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Health risks, when presented as ratios (e.g., two out of seven people), are challenging to understand, but visual displays can foster accurate understanding. We conducted three experiments to test how characteristics of numbers (Experiment 1), icon arrays (Experiments 1, 2, and 3), and number lines (Experiments 1 and 3) influenced people's ability to accurately estimate the risk of experiencing side effects. Participants in each experiment saw smaller- (e.g., 2 out of 7) and larger-component (e.g., 264 out of 924) equivalent ratios in one of three conditions: with number lines only, with icon arrays only, or in the form of Arabic numerals with no accompanying visual. We found that risk estimates were more accurate when presented in 10 x 10 icon arrays, long horizontal 1 x 99 arrays, or number lines. We theorize that hypothetical risks can be estimated more accurately when the display affords easy translation to a percentage.

The objective of this article is to discuss the development of statistical and probabilistic reasoning in childhood as a result of an interdisciplinary project, involving the fields of mathematics, statistics, and life sciences. This is a case study with three 10-year-old students from a Brazilian school. The children's oral and written narratives are used as a methodological path. It is an investigation process that examines human actions and considers social practices, subjective experience, identity, beliefs, emotions, values, context, and complexity. The results show that an interdisciplinary study involving life sciences, mathematics and statistics promoted the development of statistical and probabilistic reasoning, appropriate to the age group, enabling the children to positively rescale their eating habits.

This paper reports the statistical and probabilistic reasoning of young children in terms of randomness, variability, and data representations in the context of informal inferential reasoning (IIR). Using the IIR approach, a task was designed and conducted one-on-one with 28 children aged 5 to 6 years old, in a case study setting. The researcher used a voice recorder during interviews, took photos, and recorded field notes. The data were analyzed according to the principles of informal inferential reasoning, which are generalizing beyond the data, using data as evidence for generalizing, and using probabilistic language to acknowledge the uncertainty embedded in the data. The findings indicate that young children are capable of making informal inferences from a sample space, describing event probability, and constructing bar graph and pie chart data representations.

This study builds on previous studies that have examined guided project-based learning in undergraduate statistics courses to examine students' attitudes toward statistics after participating in a graduate-level statistics course that used guided project-based learning as an andragogical technique. This phenomenological qualitative case study utilized multiple student interviews and reflections over a semester-long statistics course in a doctoral education degree program. The results showed that guided project-based learning immersed students in the quantitative inquiry process and emboldened them to read and use statistics in their academic and professional lives. It also revealed several elements of guided project-based learning that are important for instructors looking to implement this approach in their own courses.

This research presents the results of the implementation of a model-eliciting activity called Brickyards, designed to promote the learning of the binomial distribution. The theoretical framework used was the Models and Modeling Perspective, and the participants were undergraduate students enrolled in a probability and statistics course of the Bachelor Civil Engineering Program at the University of Guadalajara, Mexico. The activity was refined during three semesters, and here we report the models generated by the students in the fourth implementation. In the first stage of the activity of this implementation, students proposed wrong solutions, which were based on ideas of proportionality and linear thinking. The activity was designed to inhibit these types of solutions and to encourage students to realize when they are dealing with a random phenomenon, and that they need a probability distribution to solve the activity. The students used RStudio software to calculate probabilities.

Integrated STEM activities are espoused as appropriate for enhancing student learning in relation to statistical concepts; however, a greater understanding of the way in which students' ideas about those concepts develop is needed to maximise the learning potential offered by engagement in STEM activities. For this study, plant growth was chosen as a topic from the Year 6 Australian Science Curriculum as an appropriate context to employ aspects of the four STEM disciplines to explore students' developing ideas about variation. Sixty-four Year 6 students across three school terms worked in groups of four to trial various treatments and their effects on the growth of radish or wheat seeds. This report considers two aspects of student learning related to this topic based on (i) the formative assessment of features of students' workbook entries specifically related to variation during the part of the classroom activity based on their "TinkerPlots" graphs and (ii) the later summative evidence of learning in responses to end-of-year questions on the activity for 56 of the students. The workbook entries are presented via a qualitative analysis to provide evidence of the forming of understanding of variation in a STEM context, with the SOLO Taxonomy being employed to assess the longer-term evidence and developmental nature of that learning. Overall, a broader picture has emerged of the potential for developing appreciation of variation in a STEM context in primary school.

