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Statistical software is commonly used in undergraduate social sciences statistics courses. Due to the increase in online/hybrid courses and the cost of SPSS, instructors may wish to switch to another statistical software. We cover seven programs: Excel, Google Sheets, jamovi, JASP, PSPP, R, and SOFA. We compare programs using the following criteria: ease of download, quality of online instructions, availability of instructor resources, sophistication of analyses available, ease of use, operating system requirements, whether it uses point-and-click or code, and whether a VPAT is available. Adopting new course materials is a valuable part of instruction but time-consuming. Therefore, this review provides information about commonly available or free open-source programs so instructors can choose based on the needs of their students and/or institutions.

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

Solving real-life problems through mathematical modeling is one of the aims of modern mathematics curricula. For this reason, prospective mathematics teachers need to acquire modeling skills and use these skills in learning environments in terms of creating rich learning environments. With this study, it is aimed to examine the reflections of using a simulation on a problem involving uncertainty on the probabilistic thinking of prospective teachers. The activity includes an experimental review of the famous Hat problem. It was observed that the hat problem, which started as a puzzle, was linked to coding theory and reached the limit of mathematics, statistics, and computer science research. Research findings revealed that the simulation-supported learning environment not only contributes to prospective teachers' probabilistic thinking skills, but also offers the opportunity to experience different methods (such as working with real data, technology assisted learning, modeling) in teaching and learning mathematics. It has been concluded that simulations have a unique potential that other methods do not have in terms of gaining statistical thinking as well as problem solving and modeling skills.

This paper aims to reveal the beliefs of students and fresh university graduates about teaching statistics during their university studies with focus on using statistical software. The objective is to detect the approach of faculties to statistics education and to find out which didactic materials and teaching methods are mainly used. Students' opinions are captured by means of a questionnaire survey and analysed both quantitatively and qualitatively. The results show the increasing importance of quantitative research and the necessity of improving statistical thinking. Unfortunately, the teaching methods used in various statistical courses are outdated and unattractive for most students. They call for an active and modern approach. Teaching statistics with the statistical software support seems to be the right way to make statistics accessible to students. The recommendation is to take students' notions into account when preparing statistical courses.

In today's world, educated individuals are expected to understand basic statistical concepts and interpret statistical messages. For this reason, despite the undeniable importance of statistical literacy in the educational process, studies on undergraduate and postgraduate students in practice reveal that students have difficulties in determining the data structure, choosing the appropriate test for the purpose, and interpreting the findings correctly. Similar studies indicate that steps should be taken in many ways to overcome such difficulties. When the respective literature is viewed, it is understood that the use of software packages in teaching has many disadvantages such as being complex, being expensive and not being compatible with mobile devices, therefore, tech-supported teaching materials suitable for the level of students, in other words, instructional software is needed. Hence, it was aimed in this study to design a mobile teaching software for the development of advanced statistical literacy skills, which are often needed in the scientific research process. For this purpose, the first type of development method, which is one of the quantitative research methods, was preferred in the research. At the end of the research process, a free mobile teaching software program was developed that can be used in the teaching of statistical concepts at the postgraduate level and can perform statistical analysis. The alternatives offered by the application developed as a result of the research in response to the needs in the literature were examined. Additionally, the application was published via Google Play Store and was made available for users for a period of one year to receive evaluations, and at the end of this period, it was downloaded by users from dozens of various countries. It has been observed that the application, which has been downloaded approximately 40 thousand times in the last six months and reached 16 thousand users, received 84.6% positive scores (4.23). It is estimated that the application, which was developed as a result of the process, will contribute to the literature in terms of statistical literacy.

