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This is the fourth in a series of statistical articles for mathematics teachers. In this article, the authors discuss topics in General Mathematics in Unit 2 Topic 1 (Univariate data analysis and the statistical investigation process) and topics in Essential Mathematics, Unit 2 Topic 1 (Representing and comparing data).

This paper describes the evolution of "recognition of need for data" and "strategical thinking", two types of thinking identified by Wild and Pfannkuch in their Framework for Statistical Thinking in Empirical Enquiry, as well as its relevance for math teacher professional development. The research was carried out with ten in-service secondary-school math teachers during an educational experience (at Bogotá, Colombia), who, in the beginning, showed high performance in procedural knowledge of data analysis. The experience was founded on project-based learning that participants proposed and conducted via a survey concerning implications of a Bill, relevant for their job context. These teachers made mistakes and showed difficulties during the two first stages of the investigative cycle, problem formulation, and research planning, due possibly to their inexperience in designing an empirical inquiry. Teacher educator's guidance, to turn mistakes into learning opportunities and teachers' active participation, promoted the development of statistical thinking, especially linked to the types aforementioned.

Research students in social science disciplines frequently struggle to master statistical analysis. A contributing factor may be the statistical software that is used, as the design of such software may not address the needs of non-statisticians or non-computer programming students. Hence, decisions about which statistical software tools are most suitable for such end-users need to be made at the introductory level. This paper first identifies key human-computer interaction (HCI) factors that may directly influence students' statistical analysis performance. Factors include technical properties such as user interface design, statistical features available, visualization, data handling, preparation, and manipulation, and usage properties such as speed/number of steps, ease of command/use, and efficiency. Four popular software systems (ie, SPSS, R within RStudio Desktop, R Commander & jamovi) were evaluated. Findings suggest that HCI usage factors from an interaction perspective are likely to be especially important for students gaining an introductory knowledge of statistics.

Teaching introductory statistics is a service requirement for many mathematics faculty, and the audience is often anxious about the subject and not always excited about the material. Making class fun, relevant, and visually stimulating is key to keeping students engaged in the material and also in promoting student learning. Collecting data from the students, be it demographic information or experimental data, can achieve this, and immediately invites the students to be interested in the data and motivated to answer-related research questions. To facilitate and speed up this process, we developed the free data collection and analysis platform Classroom Stats which is designed to make class more fun and to improve student learning through straightforward visual analysis of the data. In this paper, we will discuss the importance of using student generated data in class and how to use Classroom Stats to make the process easy and efficient.

The purpose of the research paper was to investigate the effect of eclectic learning approach on the academic achievement and retention of students in English at elementary level. A sample of forty students of 8th grade randomly selected from Government Boys High School Khurram District Karak was used. It was an experimental study and that's why sample subjects were classified into two equal groups on the basis of pre-test scores. For data collection, pre-test post-test equivalent groups designed was used. Descriptive statistics i.e., mean, standard deviation and inferential statistics i.e., t-test were employed for analyzing the data. After analyzing the data, it was come to light that eclectic learning approach has a positive effect on students' academic achievement and retention. Eclectic learning approach was found more productive, effective and successful in teaching of English as compared to traditional learning approach at elementary level. So, eclectic learning approach should be adopted by the teachers for improving students' performance in English at elementary level.

Past research have pointed out that excellent strategies have been written but extremely small have been accomplished in their implementation. It has additionally been proposed that only 10% of formulated strategies are successfully implemented. However, crafting the best strategy is not the end in itself but the ultimate result will only be realized once the plan is successfully implemented. A strategic plan is a management tool that is used to transform organizational objectives into actions. The purpose of this study was to establish the effects of strategic plan implementation on organizational performance: a case study of public Secondary Schools in Kenya. The country in the recent past has experienced challenges like student declining performance in national examinations and increased student enrolments this implies that student cannot be able to join higher learning institutions which mean their future is blurred. The specific objectives were to analyze the effects of leadership style and communication in successful implementation of the strategic plans. A descriptive survey design using stratified sampling was used. The study population comprised of the school managers including teachers, principals and deputy principals serving in selected schools. Primary data was collected through questionnaires that were administered through "drop and pick later" method while secondary data was gathered from relevant Ministry of Education, Teachers Service Commission (TSC) and Government of Kenya publications like the Strategic plan, TSC Act, Ministry of Education (MoE) records. Quantitative data was analyzed though descriptive statistics and multiple regression analysis. Quantitative data was presented using bar graphs, pie charts and frequency distribution tables.