Statistical learning (SL) plays a key role in literacy acquisition. Studies have increasingly revealed the influence of distributional statistical properties of words on visual word processing, including the effects of word frequency (lexical level) and mappings between orthography, phonology, and semantics (sub-lexical level). However, there has been scant evidence to directly confirm that the statistical properties contained in print can be directly characterized by neural activities. Using time-resolved representational similarity analysis (RSA), the present study examined neural representations of different types of statistical properties in visual word processing. From the perspective of predictive coding, an equal probability sequence with low built-in prediction precision and three oddball sequences with high built-in prediction precision were designed with consistent and three types of inconsistent (orthographically inconsistent, orthography-to-phonology inconsistent, and orthography-to-semantics inconsistent) Chinese characters as visual stimuli. In the three oddball sequences, consistent characters were set as the standard stimuli (probability of occurrence p = 0.75) and three types of inconsistent characters were set as deviant stimuli (p = 0.25), respectively. In the equal probability sequence, the same consistent and inconsistent characters were presented randomly with identical occurrence probability (p = 0.25). Significant neural representation activities of word frequency were observed in the equal probability sequence. By contrast, neural representations of sub-lexical statistics only emerged in oddball sequences where short-term predictions were shaped. These findings reveal that the statistical properties learned from long-term print environment continues to play a role in current word processing mechanisms and these mechanisms can be modulated by short-term predictions.

The Peer Assisted Learning (PAL) program at Sacramento State was established in 2012 with one section supporting introductory chemistry. The program now serves 17 courses with high rates of students who receive a D or an F or withdraw (DFW) from the course in biology, chemistry, mathematics, physics, and statistics; the program enrolls approximately 1,400 students annually. Adapting the Peer-Led Team Learning model, PAL facilitators do not teach, tutor, or even confirm answers; they ask scaffolding questions, provide encouragement, and ensure that all group members participate in problem-solving. Each PAL section is an optional credit-bearing course that supplements the targeted parent science, technology, engineering, and mathematics (STEM) course. In this article, we assess the efficacy of the program in terms of student success in the parent course. As PAL is an opt-in program, we employ propensity score matching techniques to account for confounding factors. Our analysis shows that the mean course grade point average is 1.98 for matched nonparticipants and 2.40 for matched PAL participants, indicating that the program provides an average bump of 0.42 points in the parent course. We consider data from more than 25,000 students, and our propensity score analysis uses more than 10,000 students (4,519 PAL and 5,814 non-PAL) for whom appropriate matches could be found.

The Peer Assisted Learning (PAL) program at Sacramento State was established in 2012 with one section supporting introductory chemistry. The program now serves 17 courses with high rates of students who receive a D or an F or withdraw (DFW) from the course in biology, chemistry, mathematics, physics, and statistics; the program enrolls approximately 1,400 students annually. Adapting the Peer-Led Team Learning model, PAL facilitators do not teach, tutor, or even confirm answers; they ask scaffolding questions, provide encouragement, and ensure that all group members participate in problem-solving. Each PAL section is an optional credit-bearing course that supplements the targeted parent science, technology, engineering, and mathematics (STEM) course. In this article, we assess the efficacy of the program in terms of student success in the parent course. As PAL is an opt-in program, we employ propensity score matching techniques to account for confounding factors. Our analysis shows that the mean course grade point average is 1.98 for matched nonparticipants and 2.40 for matched PAL participants, indicating that the program provides an average bump of 0.42 points in the parent course. We consider data from more than 25,000 students, and our propensity score analysis uses more than 10,000 students (4,519 PAL and 5,814 non-PAL) for whom appropriate matches could be found.

This article presents a case-study of two distance learning courses, in order to address the question of universal adoption of mobile devices and applications by students, and the impact of these devices in personal learning environments (PLEs). First, a critical discussion of the value of these concepts in the current technological context was carried out, followed by an analysis of their impact on educational use, based on data collected in online courses on physics and statistics at Universidade Aberta, the Portuguese Open University. The results indicated that all students have adopted mobile learning, and the make-up of an individual's PLE depends more on the learning resources available rather than on gender or age. These findings can help provide more efficient ways to implement learning by connecting current social needs to learners' mobile PLEs, particularly when flexibility of time and space are of utmost importance. Further studies at the Portuguese Open University will address a larger and more balanced sample of students across more course units.