Teaching practical skills is of particular interest in the study of human medicine. With regard to medical statistics this means the use of statistical software, which may be effectively taught by a flipped classroom approach. As a pilot study, we designed and implemented an elective course on medical statistics that focused on hands-on data analysis in SAS Studio. Students independently prepared for class using materials such as pretaped asynchronous lectures, and worked on exercises during synchronous class sessions. On course evaluations completed by n 15 students out of 26, students rated their satisfaction with the course a mean of 1.3 (SD 0.6) on a scale where 1 best and 6 worst. Twelve (80%) indicated that they processed all materials provided, and 11 students (73%) rated the frequency of direct contact with the instructor as sufficient. Nearly all (14 out of 15) viewed the course as an adequate substitute for a full face-to-face course. Our results suggest that the proposed course design is well-accepted. The flipped classroom format offers high flexibility and can be implemented easily online. Our pilot data are encouraging regarding the aim of designing a prospective follow-up study which compares the flipped classroom approach to a teaching format based on attendance.

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.

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.

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.

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.

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.

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.

This study investigates the support provided using technology for learning the notion of normal distribution in high school students through the implementation of a teaching experiment. A strategy was designed and implemented using Fathom software as the main teaching resource. Data analysis focused on the role of the use of technology in student learning and the simulation process, considering the initial session. The conceptual framework was based on the documentational approach to didactics, whose perspective is to study the teacher's use and design of resources in his teaching practice. Likewise, the results of the teaching experiment, whose objective was to introduce high school students to the notion of normal distribution by taking advantage of the repeated sampling resource using the Fathom software, are presented. The results show that the collaborative aspect of the lesson study methodology allowed professors to reflect and become aware of how they usually use the resources in their regular practice and thus contribute to improving their teaching activity. Evidence is provided on how students initiate a change in their reasoning to identify the probability of data collection from the simulation of problems with the software.

Visual imagery has been an effective tool to communicate ideas connected with basic mathematics concepts since the dawn of mankind. The development of educational visualisation technology allows these ideas to be demonstrated with the help of some educational software. In this paper, we specifically consider the use of GeoGebra, a free, open-source educational application developed by an international consortium of mathematics and statistics educators, but other educational software could also be used for the same visualisation tasks. In this study, we present Torricelli's method for measuring the area under arc of cycloid as an example of using GeoGebra to visualise he area of planar figures. This kind of introduction is suitable for secondary schools and for training pre-service teachers. We will also show how GeoGebra can be used to develop students' understanding of representing data (i.e. the topic from statistics education). While students explore the visualisation of data, GeoGebra allows them to create and explore representations while building the understanding that is required for analysing data and drawing figural conclusions from graphical representations.

This descriptive and correlational study investigated the effects of using PSPP in learning Statistics on students' attitudes and performance. The respondents of the study were 200 Grade 11 Senior High School students who were enrolled in Probability and Statistics subject during the Second Semester of School Year 2018-2019. The respondents were randomly selected from those classes across the different academic strands that used PSPP in their Probability and Statistics subject through stratified random sampling. The results revealed that the students have favorable attitudes towards learning Statistics with the use of the PSPP software. The students became more interested and engaged in their learning of statistics which resulted to an improved academic performance.

In the paper a software solution is presented for the generation of instances of exercises. The focus is on education in mathematics but the approach can be adopted in other fields such as computer science and natural science. The present solution uses the R environment for the generation process and LaTeX for the content presentation. In the established system, we realized the separation of computations and design which has the advantage that it is easier to find errors and shortcomings.

The use of computer simulations in the teaching of introductory statistics can help undergraduate students understand difficult or abstract statistics concepts. The free software environment R is a good candidate for computer simulations since it allows users to add additional functionality by defining new functions. In this paper, we illustrate how computer simulations with R are used in statistics classrooms and student homework assignments by examples. These examples include sampling distributions and the central limit theorem, the t-distributions, confidence intervals, hypothesis testing, regression analysis and nonparametric tests.

The purpose of this research is to examine the views of middle school mathematics teachers about the usability of VUstat and TinkerPlots software in data processing learning in the Curriculum of Mathematics Teaching in Middle School (5th, 6th, 7th and 8th grades). In the study, the phenomenology design from qualitative research patterns was employed. The study group was determined by maximum variation sampling method of purposeful sampling methods. The number of middle school mathematics teachers in the study group is 14. Pre-Interview Form, Activity Forms, Software Evaluation Forms and Focus Group Interview Form were used as the data collection tool in the research. The analysis and interpretation of the data was done by content analysis. The results of the research show that teachers have some problems regarding the use of technology in teaching mathematics and that VUstat and TinkerPlots software can be used in statistical teaching even though they have certain deficiencies. Some suggestions were made according to the results of the research.