Random forests are presented as an analytics foundation for educational data mining tasks. The focus is on course- and program-level analytics including evaluating pedagogical approaches and interventions and identifying and characterizing at-risk students. As part of this development, the concept of individualized treatment effects (ITE) is introduced as a method to provide personalized feedback to students. The ITE quantifies the effectiveness of intervention and/or instructional regimes for a particular student based on institutional student information and performance data. The proposed random forest framework and methods are illustrated in the context of a study of the efficacy of a supplemental, weekly, one-unit problem-solving session in a large enrollment, bottleneck introductory statistics course. The analytics tools are used to identify factors for student success, characterize the benefits of a supplemental instruction section, and suggest intervention initiatives for at-risk groups in the course. In particular, we develop an objective criterion to determine which students should be encouraged, at the beginning of the semester, to join a supplemental instruction section.

Educational data science (EDS) is an emerging, interdisciplinary research domain that seeks to improve educational assessment, teaching, and student learning through data analytics. Teachers have been portrayed in the EDS literature as users of pre-constructed data dashboards in educational technologies, with little consideration given to them as active producers of data analytics. This article presents the case study results of an EDS program at a large university in Midwestern U.S.A. in which faculty and instructors were provided with access to institutional data and data analytics technologies in order to explore questions related to their classroom and departmental environments. Semi-structured interviews of program participants were conducted to examine the participants' experiences as practitioner researchers in EDS. The analysis showed that participants were motivated to participate to improve their learning and educational environments through data analytics, as opposed to developing a research agenda in EDS; that participants experienced a range of barriers related to data literacy; and that participant community support in addition to administrative support are vital to teacher-focused EDS programs. This study adds to a small but growing body of research in EDS that considers teachers as producers and not just consumers of data analytics.

The purpose of this study is to look closely at how aspects of instructional leadership, and organizational learning affect the quality of madrasah in improving the quality of graduate the state madrasah aliyah. The experiment was conducted using a quantitative approach with descriptive and inferential methods, in inferential methods used correlation analysis and regression analysis. The process is first conducted analysis of data validity and reliability of data as well as test for normality using the Kolmogorov-Smirnov Test. The study population is the overall teacher the State Madrasah Aliyah at Jakarta Capital Region. The study sample size of 150 teachers. The collecting data about the instrument with research using Likert scale, to obtain data on instructional leadership, organizational learning, quality of madrassah and the quality of graduates. The results of research known that headmaster instructional leadership has a strong and positive relationship with the quality of the madrasah, the quality of graduates, organizational Learnings have strong relationships and positive impact on the quality of madrasah. The quality of graduates and have a reciprocal relationship with a high instructional leadership. It can be concluded that an increasing in the quality of madrasah and the quality of graduates at the school can be done with an increase in instructional leadership and organization of learning in the madrasah. Thus improvement instructional leadership and organizational learning have a positive influence on the improvement of the quality of madrasah and the achievement of the quality of graduates.

Understanding and analyzing data is a crucial aspect of quantitative literacy in the 21st century, leading scholars and policy makers to push for more rigorous instruction in this area rooted in statistical investigation. In this study, we examine 144 upper-elementary mathematics lessons on data and statistics topics to assess the extent to which instruction in this sample meets reformers' goals. Analyses of videos and transcripts suggest that sample lessons emphasized the analysis of data through calculations and graph construction. However, they less often featured statistical investigation, with minimal emphasis on question formulation, data collection, and interpretation and with little to no attention paid to the concept of variability. We also note issues with the accuracy of statistics content presented to students. Results suggest focusing improvement efforts on all aspects of statistical investigation and considering ways to build elementary teachers' content knowledge of statistics.