Since the early 2000s, we have seen an increase in the need for graduates in various STEM fields. The Professional Science Master's (PSM) program was created in 2001 to address this increased demand. While research has shown the benefits these programs may provide, there is limited research examining the current state of PSM programs. The current research evaluates the perspective of students, alumni, faculty and program directors concerning the benefits from the PSM. Results suggest these programs still create competitive graduate students with concepts from the PSM being implemented in non-PSM programs.

Teaching introductory statistics to postgraduate students from multidisciplinary background and with diverse mathematics ability is a huge challenge that many statistics lecturers do not deny. The large ability range can make it very difficult for lecturers to fine tune the right level for effective course delivery. Even though an introductory statistics course has been seen as a necessary component for many postgraduate programs, research has shown that students have come to perceive statistics negatively. One suggestion for improving students' attitude toward statistics is through the use of innovative instructional approaches. This paper investigates the extent to which scenario-based learning (SBL) method used in a Statistics for Research in Education course were related to improvement in postgraduate students' attitude toward statistics. Nineteen students who enrolled in the course during the first semester of 2019/2020 were taught using the SBL instructional method. Survey of Attitudes Toward Statistics-36 (SATS-36) was used to measure six statistics attitude components at the beginning and at the end of the course. Overall results show that there is a difference between mean score of attitude before and after exposure to scenario-based learning method. Scenario based learning has some positive effect on student attitude toward statistics.

Universities are trending towards electronic books (e-books) as instructional materials, displacing traditional printed books. The rapid acquisition of e-books has changed the way information is presented and one of the improvements is to make e-books interactive. However, there is an incomplete body of knowledge on how interactive e-books affect students, particularly in the learning of statistics. This paper aims to examine the effects of interactive e-books on academic achievement. This paper adopted an experimental approach to test the causal effect of the two types of e-books, namely Traditional E-book (TE) and Interactive E-book (IE) on a sample of undergraduates enrolled in an introductory statistics unit. The experimental results indicated that students who learn statistics through IE produced higher scores in academic achievement than students who learn through TE. The findings of the study first extend the existing theory by showing that TE and IE can account for the variations in academic achievement. The study implied that e-books should not be static and e-book publishers and educators can choose to design their ebooks using interactive formats with animation components depending on available resources. The study offers new insights on how academic achievement of students can be better managed through the design of e-book types.

Statistical competence is defined as the leader's feature of character, which characterizes his willingness and ability to organize, to process and interpret information, needed to implement management processes. Statistical competence should be considered as a substructure of functional competence of the leader as it is shown in the article. The evaluation of indicators for the basic level of statistical competence for different categories of principles of educational institutions was carried out. It is shown that for managers with humanitarian and historical and science education the probability of distortion is not less than 20%. In addition, the criterion of signs justifies the lack of effect of improving test results on the basics of mathematical and statistical literacy in the transition from a group of leaders with humanitarian, scientific and natural education. At the same time, the independence of the testing effectiveness on the basics of mathematical and statistical literacy of managers from teaching experience is shown. The obtained evaluation results and tested hypotheses indicate the need for the introduction of additional statistical education differentiated for groups of managers with mathematical education and natural sciences.

In this study, immediate feedback, revision opportunities, and bonuses with three levels of appreciation were implemented gradually following the challenges of improving the instruction of the Education Statistics course. The research objectives at the end of the series of improvement actions were: 1) whether the implementation of immediate feedback with unlimited plus bonus points (IFUPBP) can increase learning motivation, and 2) whether the implementation of immediate feedback with unlimited plus bonus points (IFUPBP) can increase learning achievement. This study was an action research with the time-series design of different subject groups. The participants were first semester students of the Education Technology Master Program of Teacher Training and Education Faculty at Bengkulu University, from class VIII to XII who attended the Education Statistics course. Learning motivation was measured through the number of bonus points earned by the students and the number of students who earned bonus points on each homework and exam. Learning achievement was measured using an essay test. Learning motivation and achievement data were analyzed descriptively. The results of the study showed that the implementation of immediate feedback with unlimited plus bonus points (IFUPBP) can increase student learning motivation and achievement in the Education Statistics course at Bengkulu University.