Single-period inventory models with uncertain demand are very well known in the business analytics community. Typically, such models are rule-based functions, or sets of functions, of one decision variable (order quantity) and one random variable (demand). In academics, the models are taught selectively and usually not completely. Students are exposed to applications of selected models and solution aspects usually within the Inventory Control or similar topics. This learning-case oriented paper attempts to provide a fuller coverage of the solution process, starting with mathematical model building, following with calculus-based solution development and ending with an alternative approach through simulation. A special emphasis is dedicated to the learning processes, providing students with a variety of tools selected from Algebra, Calculus, Probability, Statistics and Spreadsheet Technology. The students are expected to benefit from studying this paper to better understand business solving processes. All computational operations are implemented in a spreadsheet program.

This study aims to identify some perceived gaps in a selection of statistical skills and software abilities of professors of education in United States colleges and universities. In addition to a general U. S. sample, a sample of education professors in Historically Black Colleges and Universities (HBCUs) was examined in order to understand their unique needs. Results showed that many professors from both samples felt they were weak in their abilities with more advanced statistical methods such as structural equation modeling and propensity score matching. Professors of education at HBCUs, however, had significant perceived skill-need methodology gaps in most of the methodologies evaluated. The general U.S. sample indicated a skill-need gap with statistical software packages such as R, and the HBCU sample indicated a skill-need gap with all five software packages evaluated (Excel, SPSS, SAS, Stata, and R). Affordable training workshops addressing the greatest areas of perceived need should be helpful in reducing this skill-need gap.

Six 7th-grade students engaged with an instructional sequence involving the use of the "TinkerPlots" software to organize data sets in ways intended to help them construe two attributes: the location of quarters of the data within a sub-range of the entire set, and the spread of those portions. We present evidence of students' thinking about these attributes drawn from their responses to questions posed in the instructional sequence. Comparison of findings from a pre-test and a culminating task suggest that the students enriched their ability to imagine and create hypothetical data from a given representative box plot, and that they became oriented to the spread of portions of a data set as indicated by the length of its quarters.

The aim of the study was to examine the effectiveness of a model called Video-Based Learning (VBL). VBL is designed to improve the learning of higher education courses, especially those based on activities performed on a computer screen, or learning related to the understanding of visual objects, such as formulas, equations, diagrams, etc. The present study aims to examine the effectiveness of the model for quantitative courses, such as statistics, mathematics, computer courses, or equivalent. The research was based on six samples of students (n[subscript 1]=14, n[subscript 2]=41, n[subsript 3]=17, [subscript 4]=27, n[subscript 5]=27, n[subscript 6]=19, n[subscript total] =145) who studied three quantitative courses: Fundamentals of PSPP, Introduction to Statistics, and 5 6 total Math for Business Administration. The learners were asked to answer an online questionnaire to assess the characteristics and advantages of VBL for their studies. The findings of the study indicate that according to the students' perceptions, VBL has a significant advantage for students' learning in quantitative courses in higher education: The learning process is outstanding and is much better than reading texts or listening to live lectures and it is considerably flexible. Therefore, it is recommended to adopt the model in faculties of higher education teaching quantitative courses.

