new learning technologies are enabling students to build and explore probability models, we believe that there is a need to determine the big enduring ideas that underpin probabilistic thinking and modeling. By uncovering the elements of the thinking modes of expert users of probability models we aim to provide a base for the setting of new and more relevant goals for probability education in the 21st century. We interviewed seven practitioners, whose professional lives are centered on probability modeling over a diverse range of fields including the development of probability theory. A thematic analysis approach produced four frameworks: (1) probability modeling approaches; (2) probabilistic thinking approaches to a problem; (3) a probability modeling cycle; and (4) core building blocks for probabilistic thinking and modeling. The main finding was that seeing structure and applying structure were important aspects of probability modeling. The implications of our findings for probability education are discussed.

Informed, critical business journalism is vital to a well-functioning society. But students are typically reluctant to study business journalism, often finding the topic intimidating. This article outlines how the author has taught a business journalism course in New Zealand and the United States. The course uses a variety of methods to help the students learn and remain engaged with the material. The course has been successful, with students--who often have no business backgrounds--subsequently becoming business journalists. The article reports on student and industry responses to the course and reflects on what could be done to enhance it further.

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.

For many years, students have been taught to visualise data by drawing graphs. Recently, there has been a growing trend to teach statistics, particularly statistical concepts, using interactive and dynamic visualisation tools. Free down-loadable teaching and simulation software designed specifically for schools, and more general data visualisation tools are increasingly being used in New Zealand classrooms. This paper discusses four examples: the use of GenStat for Teaching and Learning Schools and Undergraduate (GTL); Auckland University's iNZight and VIT (Visual Inference Tools) for teaching bootstrapping and randomisation; the CAST e-books, and the use of data visualisation tools to assist learning concepts in official statistics. All these tools are publically available and several are already being used internationally.

Many adults who need an understanding of statistical concepts have limited mathematical skills. They need a teaching approach that includes as little mathematical context as possible. Iterative participatory qualitative research (action research) was used to develop a statistical literacy course for adult learners informed by teaching in traditional first year university courses, workplace based training, teacher workshops and Masters of Public Policy courses. The latter learners in particular regularly come across confidence intervals and statistical significance in their everyday reading. The goal is to give them a conceptual rather than theoretical understanding of inferential concepts by developing inferential statistics logic through the introduction of exact probabilities in simple non-parametric tests (two-tailed coin tossing) and then contingency tables and parametric situations. The final course developed for the New Zealand Certificate of Official Statistics uses "hands-on" examples to reinforce concepts before proceeding to computer simulations. It emphasizes evaluation of the strength of statistical significance and its relationship to the possible cost of making an incorrect decision. Case studies that have influenced government policy reinforce inferential concepts and demonstrate the importance of statistics in complex real problems.

Over the past decade, many researchers have discussed the effectiveness of clickers and their potential to change the way we teach and interact with students. Although most of the literature revolves around elementary usage of clickers, the deeper questions of how to integrate this technology into teaching are largely unanswered. In this paper, we present an implementation of a teaching model in a third year undergraduate Bayesian statistics class. The model is based on Schoenfeld's interactive teaching routine and it is enhanced by Draper and Brown's contingent teaching and Beatty et al.'s Question Driven Instruction (QDI) and the use of clickers. It illustrates a teaching paradigm which is flexible, contingent to students' needs, makes use of the most up to date information from students' feedback via clickers and benefits from the teacher's decision making at appropriate moments. We will discuss the pedagogical implications of this model in teaching.

We discuss a major change in the way we teach our first-year statistics course. We have redesigned this course with emphasis on teaching critical thinking. We recognized that most of the students take the course for general knowledge and support of other majors, and very few are planning to major in statistics. We identified the essential aspects of a first-year statistics course, given this student mix, focusing on a simple question, "Given this is the last chance you have to teach statistics, what are the essential skills students need?" We have moved from thinking about statistics skills needed for a statistician to skills needed to participate in today's society. We have changed the way we deliver the course with less emphasis on lectures and more on alternative resources including on-line tutorials, Excel, computer-based skills testing, web-based learning materials and smaller group activities such as study groups and example classes. Feedback from students shows that they are very receptive and enthusiastic. (Contains 2 tables.)

This article is devoted to practical aspects of teaching and learning of probability at university. It presents the difficulties and attitudes of first-year university science and engineering students towards using paradoxes and counterexamples as a pedagogical strategy in teaching and learning of probability. It also presents a student's point of view on the effectiveness of this pedagogical strategy. (Contains 4 tables and 2 figures.)

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.)

Computer simulations and animations for developing statistical concepts are often not understood by beginners. Hands-on physical simulations that morph into computer simulations are teaching approaches that can build students' concepts. In this paper we review the literature on visual and verbal cognitive processing and on the efficacy of animations in promoting learning. We describe an instructional sequence, from hands-on to animations, developed for 14 year-old students. The instruction focused on developing students' understanding of sampling variability and using samples to make inferences about populations. The learning trajectory from hands-on to animations is analyzed from the perspective of multimedia learning theories while the learning outcomes of about 100 students are explored, including images and reasoning processes used when comparing two box plots. The findings suggest that carefully designed learning trajectories can stimulate students to gain access to inferential concepts and reasoning processes. The role of verbal, visual, and sensory cues in developing students' reasoning is discussed and important questions for further research on these elements are identified. (Contains 12 figures and 1 table.)

