## How to Teach Statistical Thinking in Mathematics Education in Elementary or Secondary School

The report will clarify the standardized roles of statistical thinking for general problem solving that should be introduced into elementary and mathematics secondary education in Japan, with the goal of developing more effective active learning by utilizing both pure mathematical knowledge and statistical thinking.

Key words: PPDAC cycle, QC story, problem finding, causal analysis, confirmatory analysis.

## Statistical Inquiry Process and Assessment

In the data-driven society using Cyber Physical System (CPS), decision-making processes using large data sets, including so-called `big data,' are essential in all industrial and social endeavors. Due to the expansion of the Internet and the evolution of the mobile society, the Internet of things (IoT), and artificial intelligence (AI), the size of the available data continues to grow without limit. People who had traditionally relied on intuition or experience have shifted their decision-making to depend instead on the results of data analysis. Consequently, the importance of the ability to explore problems in a statistical manner, and to answer questions scientifically, has increased dramatically. In this paper, we surveyed and studied various methods of statistical education, with the goal of nurturing both scientific exploratory power and judgment ability. We also have summarized class design and performed evaluations including overseas cases, e.g., in the UK, USA, and NZ. As a class design that will foster empirical scientific abilities such as exploration, we propose a project-oriented practical lecture in which students can solve multiple kinds of problems by statistical inquiry and analysis. For evaluation, we propose ``Statistics Project-based Assessment Rubric Tables: SPART'' as a criterion for recognizing students' abilities in each phase of the statistical inquiry process.

Key words: Statistical education, statistical problem solving, PPDAC cycle, inquiry, assessment.

## Development of Statistics Teaching Materials Presented in Textbook Format at a Private Combined Junior and Senior High School

According to the new curriculum guidelines announced by the Ministry of Education, Culture, Sports, Science and Technology in February 2017, the field of statistics has become more important than ever in elementary school arithmetic and junior high school mathematics classes. Considering current worldwide trends, the importance of statistics will also increase at the high school level.

However, most current teachers did not learn statistics in primary school, junior high, or senior high, and even most mathematics teachers barely studied statistics in college. It is also very likely that the new national statistics textbooks authorized by the government are not sufficiently descriptive in terms of content.

Accordingly, this paper describes the contents of an originally developed statistics textbook that was formulated to address this issue. In addition, we summarize the type of educational effects that can be expected from this textbook.

Key words: Statistics textbook, private combined junior and senior high school, junior high school, senior high school.

## Cultivation of Clinical Biostatisticians

The Japanese society demands cultivation of clinical biostatisticians. In 2016, graduate schools at Kyoto University and University of Tokyo launched education projects funded by the Japan Agency for Medical Research and Development (AMED). In 2017, the Biometric Society of Japan also started certification of trial statisticians. This paper describes recent activities and issues related to cultivation of clinical biostatisticians, introducing Clinical Biostatistics Course at Kyoto University as a model course for schools of public health (SPH). Educating clinical biostatisticians at a SPH is advantageous in following aspects: (1) a variety of classes on medicine, (2) cultivation of abilities which are difficult through classroom lectures, such as experience in medical research, ethics and communication skills, and (3) spillover effects on students and teachers other than the biostatistics course. On the other hand, concerns over education at a SPH are: (1) alimited number of teachers of biostatistics, (2) difficulties of student-recruitment from other fields, and (3) ideal education from a long-termperspective.

Key words: Clinical biostatistician, clinical trials, biostatistics education, school of public health, Japan Agency for Medical Research and Development (AMED).

## Shiga University Model of Data Science Education

One method for extracting value from big data is data science. The technical foundations of data science are data engineering (information science) and data analysis (statistics). Shiga University established a faculty of data science in April 2017, in order to cultivate data scientists with liberal arts educations along with skill in the physical sciences. In this article, we explain the content of data science education at Shiga University. First, we summarize the Shiga University Model. Then, we describe the curriculum for information science and the statistics of data science, respectively, and we describe a learning environment to support these curricula. Furthermore, we introduce examples of cooperation with domestic organizations for Project-Based Learning (PBL) practices. We anticipate that many universities in Japan will strengthen education in the field of data science using the Shiga University model as a reference.

Key words: Big data, project-based learning, active learning, MOOC.

## A Large-scale Testing System for Learning Assistance and Its Learning Analytics

One of the most crucial issues in universities, where a variety of enrolled studentsare educated to the level of universities' diploma policies, is to identify students at risk for failing courses and/or dropping out early, to take care of these students, and to reduce their risk. For this purpose, in April 2016, Hiroshima Institute of Technology implemented a newly developed online testing system to evaluate students' abilities into the follow-up program for fundamental undergraduate education; the system is based on item response theory. Since then, the system has been operating well. The subjects are basic analysis (calculus) and linear algebra. The accumulated learning data are sufficient for assessment of primary learning analytics. In this paper, we describe our case as a large-scale testing system for steadily accumulating learning data, and then explore whether we can identify students at risk by analyzing such data in the early stages. It is worth mentioning that risk factors that were originally ambiguous have revealed by statistical analysis of the data. Although the academic subject examined in this study was mathematics, this kind of system could easily be applied to other subjects, including statistics, statistics education, and STEM (science, technology, engineering, and mathematics).