The role of any statistics course is to increase the understanding and comprehension of statistical concepts and those goals can be achieved via both theoretical instruction and statistical software training. However, many introductory courses either forego advanced software usage, or leave its use to the student as a peripheral activity. The purpose of this study was to determine if there was instructional value in replacing classroom time with laboratory time dedicated to statistical software usage. The first approach used classroom lecture presentations, while the second replaced one classroom period per week with statistical software laboratories. It was hypothesized that replacing classroom time with software based laboratories would increase the level of statistics knowledge as compared to an otherwise identical class with no lab based component. Both pre-course and end-of course surveys were used, as well as identical examination questions. Comparisons within a time point, and longitudinal performance over the course were both evaluated. Survey results indicated that students would recommend lab based instruction significantly more than a primarily lecture based instruction (32% more, p=0.020). Additionally, the performance improvement over the course of the semester was significantly higher for those students participating in laboratories (19.2% increase, p=0.011). These findings indicate that sacrificing classroom time for a laboratory period improves the educational experience in an introductory statistics course and may help with the understanding and retention of difficult topics.

Students in this era need to grasp the concept of geometry instead of memorizing formulae. This is important for them to further their knowledge in geometry. The purpose of the research was to determine whether GeoGebra software influences year one students' performance in geometrical reflection. The research utilized an experimental research method. A total of 24 Year One students were randomly selected from an international school. The research used pre-test and post-test. The sample selected were taught and learnt by using GeoGebra software after the pre-test. Then, a post-test was given to them. A paired sample t-test was conducted and the results indicated a significant difference between pre-test and post-test. ANOVA was also conducted to test the influence of gender and ability level on student performance in geometrical reflection. The findings show a significant difference in the scores between genders. Similarly, the results also found statistically significant difference in scores among the three student ability groups. In conclusion, the study implies using GeoGebra enhances students' performance in geometrical studies. Implementing teaching and learning geometry using GeoGebra would help students to explore the concept more in detail and help them to build and develop their geometry knowledge.

The statistical computing and graphics software R, despite its many advantages, is sometimes considered too complex to be introduced to undergraduate political science majors. In this article I showed that when taught appropriately, R could be a valuable and well-received aspect of an introductory research methods course. It is important to teach R throughout the semester and take preventative measures to deal with common problems. I began with a comparison of four frequently used software in undergraduate research methods courses and a discussion of the pros and cons of teaching R. I then introduced a R sequence that I developed and implemented with success in my introductory research methods course, including example course notes, homework, and common problems and solutions, with the goal of providing research methods instructors a template to develop their own R workshops as part of an introductory political science research methods course.

Quantitative literacy is necessary to keep pace with the exponentially increasing magnitude of biological data and the complexity of statistical tools. However, statistical programming can cause anxiety in new learners and educators alike. In order to produce graduates that are well-prepared for quantitative research, overcoming the initial hurdles associated with statistical programming is a must. Often, valuable class time is dedicated to teaching introductory concepts of statistical programming, leaving instructors short on time. Here we present an introductory tutorial to statistical programming in the language R. Our tutorial is easily customizable, self-paced, and can be used in secondary through graduate level classrooms. Student questionnaire responses suggest that perceptions towards R became generally more favorable following an introduction to the program, with an increased likelihood of returning to R. Similar results were found across multiple formats for introducing statistical programming in R and suggest a tutorial-style introduction is as effective as a series of lectures and computer exercises for altering student perceptions towards statistical programming for graduate students. Our tutorial provides a self-paced introduction that covers basic programming in R and offers students an opportunity to learn the basic skills that often act as a roadblock to learning and utilizing more complex quantitative tools, while reserving class time for instruction.

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.

The Boltzmann distribution lies at the heart of essentially all of statistical thermodynamics. In most textbooks, this distribution is introduced either "ad hoc" or it is mathematically derived by constrained entropy optimization using the method of Lagrange multipliers. Unfortunately, when students enroll in a statistical thermodynamics course, many are not familiar with this method from their prerequisite calculus courses. The recent availability of powerful computational devices for essentially all students provides an alternative way to explore the origin of qualitative and quantitative aspects of the Boltzmann distribution. Here we demonstrate a straightforward simulation approach to obtain an intuitive understanding of this distribution. We also make available concise and easily understandable computer programs in MATLAB and Python, providing an opportunity for an active learning experience of this fundamental law.