Context is identified as an important factor when considering the learning of informal statistical inferential reasoning, but research in this area is very limited. This small exploratory study in one grade 10 (14 year olds) classroom seeks to learn more about the role context plays in learners' inferential reasoning, where both teacher and students are positioned as learners. Two frameworks for context are used to analyze the classroom dialogue: The data-context used in statistical enquiry and in the formation of statistical concepts and the learning-experience-contexts such as prior statistical knowledge, which can affect the learning process. The analysis tracks the learning of informal inferential reasoning before, during, and after the introduction of sampling variability concepts. Data-context was found to assist learners in finding meaning from observed patterns, but could divert their attention during the construction of concepts and when attempting to apply newly-learned theory. Learning-experience-contexts played a significant role in mediating learners' development of informal inferential reasoning. Implications for developing concepts for informal inferential reasoning and for research are discussed. (Contains 2 tables and 3 figures.)

This study seeks to describe the subject matter knowledge needed for teaching statistical association at the secondary level. Taking a practice-based qualitative approach, three experienced teachers were observed as they taught statistical association and interviewed immediately following each observation. Records of practice were assembled to create a compilation document to recreate each of the fifty observed class sessions along with related materials including textbook pages and student work. Analysis of the compilation documents focused on the demands upon teachers' subject matter knowledge involved in the practice of teaching. Findings regarding the knowledge required for teaching correlation coefficient are highlighted, including its computation, interpretation, sensitivity, estimation, and related terminology. (Contains 3 tables and 1 figure.)

Sample surveys are widely used in the social sciences and business. The news media almost daily quote from them, yet they are widely misused. Using students with prior managerial experience embarking on an MBA course, we show that common sample survey results are misunderstood even by those managers who have previously done a statistics course. In general, they fare no better than managers who have never studied statistics. There are implications for teaching, especially in business schools, as well as for consulting. (Contains 6 tables.)

Given the recent radical overhaul of secondary school qualifications in New Zealand, similar in style to those in the UK, there has been a distinct change in the tertiary entrant profile. In order to gain insight into this new situation that university institutions are faced with, we investigate some of the ways in which these recent changes have impacted upon tertiary level mathematics in New Zealand. To this end, we analyse the relationship between the final secondary school qualifications in Mathematics with calculus of incoming students and their results in the core first-year mathematics papers at Canterbury since 2005, when students entered the University of Canterbury with these new reformed school qualifications for the first time. These findings are used to investigate the suitability of this new qualification as a preparation for tertiary mathematics and to revise and update entrance recommendations for students wishing to succeed in their first-year mathematics study. (Contains 3 tables, 5 figures and 2 notes.)

Drawing conclusions from the comparison of datasets using informal statistical inference is a challenging task since the nature and type of reasoning expected is not fully understood. In this paper a secondary teacher's reasoning from the comparison of box plot distributions during the teaching of a Year 11 (15-year-old) class is analyzed. From the analysis a model incorporating ten distinguishable elements is established to describe her reasoning. The model highlights that reasoning in the sampling and referent elements is ill formed. The methods of instruction, and the difficulties and richness of verbalizing from the comparison of box plot distributions are discussed. Implications for research and educational practice are drawn. (Contains 3 figures.)

A postal survey was conducted regarding statistical techniques, research methods and software used in the workplace by 913 graduates with PhD and Masters degrees in the biological sciences, psychology, business, economics, and statistics. The study identified gaps between topics and techniques learned at university and those used in the workplace, and points to deficiencies in statistical preparation for employment. Courses requested include multivariate statistics, generalized linear models, research design and power analysis taught with minimal emphasis on probability and mathematics. Recommendations are presented, such as expanding statistical service courses to eliminate gaps, the development of intensive workshops for postgraduate students and for workplace retraining, or involving staff from other departments to provide context for statistics teaching. (Contains 7 tables.)

Evaluating the statistical process is considered a higher order skill and has received little emphasis in instruction. This study analyses thirty 15-year-old students' responses to two statistics assessment tasks, which required evaluation of a statistical investigation. The SOLO taxonomy is used as a framework to develop a hierarchy of responses. Focusing on the quality of response allowed insight into and suggestions for how instruction might be improved. The implications for teaching, assessment, and the curriculum are discussed. (Contains 3 tables and 2 figures.)

Identifies and describes students' variation-type thinking observed in a small sample of middle-school students as they conducted a statistical investigation. (KHR)

Examines how the wording of statistical problems affects 11-12 year old children's answers. Ninety-six children were given statistical problems on two statistical concepts (base-rate and the law of large numbers). Indicates that the children had a high level of statistical intuition and knew when to reason statistically. (CMK)

Assesses students in a statistics laboratory of an educational psychology course for mathematics self-concept and mathematics anxiety at the beginning and end of the course. Finds that self-concept improves in a positive learning environment but that anxiety does not decrease. Reports that attitudinal factors are mediated by prior experience in mathematics. (DSK)

Advances in technology and communication have increased the amount of statistical information delivered through everyday media. The importance of statistics in everyday life has led to calls for increased attention to statistical literacy in the mathematics curriculum (Watson 2006). Gal (2004) sees statistical literacy as the need for students to be able to interpret results from studies and media reports and to be able to pose critical and reflective questions about those reports. Aspects of Gal's notion of statistical literacy have been incorporated in the New Zealand Curriculum (Ministry of Education 2007). The implementation of the above-extended notion of statistical literacy is likely to pose a challenge to teachers. Teachers may need practical ideas and learning activities to enhance statistical literacy in the classroom. One way to develop an effective sequence of activities is through design research (Cobb 2000), which generally involves cycles of three phases: preparation; teaching experiment; and retrospective analysis. In the current study, students evaluated statistical investigations undertaken by others, considering data collection methods, choice of measures and validity of findings (Ministry of Education 2007).