Understanding and analyzing data is a crucial aspect of quantitative literacy in the 21st century, leading scholars and policy makers to push for more rigorous instruction in this area rooted in statistical investigation. In this study, we examine 144 upper-elementary mathematics lessons on data and statistics topics to assess the extent to which instruction in this sample meets reformers' goals. Analyses of videos and transcripts suggest that sample lessons emphasized the analysis of data through calculations and graph construction. However, they less often featured statistical investigation, with minimal emphasis on question formulation, data collection, and interpretation and with little to no attention paid to the concept of variability. We also note issues with the accuracy of statistics content presented to students. Results suggest focusing improvement efforts on all aspects of statistical investigation and considering ways to build elementary teachers' content knowledge of statistics.

Statistical thinking is essential to understanding the nature of scientific results as a consumer. Statistical thinking also facilitates thinking like a scientist. Instead of emphasizing a "correct" procedure for data analysis and its outcome, statistical thinking focuses on the process of data analysis. This article reviews frequentist and Bayesian approaches such that teachers can promote less well-known statistical perspectives to encourage statistical thinking. Within the frequentist and Bayesian approaches, we highlight important distinctions between statistical evaluation versus estimation using an example on the facial feedback hypothesis. We first introduce some elementary statistical concepts, which are then illustrated with simulated data. Finally, we demonstrate how these approaches are applied to empirical data obtained from a Registered Replication Report. Data and R code for the example are provided as supplementary teaching material. We conclude with a discussion of key learning outcomes centred on promoting statistical thinking.

The African Data Initiative started as a crowd-sourced campaign to improve the teaching of statistics in African universities. The analysis of climate data provides one suitable context to illustrate ideas that lead to a radical new form of teaching. The problem within the context comes first, the technicalities are largely reduced -- mathematics is supported by meta knowledge and backed up by modelling; calculations are reduced by user-friendly software that is also used by experts. The problems are treated similarly to research questions and the results are often easier to interpret, making sense as potential answers in their context. The criteria of this approach are compared to the framework proposed by W. G. Cobb to reform statistics education in the light of the latest developments in statistics, driven by the huge increase of data. Implementation details are presented around three components: case studies, data, and the required skills. Together, these three components describe an alternative education pathway centred around statistical problem solving. The focus on interpretations of results within a real context enables software, mathematical thinking and modelling to play a supportive role, which flattens the prerequisites of complex methods and encourages their use across all levels of education.

Typically, training in Russia for professionals includes school, university, and postgraduate education. People make their choice regarding university or job after school, and they choose jobs after university. These are very sensitive matters. Help in making the right choice is a real asset. The Russian Association of Statisticians (RASt) is an independent, non-profit organisation that does not provide statistical education as a university and does not collect and process data as a statistical institution. But RASt helps students, universities, and producers of statistical data find each other. The paper describes the activities of RASt which organises the school competition in statistics called "Trend" to support students in choosing a profession and the kick-off competition "Career" for university students to help them get to know their employers. The organisers of the competition for school children usually face a number of problems related to the young age of participants and to limited funding. If we are talking about such a country as huge as Russia, the problems increase. To solve these problems, organisers use a combination of competition of presentations about original statistical researches provided by school teams in regions and an online quiz on statistical topics at the final stage. Technologically, the entire process is supported by ROSSTAT with its IT network. The organisers hope that the competition will make the profession of statistician more popular in Russia and attract more students to statistical programmes in universities.