In this study, the feasibility of using Excel software in teaching whole Basic Statistics Course and its influence on the attitudes of pre-service science teachers towards statistics were investigated. One hundred and two pre-service science teachers in their second year participated in the study. The data were collected from the prospective teachers before and after the compulsory Basic Statistics Course. This is a course offered in the third term aiming at introducing the most basic concepts and operations in descriptive and inferential statistics. In the context of this course, it could be argued that in most universities basically four concept groups are addressed: 1) Data and distributions, 2) How values cluster and/or disperse, 3) How variables move, classify or cluster jointly and 4) How the means between different groups differentiate. The statistics course with the content mentioned above is usually handled theoretically and nearly no statistical software is used considering the needs and expectations of pre-service science teachers. In case a software is used, it is generally SPSS in Turkey. SPSS is nearly the standard in the field here and dominates all other software such as SAS etc. On the other hand, Excel with much of its capabilities, accessibility and ease of use, is not considered by most of the academics as sufficient statistical software. In this paper the capabilities, accessibility and practicality of Excel program in teaching most basic statistics course topics to pre-service science teachers were demonstrated and its superiority to other softwares and traditional instruction were discussed. In addition, the positive effect of such an instruction on the attitudes of pre-service teachers towards statistics was shown.

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.

Since many decisions in politics, economics, and social sciences are based on statistics, statistical literacy is a key component for an active citizen. Statistical skills and statistical reasoning can already be enhanced in primary school. Therefore, not only in Germany, statistics is an element of the primary-school curriculum, which usually includes issues of posing questions, collecting data, and of drawing displays such as pie charts or bar graphs. But to engage students and to start building future generations of statisticians at an early stage, more challenging incentives should engage students in meaningful statistical inquiries. In this paper, we describe activities that are part of a larger, long-term project that investigates how and if teaching units can be designed for primary schools and what their effect on students at that early age is. We focus on specific activities that have been tested for students at age 10. The empirical results show that -- beyond learning techniques and the use of software (TinkerPlots) -- the students acquired a way of statistical reasoning about the posed problems. Besides the cognitive development, we also documented the affective impact of our course on the young learners, which was very good. Our studies corroborate that it is possible to lead students to sophisticated statistical activities such as comparing groups with the help of suitable software. Furthermore, a positive attitude towards statistics could be observed as a result of the course, which may be the basis for further success in learning statistics. All in all, we can pave the way to the future generation of statisticians already at an early age in primary school.

This quasi-experimental, pre-post study with non-equivalent comparison groups explores the potential for resequencing of course content to affect positive change in an undergraduate, introductory statistics course at a mid-sized, flagship university that is located in a southern state. Quantitative analyses suggest that the implementation of resequencing not only expands content coverage, but also improves student success rates, student learning, and student perceptions of the course. These findings, filling a gap in the statistics education literature, point to resequencing as one possible curriculum design that might improve student outcomes and further the future investigation of content sequencing in statistics and related disciplines.

Increasingly students, particularly those in the social sciences, work with survey data collected through a more complex sampling method than a simple random sample. Failing to understand how to properly approach survey data can lead to inaccurate results. In this article, we describe a series of online data visualization applications and corresponding student lab activities designed to help students and teachers of statistics better understand survey design and analysis. The introductory and advanced materials presented are designed to focus on a conceptual understanding of survey data and provide an awareness of the challenges and potential misuse of survey data. Suggestions and examples of how to incorporate these materials are also included. Supplementary materials for this article are available online.

This article illustrates ways that dynamic software using some sophisticated techniques in Excel can be used to demonstrate fundamental ideas related to hypothesis testing to increase student understanding of the concepts and methods in elementary statistics courses. The article considers hypothesis tests for the population mean with large or small samples, for the population proportion, for the difference of means, and for the difference of proportions. In each instance, spreadsheets are used that draw repeated random samples of selected sizes from a variety of underlying populations and display the sample means or sample proportions graphically. In the process, students come to see how the decision of rejecting or failing to reject the null hypothesis clearly depend on the sample drawn, which in turn depends on the size of the sample and the shape of the underlying population.