It is time to reform the quantitative methods courses in leadership programs -- typically, these are statistics courses with arcane statistics textbooks. There is growing evidence that these "rigorous" scientific methods actually mislead practice because the vast majority of practices found to be "effective" or "evidence-based" using these methods do not work in schools -- including those validated by the federal What Works Clearinghouse. Fortunately, there are other quantitative methods that are more intuitive, and more accessible to leaders, leadership students, and leadership faculty -- methods that are more relevant for improving practice and identifying "evidence-based" practices that are likely to actually improve schools. However, those who control the content of quantitative methods courses tend to be those with the most technical expertise in the traditional methods and will oppose any methodological alternatives as being "non-rigorous." The newer quantitative methods will not be emphasized in EdD and Masters programs until all leadership faculty exert greater voice on the content of such courses. A first step is to stop calling quantitative methods courses "Statistics" courses. They should be "Applied Quantitative Methods" courses. This non-technical article (a) outlines the problems with traditional statistics, (b) highlights some of the newer and simpler quantitative methods that are more relevant for improving schools, and (c) describes an alternative textbook as a key resource for transforming the quantitative methods course.

Accompanied by increasing demands on school administrator preparation and rapid development of computer technology, educational statistics courses are exposed to unprecedented pressures for changing both curriculum content and computing platforms. In this article, the intended curriculum is reviewed according to data analysis expectations from state and national guidelines. Past recommendations on statistics instruction are examined to justify the need for quantitative research skills in school administrator preparation. The curriculum implementation is further investigated to reflect a fundamental revision of statistics content by the American Statistical Association. The article ends with an overview of the cutting-edge software development in R that is likely to reshape the future data processing, text analytics, and graphical display for school administrators.

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.

The present study aims to examine the effect of teachers' attitudes towards statistics on their attitudes towards postgraduate education. Accordingly, the "Attitude Towards Statistics Scale" and the "Attitude Towards Postgraduate Education Scale" were applied to 511 teachers working in different fields of primary schools, middle schools, and high schools in the spring semester of the 2018-2019 academic year. The study was designed in the survey model and the convenience sampling method was used in sample selection. In the analysis of the sub-problems of the study, parametric analysis techniques were used by determining the kurtosis and skewness coefficients between -1.5 and +1.5. As a result of the study, it was determined that teachers possessed a positive attitude towards statistics ([X-bar] =3.66; Sd=0.705) and postgraduate education ([X-bar] =3.72; Sd=0.727) and additionally,there was a high correlation between attitudes towards statistics and postgraduate education (p<0.01; r=0.972**). Furthermore, it was concluded that there was not a statistically significant difference between variables such as gender, which is a demographic variable, participation in scientific research, and educational background and attitudes towards statistics and postgraduate education (p>0.05). [Paper presented at the International Congress on New Trends in Education (11th, Turkey, Apr 18, 2020).]

Using statistical software only or Excel only was not effective to increase the learning achievements of undergraduates. The research aimed to describe the effect of using Minitab and Excel with teaching teams toward the undergraduates' achievements of Advanced Statistics course. The research design was an experimental study. The research was conducted in nine stages. The participants were all mathematics education undergraduates from one of the state universities of Palangka Raya in three academic years, i.e. from 2015/2016 to 2017/2018. The instruments were lecture plans, midterm and final tests, and textbook of Advanced Statistics. The conclusion was drawn using covariance analysis and t-test of normalized gain. The research result showed that implementation learning of Advanced Statistics integrated Minitab and Excel with teaching teams increase the undergraduates' achievements in which the normalized gain was more than 0.3 (moderate increasing). In addition, the increase was also indicated by the average differences of the final and the initial scores at the first, the second, and the third years were 7.0, 12.5, and 19.4 respectively. The increase consistently occurred for the three academic years with a confidence level of 95%. The lecture plans could be used as an alternative way to teach Statistics courses.

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.

Learners intending to enter some higher education (HE) institutions in South Africa write the National Benchmark Tests (NBTs) that are expected to provide a measure of their readiness for HE. A large gap exists between the quantitative literacy competencies of many of these learners and expectations at HE level. In this article I explore the following research question: Which quantitative literacy competencies required in HE, as identified through the National Benchmark Test Project (NBTP), are not well developed in the test takers, and what does this imply for teachers? Twelve test-item results in which candidates performed the poorest were analysed (N = 2348). The focus areas identified for teachers included quantity, number and operations, data representation, and change. The research indicates that, to enhance learners' competence in these areas, teachers should provide them with more challenging tasks than, for example, reading a single value from a graph, chart or table. Instead, learners should be required to integrate information from more than one graph/chart.