In the contemporary society a massive amount of data is generated continuously by various means, and they are called Big-Data sets. Big Data has potential and limits which need to be understood by statisticians and statistics consumers, therefore it is a challenge to develop Big-Data Literacy to support the needs of constructive, concerned, and reflective citizens. However, the development of the concept of statistical literacy mirrors the current gap between purely technical and socio-political characterizations of Big Data. In this paper, we review the recent history of the concept of statistical literacy and highlight the need to integrate the new challenges and critical issues from data science associated with Big Data, including ethics, epistemology, mathematical justification, and math washing.

Students in many Australian universities start their studies mathematically underprepared as there are no prerequisites for mathematics, and assumed knowledge requirements are often overlooked. Many degrees include at least one statistics subject for which students require a reasonable level of mathematical ability to successfully complete. Students' efforts to grasp quantitative skills often lead to feelings of anxiety, stress, and lack of self-confidence. The Mathematics Education Support Hub (MESH) at WSU provides free support in mathematics and statistics to all students, both undergraduate and postgraduate, to increase their engagement, understanding, and abilities in statistics as well as to overcome their anxiety. In this paper we focus on the drop-in consultation service, which provides "just in time" help in campus libraries. Data is collected for every consultation, which enabling an investigation in relation to the mathematics background of students and the problematic topics in statistics. Text mining is used to examine students' queries to identify the topics in statistics subjects that students struggle most with. Outcomes of this analysis can be used by statistics instructors and mathematics support centres to improve students' experience in learning and to help to reduce statistics anxiety in future generations of statistics students.

Training programs for statisticians and data scientists in healthcare should give greater importance to fostering inductive reasoning toward developing a mindset for optimizing Big Data. This can complement the current predominant focus on the hypothetico-deductive reasoning model, and is theoretically supported by the constructivist philosophy and Gestalt theory. Big-Data analytics is primarily exploratory in nature, aimed at discovery and innovation, and this requires fluid or inductive reasoning, which can be facilitated by epidemiological concepts (taxonomic and causal) as intuitive theories. Pedagogical strategies such as problem-based learning (PBL) and cooperative learning can be effective in this regard. Empirical research is required to ascertain instructors' and practitioners' perceptions about the role of inductive reasoning in Big-Data analytics, what constitutes effective pedagogy, and how core epidemiological concepts interact with the evidence from Big Data to produce outcomes. Together these can support the development of guidelines for an effective integrated curriculum for the training of statisticians and data scientists.

Maps are a primary method of displaying statistical data that comes from a geographical frame. Maps are esthetically appealing and make it easier to identify geographic patterns in a dataset. However, few introductory statistical texts and courses explicitly present maps as a way to display data. In this article, we will present examples of different types of statistical maps and illustrate how these maps can be used in the instruction of an introductory statistics course.

Posing statistical questions is a fundamental and often overlooked component of statistical inquiry. In this paper, we provide an overview of shared understandings regarding what constitutes a good statistical question. We then describe three approaches--a checklist for improving statistical questions, a three-phase feedback activity, and a matching game--that we find useful with preservice teachers to support the development of high-quality statistical questions for the comparison of data sets.

With the creation of interactive tasks that allow students to explore spatial ways of knowing in conjunction with their other ways of knowing the world, we create a space where students can make sense of information as they organize these new ideas into their already existing schema. Through the use of a Common Online Data Analysis Platform (CODAP) and data from Public Use Microdata Areas (PUMA), students can explore the communities in which they live and work, critically examining opportunities and challenges within a defined space.

In this paper, we investigate an interesting question that came up when reading a problem in a school textbook: What happens to the variance of a dataset in the case of changing one single data point, and why? Some of the answers are not surprising but here we find the full answer and demonstrate the understanding of it suitable for school students.

Peter Dunn and Margaret Marshman present the second of their data files articles in which they discuss the statistical investigation cycle which describes the whole process of conducting a statistical research study. [For "The Data Files: A Series of Articles to Support Mathematics Teachers to Teach Statistics," see EJ1259108.]