Scientific statistical working in a team is a special challenge for students in high schools, especially with a civic statistical problem. Ideally, they are following the PPDAC cycle: they formulate a problem together, plan an investigation, collect the data, use software to analyze the data, and formulate results in a seminar paper. This article is written jointly by a student and a computer science teacher involved in the project, offering insights from both perspectives.

This study investigates the effectiveness of two statistical software packages, the commercial software, SPSS, and the free software, R Version 3.5.0, in teaching statistics, by comparing grades earned by students in an introductory statistics course. Students taught using R earned slightly higher grades overall than those in the SPSS class, although the difference between the two groups of students was found to be not significantly different. The responses given by students on the end of semester survey for the use of technology indicated that students felt comfortable with both software packages, and the software R was recommended more strongly for future use in a statistics course than the software SPSS. These findings provided some insights on the use of different software packages in statistics education, which might support the use of free software in teaching statistics at college level.

The current study examines whether R or SPSS output induces greater initial anxiety in students and whether anxiety toward one or both changes after being taught one type of software output throughout the course. The authors each taught an introductory statistics course, with the first course (n = 43) teaching R output exclusively and the second course (n = 39) teaching SPSS output exclusively. Students in both courses were given surveys assessing their anxiety and confidence toward R and SPSS output on the first and last days of class. Students initially reported greater anxiety and lower confidence when viewing R compared to SPSS output. However, the initial difference between R- and SPSS-related anxiety and confidence level disappeared when students were taught R and decreased substantially when students were taught SPSS. The results suggest that although R output may seem more intimidating initially, students adapt to it as well as they do to SPSS.

Generalizability theory (G theory) provides a broad conceptual framework for social sciences such as psychology and education, and a comprehensive construct for numerous measurement events by using analysis of variance, a strong statistical method. G theory, as an extension of both classical test theory and analysis of variance, is a model which can deal with multiple sources of error. In conducting the analysis of the G theory, there are several software programs that can be used such as GENOVA, SPSS, SAS, EduG, and G-String. In this study, the general perspectives of G theory are first explained broadly. Then, the SPSS and EduG software programs are used to conduct generalizability analyses on the data obtained from the answers of 30 students (p) to nine open-ended questions (i) as rated by three raters (r). There are three different designs in the study. Two of them are random effects designs, pxixr and pxi:r, and the last one is pxixr design using a fixed rater. According to the findings from the study, SPSS and EduG give the same results for variance component estimates as well as for G (Generalizability) and D (Decision) studies of all designs, as expected. Besides comparing the program outputs, their weaknesses and strengths were also discussed regarding different designs and data sets in this study.

We can consider two basic views, when using mathematical software in the teaching of mathematical subjects. First: How to learn to use specific software for the specific tasks, e. g., software Statistica for the subjects of Applied statistics, probability and mathematical statistics, or financial mathematics. Second: How to learn to use the software that is available to us to solve specific mathematical problems from different areas of mathematics and applied mathematics. My article describes the practical use of the software in the teaching of mathematical subjects and my experience with its use by the students and the pedagogues. In our computer laboratory our students use the following software: MS Office (MS Excel), LibreOffice (LO Calc), MATLAB 2010b, Octave, wxMaxima, and LATEX. We use this software in the following mathematical subjects: Operational Analysis, Linear and Quadratic Programming, Numerical Mathematics, Applied Statistics, Queuing Theory, and Fundamentals of the LATEX. Eight years of experience with the usage of these programs have shown us, how we can improve the teaching process of the mathematical subjects at the technical universities with freely available software.

The focus of assessment in statistics has gradually shifted from traditional assessment towards alternative assessment where more attention has been paid to the core statistical concepts such as center, variability, and distribution. In spite of this, there are comparatively few assessments that combine the significant three types of statistical reasoning (reasoning about center, spread, and distribution) with information technology in the context of secondary school students. Hence, this paper intends to discuss the development and initial validation of a technology-based statistical reasoning assessment tool that has been created based on a previously developed statistical reasoning framework. This framework has been useful in evaluating students' statistical reasoning levels in task-based interviews. The assessment tool formulated through this study will be used to refine and validate the initial statistical reasoning framework. There are five tasks in this instrument and each item is labeled according to four key constructs. The technological tool that has been used in solving tasks is dynamic mathematics software. This technology-based statistical reasoning assessment tool can be applied for further investigation.