This study proposes and examines an analytical method with the aim of improving the quality of education and learning by situating the answers to full descriptive questions in probability and statistics to make variables of learners' comprehension of learned content as answer characteristics, based on actual student mistakes. First, we proposed and examined a method for extracting answer characteristics from the answers to the questions in probability and statistics as variables. Second, we proposed a method for obtaining answer characteristics to accurately describe learners' comprehension of each problem and indicate learning and educational policies for learners to improve learning by using regression trees. In addition, the relationship between learners' general ability and answer characteristics was visualized in an item characteristic chart to indicate the general comprehension of the learners. Further, the relationship between learners' learning strategy and answer characteristics was structuralized using Bayesian network models, and effective learning strategies for both learners as a whole and individual learners were extracted and evaluated towards the qualitative improvement of their comprehension using probabilistic reasoning. Our findings showed that the effectiveness of a learning strategy varies with each concept treated in a given problem; with the degree of basical or applied answer characteristics, indicating that the required learning strategy varies according to a given learner's stage of learning. Moreover, the improvement of hours studying dispersion for both mid-term and final examinations was revealed as effective for a wide range of subjects.

Based on empirical data, student learning outcomes on statistical material are not in accordance with the expectations of teachers so it is necessary to apply the Contextual Teaching and Learning (CTL) approach. A CTL implementation can help students to understand concepts and skilled resolve issues. The research purpose is to see whether the students learning outcomes on statistics materials that are taught using the CLT approach are better than conventional approaches. The methods used are experimental studies and the data will be obtained from the pre-test and post-test learning outcomes. The population are the entire class IX student while samples taken by random sampling techniques, two classes, namely as an experimental class and control. Research design is a Non-equivalent Control Group Design. Based on the results with two average difference tests on T-Test statistics were obtained that student learning outcomes in experimental class is higher than the controls. This means learning by applying the CTL approach can improve learning outcomes and the benefits for mathematics teachers gained insight into the CTL learning process.

The problem of the research is urgent due to the need to develop a special style of thinking. This type is based on problem cognitive activity, focused on lean production, resource conservation, and supported by an automated system that provides resources for solving socioeconomic problems in the conditions of the fourth industrial revolution and the digital economy formation. The purpose of the research is to theoretically prove and experimentally verify the need to change methods, tools, organizational forms of teaching robotics for the purposeful development of environmental thinking and lean manufacturing as the demanded competencies of future specialists in the context of digital transformation. The research methodology is the analysis of psychological and pedagogical work, development strategies, concepts of education; methods of mathematical statistics, methods of psychodiagnostics and survey. The pedagogical experiment is based on the example of assessing the ecological thinking formation and the energy conservation skill in teaching robotics to train engineering, technical and management specialists. The research results. The study clarifies the concepts "environmental thinking", "lean production", and "environmental competence" in the context of training specialists for the digital economy, in particular, engineering and technology. The study substantiates the didactic potential of a robotics course for the formation of environmental thinking as a demanded skill of future engineers. The authors describe didactic principles, a model for teaching robotics in a personalized environment for the formation of environmental thinking as the basis for the introduction of innovations and the challenges of automation, globalization and competitiveness. The authors conclude that a robotics course with specially organized interdisciplinary design forms of activity supported by appropriate means and training methods is necessary. It will create additional conditions for the formation of environmental thinking and lean production skills as key professional competencies in the training of demanded specialists in the digital economy.

Variation and variability are key concepts in K-16 statistics education. Prior research has investigated students' reasoning about variability in different contexts. However, there is a lack of research on students' development of understanding of variability when comparing distributions in bar graphs, dot plots, and histograms as they took an introductory college-level statistics course. This exploratory case study conducted three interviews with each of the ten participants through a four-month period, at the beginning, middle, and end of the course. The Structure of Observed Learning Outcomes (SOLO) taxonomy was used to analyze participants' responses. Results indicated that overall the group of participants demonstrated a stable understanding of variability over the semester (i.e. lack of improvement). However, when examining each student's reasoning, four types of reasoning development paths were found: improvement, lack of change, decline, and inconsistent. This study provides implications in teaching college introductory statistics course and recommendations for future research.