Data reproducibility is becoming increasingly important in the social sciences, but it has yet to be incorporated into many undergraduate sociology programs. This note describes a service-learning activity that can be added to an introductory statistics course. Students partner with a nonprofit and analyze quantitative data to answer questions selected by the agency. Reproducibility is the central mechanism of communication between the nonprofit, the students, and the course instructor. An assessment of the project suggests that students achieve an understanding of how to create reproducible data. They also come to see its value as a method of communication about data decisions.

With developing technology statistical information and data sources become a very important issues and from primary school it has become necessary to gain the skills for making interpreting and making sense of data. These skills consist of collecting information, arrangement and analysis of collected data and the interpretation of the results. The duty of guiding students in their process of making statistical information meaningful falls upon teachers. This study, whose aim was to investigate prepared course content for sub-learning area in grade 1-4 math course and obtained experiences by pre-service elementary teachers in the schools they went as a part of teaching practice course, was conducted with nine fourth-year students attending an undergraduate program of elementary teaching in a state university during 2013-2014 academic year. Pre-service teachers were each asked to prepare and conduct a lesson plan suitable for the lesson outcomes and the level of the classes that they were to teach. Their applications were assessed by semi-structured observation form about data teaching developed by the researchers. It was observed that pre-service teachers could not reflect given lesson outcomes on the topic of data to the lessons they prepared to teach during their teaching practice. In the implementations, it was noted that pre-service teachers could not effectively include students in both collecting and arrangement as well as interpretation processes of the information and that they taught in teacher-centered manner although they prepared a correct activity. It was also noted that pre-service teachers could not well enough differentiate category and concept of variable in table and graph activities.

This monograph provides a neuroscience-based systemological, epistemological, and methodological rational for the design of an advanced and novel parametric statistical analytics designed for the biological sciences referred to as "Biotrichotomy". The aim of this new arena of statistics is to provide dual metrics designed to analyze the Pre and the Post Hoc outcomes of biological phenomena. The data analysis methodology of "Biotrichotomy" as "Biotrichotometrics" uses the unique instrumentation of the qualitative to quantitative "Tri-Squared Test" and its associated Post Hoc statistic "Tri-Center Analysis" as in-depth data analytic psychometrics. Using these two tools together the researcher has a seamless longitudinal research methodology. Access through these procedures also allows the use of the traditional parametric statistical measures of central tendency within the trichotomous research design framework. In terms of post hoc metrics, Tri-Center Analysis involves the computation of normal distribution parametric measures to examine the values of an independent statistically significant Tri-Squared Test. Both systems of statistical analysis were initially introduced in the i-manager's "Journal on Mathematics" and i-manager's "Journal of Educational Technology" respectively, and the result of this paper illustrates their utility, usability, and viability.

In this paper the complex problems of developing quantitative and analytical skills in undergraduate first year, first semester business students are addressed. An action research project, detailing how first year business students perceive the relevance of data analysis and inferential statistics in light of the economic downturn and the challenges society faces is discussed. Students' attitudes were evaluated via an online survey consisting of both quantitative and qualitative responses. While two thirds of respondents do acknowledge the relevance of such a course for future business roles, it is shown that more work must be done to distinguish between why data analysis is relevant and how data analysis is performed. Also discussed are findings related to student learning, their intellectual development, and their motivation and expectations upon enrolling on the "Data Analysis for Decision Makers (DADM)" module. The challenges in teaching such a mandatory module to Business students are discussed and a pedagogical framework for promoting deeper student engagement through active learning, regular continuous assessment and technology are also examined.

Many universities and colleges are increasingly concerned about enhancing the comprehension and knowledge of their students, particularly in the classroom. One of the method to enhancing student success is teaching effectiveness. The objective of this research paper is to propose a novel research model which examines the relationship between teaching effectiveness and student learning outcomes qualitatively. This new model will use a unique and in-depth qualitative case study methodology especially designed for the instructional setting. The anticipated qualitative data collecting techniques will include, but not limited to the following: observations, personal interviews, qualitative survey questionnaires, research field notes, document review, etc. The proposed Model used assumed data and applied statistical Cross-Tabulation and Chi-Square Tests, including a theoretical analysis of the open-ended responses and field notes recorded from participants (a sample of 32 students presently enrolled in a Semester-long English ENG 1200-01 course at a public university in North Carolina). The associative statistical findings found a positive relationship between the teaching effectiveness and student learning. The outcomes of the study will increase the current lack of information on the use of qualitative research designs by determining teaching efficacy and its effects on student achievement. This new model expands the existing measures by providing new measures to examine the teaching effectiveness and its effect on student learning.