Statistical graphs, measures of central tendency and measures of spread are key concepts in the statistics curriculum, so we present here a dynamic method (software) that may be used in the classroom. In this work we begin with an introductory approach. This is done to emphasize the importance of stimulating the visualization of statistical measures by using available technology as a means of overcoming difficulties and errors related to interpretations and also to motivate students in the classroom. With the help of the dynamic geometry software Cabri-Géomètre II Plus, some applications will be presented from a didactic viewpoint as a means to give visual stimulation, to motivate and to facilitate the familiarization with statistical concepts involved in statistical graphs, measures of central tendency and measures of spread. The applications presented here may be implemented by any teacher with basic knowledge of Cabri-Géomètre or any other dynamic geometry software. We hope that they will also be elements that promote further interaction within the classroom.

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.

Two controversial topics related to the teaching of statistics to psychology students are (a) when to introduce statistical software and (b) which statistical software package to use. The current research looked at the use of statistical software in statistics classes from every university with a psychology program in Canada. Researchers collected data from 321 statistics courses offered to psychology students at 65 Canadian universities and coded the type of statistical software used (if any) in each course. Results show that slightly more than half of all universities introduce software at the introductory level. Point-and-click software is most popular, particularly SPSS. There is a considerable amount of variability in when and which software is introduced to students. Departments can use these data to inform their own practices.

Computer-assisted instruction can change the way introductory statistics and quantitative methods courses are taught. Using a two-group pretest-posttest design, we conducted an experiment using an undergraduate social science student sample to investigate whether the introduction of statistical software to teaching quantitative methods would improve knowledge acquisition and attitudes toward quantitative methods courses. Our project confirmed that implementing computer-assisted instructional methods increased knowledge acquisition in quantitative methods courses compared with students' academic performance in other courses, measured by grade point average. We also found that student attitudes have weak and mostly nonsignificant influence on quantitative methods knowledge tests. Additionally, the paper suggests a curriculum-level approach to teaching quantitative methods to undergraduate students.

Simulation is an effective tool for analyzing probability models as well as for facilitating understanding of concepts in probability and statistics. Unfortunately, implementing a simulation from scratch often requires users to think about programming issues that are not relevant to the simulation itself. We have developed a Python package called Symbulate (https://github.com/dlsun/symbulate) which provides a user friendly framework for conducting simulations involving probability models. The syntax of Symbulate reflects the "language of probability" and makes it intuitive to specify, run, analyze, and visualize the results of a simulation. Moreover, Symbulate's consistency with the mathematics of probability reinforces understanding of probabilistic concepts. Symbulate can be used in introductory through graduate courses, with a wide variety of probability concepts and problems, including: probability spaces; events; discrete and continuous random variables; joint, conditional, and marginal distributions; stochastic processes; discrete- and continuous-time Markov chains; Poisson processes; and Gaussian processes, including Brownian motion. In this work, we demonstrate Symbulate, discuss its main pedagogical features, present examples of Symbulate graphics, and share some of our experiences using Symbulate in courses.

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.

We describe a statistical seminar designed to provide a common foundation in core statistical concepts among all students as they enter a social work PhD program. Student feedback surveys assessed students' statistics preparation prior to entering the program, and pre- and posttests were compared for increases in statistical knowledge. Nearly half (42.1%) reported no prior statistics training, and exposure to IBM SPSS Statistics software was low (M=1.54 out of 5, SD=1.38). Students showed significant gains in posttest knowledge. Findings suggest substantial variability in students' statistical preparedness, and for many, knowledge of basic concepts is rudimentary. Such a seminar may allow programs to begin with more advanced quantitative course work and move to increasingly more complex topics over time (e.g., multilevel modeling).