This study examined the influence of the jigsaw co-operative learning strategy integrated with GeoGebra (JCLGS), on Ethiopian undergraduate statistics and chemistry learners' conceptual knowledge development and attitudinal change towards calculus. The post-positivism quantitative methods approach employed in a non-equivalent pre-and post-test comparison group quasi-experimental design. The samples had drawn using two-stage random sampling techniques. The sample size was 150 in both the experimental and comparison groups. Data were collected by using the calculus classroom achievement test and the five points Likert-scale attitude questionnaire. Data were analyzed using descriptive analysis, an independent-samples t-test and Two-Way ANOVA for repeated measures using SPSS 23.0. The results showed a statistically significant difference between the two groups of pre-post test scores on the Two-Way ANOVA, F(1,148)=106.913; n[superscript 2] = 0.419; p<0.01. The finding also implies that the blended learning strategy grounded in Vygotsky's social constructivism cognitive development learning theory had big practical significance on learners' conceptual knowledge development. Learners viewed the JCLGS as enjoyable and interesting. It was also a socially interactive and collaborative environment that allows learners' to be reflective, share prior experience and knowledge and independent learners. It encourages them to have a positive attitude towards calculus and GeoGebra. Because of this finding, mathematics and science educators are advised to model a similar blended learning strategy in a classroom instructional setting. It will benefit their learners to adequately construct conceptual knowledge and positively change their attitude towards mathematics.

Recent studies report that students' attitudes toward statistics play an important role in their statistics achievement. The goal of this study was to test the psychometric properties of the "Survey of Attitudes Towards Statistics" (SATS-28) among undergraduate health science students enrolled in an introductory statistics course. Most students held positive attitudes towards statistics. The average SATS scores were above neutral. Confirmatory factor analysis validated the four-factor structure of the questionnaire (Affect, Cognitive Competence, Value, and Difficulty), albeit with a few modifications. The RMSEA value of 0.065 was below the suggested cutoff of 0.07. Cronbach's alpha for the entire scale was .907, which was well above the recommended cutoff value of 0.7. The study provided evidence for the appropriate metric properties of the SATS-28 as a valid instrument for measuring the statistics attitudes of a sample of first year students at the University of Minnesota Rochester.

This mixed research aims to analysis and design the Web Game On Descriptive Statistics (WGODS) through the ADDIE model, data science and machine learning. The sample consists of 61 students from a university in Mexico. WGODS is a technological tool (quiz game) that presents various questions and answers about statistics (quantitative and qualitative data). The results of the linear regression (machine learning) indicate that the content and aesthetics of WGODS have a positive influence on the educational process. The ADDIE model allows the organization of WGODS considering the needs of the students. Also, data science identifies 4 predictive models on the use of WGODS in the field of statistics through the decision tree technique. Finally, teachers can transform the organization and development of school activities through the ADDIE model and technology. In particular, WGODS improves the educational process on the quantitative and qualitative data through a pleasant, attractive, simple, easy and useful web interface.

Statistics and methodology play a crucial role in psychological research, and university psychology courses teach students the theory and application of various statistical methods. However, students who conduct their own research projects oftentimes face problems which are specific to their data and cannot be solved using standard curricular procedures. Instead, these issues need to be solved on a case-by-case basis. This article presents the organisation and evaluation of a statistical consulting service for students who face methodological issues in applied research. We describe the scope, contents, workload, and administrative framework of the service and evaluate its effectiveness and helpfulness as reported by the consultees over a two-semester period. Results show that the service is frequently used and well-received, and that consultants are adequately compensated for their work. We further provide recommendations for teachers and consultants regarding the organisation of the service and the consulting process from a practical perspective.

Statistics play an important role in psychology, but statistics modules are notoriously unpopular amongst psychology students. We examined attitudes toward statistics and attitudes toward the statistical software package R in both undergraduate and postgraduate students across the duration of a statistics module. Participants' responses were analysed using both quantitative and qualitative techniques. Results demonstrated that, on average, students in introductory level modules held neutral (not negative) attitudes, but students at higher study levels held somewhat positive attitudes towards R and statistics. While not all students enjoyed learning R, our findings demonstrate that many students enjoyed statistics or R, most students found statistics/R valuable and they generally reported feeling competent using software by the end of their module. These results challenge the argument that R is not suitable for undergraduate psychology students. Consequently, benefits, challenges, and implications of teaching R to psychology students are discussed.