AACSB has now mandated that analytics be integrated into the undergraduate business curriculum. Given that the subject of statistics provides the underpinnings of the developing discipline of business analytics, this article focuses on effective course delivery aimed at enhancing the learning of introductory business statistics in the modern world of big data. To this end, the choice and use of computational software tools are essential to the successful delivery of the course. A set of seven competing tools are compared and contrasted, their advantages and disadvantages are discussed, and a link is provided to show demonstrations of needed instructions and resulting output.

In psychological and survey research, the prevalence and serious consequences of careless responses from unmotivated participants are well known. In this study, we propose to iteratively detect careless responders and cleanse the data by removing their responses. The careless responders are detected using person-fit statistics. In two simulation studies, the iterative procedure leads to nearly perfect power in detecting extremely careless responders and much higher power than the noniterative procedure in detecting moderately careless responders. Meanwhile, the false-positive error rate is close to the nominal level. In addition, item parameter estimation is much improved by iteratively cleansing the calibration sample. The bias in item discrimination and location parameter estimates is substantially reduced. The standard error estimates, which are spuriously small in the presence of careless responses, are corrected by the iterative cleansing procedure. An empirical example is also presented to illustrate the proposed procedure. These results suggest that the proposed procedure is a promising way to improve item parameter estimation for tests of 20 items or longer when data are contaminated by careless responses.

This article describes a collaborative project across three institutions to develop, implement, and evaluate a series of tutorials and case studies that highlight fundamental tools of data science--such as visualization, data manipulation, and database usage--that instructors at a wide-range of institutions can incorporate into existing statistics courses. The resulting materials are flexible enough to serve both introductory and advanced students, and aim to provide students with the skills to experiment with data, find their own patterns, and ask their own questions. In this article, we discuss a tutorial on data visualization and a case study synthesizing data wrangling and visualization skills in detail, and provide references to additional class-tested materials. R and R Markdown are used for all of the activities.

The Fatih Project in Turkey has improved software in mathematics teaching such as data analysis software. As a result, the need to inquire into the efficiency of computer-supported learning environments has emerged. This study aims to examine the effect of dynamic data analysis software-supported learning environments on secondary school students' achievement and attitude. The research method employs a quasi-experimental design with a pre-test, post-test control group. Basic topics related to data analysis were introduced through dynamic statistics software in the experimental group while the students were taught with the help of smart boards, course books and exercises in the control group. Data were collected with an achievement test, attitude scale and semi-structured interviews. Also, interviews were conducted with four students from the experimental group in order to get more detailed information from students. The data gained in the study were analysed both quantitatively and qualitatively. The findings revealed that statistics teaching through statistics software is more efficient than the one with the traditional method on achievement and attitudes. In accordance with this result, it is suggested that computer-supported statistics software should be used in statistics teaching.

In several sporting events, the winner is chosen on the basis of a subjective score. These sports include gymnastics, ice skating, and diving. Unlike for other subjectively judged sports, diving competitions consist of multiple rounds in quick succession on the same apparatus. These multiple rounds lead to an extra layer of complexity in the data, and allow the introduction of graphical constructs and interrater-agreement methods to statistics students. The data are sufficiently easy to understand for students in introductory statistics courses, yet sufficiently complex for upper level students. In this article, I present data from a high-school diving competition that allows for investigation in graphical methods, data manipulation, and interrater agreement methods. I also provide a list of questions for exploration at the end of the document to suggest how an instructor can effectively use the data with students. These questions are not meant to be exhaustive, but rather generative of ideas for an instructor using the data in a classroom setting. Supplementary materials for this article are available online.

We report on five-year professional development collaboration with a group of middle-school mathematics teachers during which their views of what constitutes a productive classroom statistical activity changed. The teachers' statistics instruction was initially typical in the US context and focused on producing calculations and following conventions for making graphs. In contrast, towards the end of the collaboration, teachers routinely planned statistical activities in which the generation and analysis of data was driven by a need to gain insight into a specific problem at hand. We document the changes in teachers' views of a productive classroom statistical activity and the means by which these changes were supported. In doing so, we highlight how explorations of the role of problem context in statistics provided a productive professional development focus, where teachers both built on their existing practices, and tested, in their classrooms, ideas that were novel or incongruent with their prior experiences.

"Data science" is a discipline that provides principles, methodology, and guidelines for the analysis of data for tools, values, or insights. Driven by a huge workforce demand, many academic institutions have started to offer degrees in data science, with many at the graduate, and a few at the undergraduate level. Curricula may differ at different institutions, because of varying levels of faculty expertise, and different disciplines (such as mathematics, computer science, and business) in developing the curriculum. The University of Massachusetts Dartmouth started offering degree programs in data science from Fall 2015, at both the undergraduate and the graduate level. Quite a few articles have been published that deal with graduate data science courses, much less so dealing with undergraduate ones. Our discussion will focus on undergraduate course structure and function, and specifically, a first course in data science. Our design of this course centers around a concept called the data science life cycle. That is, we view tasks or steps in the practice of data science as forming a process, consisting of states that indicate how it comes into life, how different tasks in data science depend on or interact with others until the birth of a data product or a conclusion. Naturally, different pieces of the "data science life cycle" then form individual parts of the course. Details of each piece are filled up by concepts, techniques, or skills that are popular in industry. Consequently, the design of our course is both "principled" and practical. A significant feature of our course philosophy is that, in line with activity theory, the course is based on the use of tools to transform real data to answer strongly motivated questions related to the data.

Elements of statistical modeling can be implemented already in primary school. A prerequisite for this approach is that teachers are well-educated in this domain. Content knowledge, pedagogical content knowledge and (pedagogical) content related technological knowledge are core components of teacher education. We designed a course for elementary preservice teachers with regard to developing statistical thinking including the mentioned knowledge facets. The course includes exploring data and modeling and simulating chance experiments with TinkerPlots. We use the 'data factory metaphor' in fictive contexts and in contexts stemming from civic statistics for supporting the idea of modeling. We interviewed four participants of the course to assess and analyze their reasoning. We analyze how they model a given civic statistics contextual problem using the TinkerPlots sampler and how they evaluate their model with regard to a civic statistics context (the situation of hospitals in Germany).

Publicly-available datasets, though useful for education, are often constructed for purposes that are quite different from students' own. To investigate and model phenomena, then, students must learn how to repurpose the data. This paper reports on an emerging line of research that builds on work in data modeling, exploratory data analysis, and storytelling to examine and support students' data repurposing. We ask: What opportunities emerge for students to reason about the relationship between data, context, and uncertainty when they repurpose public data to explore questions about their local communities? And, How can these opportunities be supported in classroom instruction and activity design? In two exploratory studies, students were asked to pose questions about their communities, use publicly-available data to investigate those questions, and create visual displays and written stories about their findings. Across both enactments, opportunities for reasoning emerged especially when students worked to reconcile (1) their own knowledge and experiences of the context from which data were collected with details of the data provided; and (2) their different emerging stories about the data with one another. We review how these opportunities unfolded within each enactment at the level of group and classroom, with attention to facilitator support.

This paper addresses how students explore, construct, validate and use statistical models when facing situations designed from a socio-critical perspective. The case study used is a statistics lesson designed by a statistics teacher and a researcher. The lesson centers on nutritional information and was implemented in a 7th-grade classroom at a public school in a Northwest Colombian city. In small groups, students gathered their own data, and subsequently organized and analyzed the data, and presented their findings to the class. The main sources of data were students' discourse in the classroom, students' artifacts and the researcher's journal. The findings describe a route in which students explore, construct, use, and validate their models. The results elaborate the technological and the reflective knowledge that took place in the model building activity.