The following action research depicts how two researchers from two universities merged their courses and goals of instruction to impact change in future teachers. Two currently practicing middle school teachers from one university worked with researchers to develop a social justice lesson that had relevance to seventeen K-8 pre-service teachers at another university to promote changes in beliefs about equitable teaching practices and policy. Findings from pre- and post-surveys, field notes during enactment, and reflections teachers found teaching statistics for social justice (TS4SJ) in this setting provided an increased responsiveness to the needs of students and statistical connections while also attending to excuses by those facing dilemmas in belief and racial dominance.

Recent standards reform documents across the globe have called for statistical literacy by the end of high school. Thus, it is important for teachers to develop a deep understanding of the content. Despite the relatively thick literature base connecting students' content knowledge and reasoning, research on these connections among practicing teachers is in critical need. Our study contributes to this lack of research by examining the knowledge structures and statistical reasoning--and possible ways knowledge structures supported reasoning--of a stratified purposeful sample of nine middle and secondary mathematics teachers as they responded to released items from the Levels of Conceptual Understanding in Statistics (LOCUS) assessment during two 60-90 minute task-based clinical interviews. Knowledge structures were categorized as compatible-connected, incompatible-connected, and incompatible-disconnected. Teachers with less incompatible knowledge elements in their structures engaged more frequently in reasoning coded as sound. However, teachers frequently engaged in both sound and unsound forms of reasoning on the same task item. Implications are offered for teacher education and future research.

Middle school mathematics teachers often do not emphasise statistics and geometry in their lesson plans for a variety of reasons. However, these are integral topics in mathematics, and using direct lecture or hands-on activities may have different effects on teacher confidence when approaching these subjects. Using qualitative and quantitative methods, anxiety was found to improve with lecture-based workshops, while confidence and effectance was found to improve with manipulatives-based workshops. The results showed some surprising and unsurprising reasons for these conclusions.

This paper reports some experiments on probabilistic reasoning designed to investigate the impact of the probabilistic problem presentation format (verbal-numerical and graphical-pictorial) on subjects' confidence in the correctness of their performance, other than the calibration between confidence and accuracy. To understand the potential effect of the format, these dimensions were assessed by monitoring contextual and individual variables: time pressure, numerical and visuospatial abilities, statistical anxiety and attitudes towards statistics. The participants included 257 Psychology students without statistical knowledge, recruited from Italian and Spanish universities, who fulfilled self-report validated measures. The students expressed their retrospective judgments of confidence item-by-item in relation to each probabilistic problem. This approach enabled the computation of two measures of calibration (the Bias Index - the Confidence-Judgment Accuracy Quotient). The results indicated that the problem presentation format did not exert a significant main effect on confidence, with the exception of when the interaction between the format and one subscale of the attitudes towards the statistics test was considered. The Bias Index, however, was significantly related to the interaction between format and time pressure. The study offers a point of reflection in relation to the potential effect exerted by the problem format and time constraint in calibration.

For decades, self-report instruments -- which rely heavily on students' perceptions and beliefs -- have been the dominant way of measuring motivation and strategy use. Event-based measures based on online trace data arguably has the potential to remove analytical restrictions of self-report measures. The purpose of this study is therefore to triangulate constructs suggested in theory and measured using self-reported data with revealed online traces of learning behaviour. The results show that online trace data of learning behaviour are complementary to self-reports, as they explained a unique proportion of variance in student academic performance. The results also reveal that self-reports explain more variance in online learning behaviour of prior weeks than variance in learning behaviour in succeeding weeks. Student motivation is, however, to a lesser extent captured with online trace data, likely because of its covert nature. In that respect, it is of importance to recognize the crucial role of self-reports in capturing student learning holistically. This manuscript is 'frontline' in the sense that event-based measurement methodologies with online trace data are relatively unexplored. The comparison with self-report data made in this manuscript sheds new light on the added values of innovative and traditional methods of measuring motivation and strategy use.

Large-scale language testing uses statistical information to account for the quality of an assessment system. In this reflection article, I explain how basic statistics can be used meaningfully in the context of classroom language assessment. The paper explores a series of statistical calculations that can be used to examine test scores and assessment decisions in the language classroom. Therefore, interpretations for criterion-referenced assessment underlie the paper. Finally, I discuss limitations and include recommendations for teachers to use statistics.