While aggregate reasoning is a core aspect of statistical reasoning, its development is a key challenge in statistics education. In this study we examine how students' aggregate reasoning with samples and sampling (ARWSS) can emerge in the context of statistical modeling activities of real phenomena. We present a case study on the emergent ARWSS of two pairs of sixth graders (age 11-12) involved in statistical data analysis and informal inference utilizing TinkerPlots. The students' growing understandings of various statistical concepts is described and five perceptions the students expressed are identified. We discuss the contribution of modeling to these progressions followed by conclusions and limitations of these results. While idiosyncratic, the insights contribute to the understanding of students' aggregate reasoning with data and models, with regards to samples and sampling.

In this study, we examined how in-service middle-level mathematics teachers used statistics in their own classroom research. Using an embedded single-case design, we analyzed a purposefully selected sample of nine teachers' classroom research papers, identifying several themes within each phase of the statistical problem solving process to summarize how teachers 1) planned studies and collected data, 2) analyzed data, and 3) interpreted results. The results illustrate the varying ways in which teachers used statistics to make data-based decisions about their classrooms, revealing teachers' early development in their statistical thinking and suggesting that teachers' required knowledge of statistics is multi-faceted, requiring both a pedagogical component and statistical knowledge for the teaching profession. Such findings have important implications for how we, as teacher educators, can best meet teachers' professional needs.

Information and communications technologies today are used in virtually any university course when students prepare their papers. ICT is also needed after people are graduated from university and enter the job market. This author is an instructor in the field of informatics related to health care and social sciences at the Riga Stradins University. In practice, he has found that after completing informatics courses (IC) at the university level, students and practicing specialists at various levels find it hard to decide on what data processing method to use in order to interpret extracted results in the relevant area of specialisation. There are various data processing methods in the literature, presented individually and without adequate linkages. The author has found in practice that when such assignments are handled, there is closer linkage among data processing methods than the literature would suggest. In this article, the authors deal with the following issues: (1) how assignments given during informatics courses at the university level can be integrated with the relevant area of specialisation by making use of professional standards, guidebooks to studies in other courses, descriptions and scholarly publications so as to help students and practicing specialists to take decisions on data processing methods, their use, and the interpretation of their results; (2) how to ensure that educational data related to the area of specialisation are obtained on the basis of statistics in scholarly publications; (3) what kind of content is to be used for students of health care and the social sciences; (4) how to choose methods to resolve data processing issues; and (5) what are the recommended principles for evaluating the knowledge, skills and talents of students? The views that are presented in this paper are those of the authors or of other authors.

This paper presents an example of a project used in an undergraduate business intelligence class which integrates concepts from statistics, marketing, and information systems disciplines. SAS Enterprise Miner software is used as the foundation for predictive analysis and data mining. The course culminates with a competition and the project is used to enhance communication and presentation skills.

Advances in statistics provide new methods for analyzing practice data. These advances include person-centered methods (PCMs) that identify subgroups of research participants with similar characteristics. PCMs derive from a frame of reference that is similar to the risk factor perspective in practice. In practice, the delivery of services is often contingent on identifying at-risk populations and then providing interventions to groups based on shared risk profiles. PCMs use this perspective. Moreover, PCMs provide a means for identifying high-risk groups with a precision rarely afforded by routine variable-centered methods. This article describes a latent profile transition analysis (LPTA), one of several PCMs. To demonstrate LPTA, we estimate risk profiles and treatment effects using data from a cohort study of a school-based social skills training program. We define four steps in PCMs analysis, describe key statistical tests, and conclude with a discussion of the strengths and limitations of PCMs for practice research. [This article was published in "Journal of Community Psychology" (EJ955395).]