Key words: Learning analytics, dropout, follow-up program, item response theory, learning check testing, adaptive testing.

## Consideration of Realization of Lessons with Statistical Problem Solving

—Focusing on the Differences between Processes Using Existing Data—

Statistical education has been fulfilled in next national course of study for elementary and junior high schools, especially focused on statistical problem solving. Although in the guidebook of course of study ``PPDAC Cycle'' has been presented, it is very difficult for teachers to realize that in their lessons. On the other hand, it is easier for them to do lessons with existing data. But it is different with PPDAC process between lessons using existing data and not using those, because there is not the process of gathering data with lessons using existing data. The aim of this article is to analyze the differences of PPDAC Cycle through lesson examples, and derive suggestions for realization of statistical lessons with problem solving.

Key words: Statistics education, strand of the ``Making use of Data'', statistical inquiry, PPDAC Cycle.

## Status of Basic Statistics Education from Survey Results on Data Science Education

Since 2010, business journals, the media, and other entities have begun to focus to statistics and data science. In education as well, there is a similar movement in elementary school, junior high school, senior high school, as reflected by the courses of study presented in February 2017. Although statistics departments are widely established overseas, they are not commonplace in Japan. However, in April 2017, the Faculty of Data Science was established at Shiga University. In these cases, education in statistics and data science is important, but based on research studies published by related academic societies, it is difficult to say whether its significance has been sufficiently recognized by teachers and students. Under these circumstances, we aim to advise everyone of the importance of statistics literacy and basic data science. To this end, we conducted a web survey. Based on the results of this study, we found that many people have not studied statistics and data analysis at university, but many of those who have not still want to learn these subjects in the future. In particular, they wanted to learn how to collect data and materials, read numerical values of graphs and tables, quantitatively recognize problems, and analyze data using PCs and statistics software. However, many of these abilities (e.g., planning experiments and data collection, analysis of data to explore factors and prediction, and problem solving based on analytical results) are not realized at a high level at university. These findings are consistent with the results of past surveys. Some companies conduct collective training. However, many companies are expected on voluntary learning, or not being implemented. Therefore, students expect to learn statistics and data analysis at university. Over the course of this education, they require not only lessons that communicate knowledge, but also hands-on lessons such as exercises, social surveys, and experiments.

Key words: Active learning, data literacy, data science education, higher education, teaching methods.

## Development of Teaching Materials for Statistical Education: Practice in a High School Mathematics Class

As of 2018, data analysis has been included in high school mathematics education for 7 years. In this research note, we explain how we introduced a class practice using teaching materials developed to promote the learning of data analysis. Following lectures by experts on drug development and clinical trials, we explainedanalysis to the students the relationship between these topics and data in a special lecture in which these materials were used. Students also participated in a workshop that enabled them to review the contents of the data analysis in the same class. We also introduced another class practice in which the materials were used without the experts. The class was taught by a conventional high school mathematics teacher. Depending on the impressions of the students after the class, our materials may be useful in mathematics education.

Key words: Teaching material development, improvement of class, statistical education, mathematical education.

## A High School Case Study of Statistical Education Practice after Completion of a Unit on ``Data Analysis''

—From the Viewpoint of Fostering the Ability to Utilize Data—

2016 marked the fifth year since ``Data Analysis'' became a unit of study (i.e., part of the content) of ``Mathematics I'' in upper secondary schools. However, based on the analysis of the University Entrance Examination Center, few high school students enroll for the course on ``Probability Distribution and Statistical Inference,'' a statistics course in the ``Mathematics B'' program. However, to enhance problem-solving statistical education in elementary and secondary school, it is indispensable to further cultivate each student's statistical literacy. Therefore, we considered it important that students routinely deal with actual data from the elementary/secondary stage of education and are trained in the concept of uncertainty. In this paper, we report on the practical teaching of inference statistics at a high school. At the beginning of the practice, there was insufficient establishment of the understanding of ``data analysis,'' and high school students were unfamiliar with actually using the data. However, by exposing the students to lessons, exercises, and cooperation with others, we were able to see how high school students utilized data as a learning task.

Key words: Data analysis, inferential statistics.

## A Practical Report on Statistical Education for Undergraduates

—Active Learning Connecting Deduction and Induction—

This letter is a practical report about a lecture introducing active learning in undergraduate statistics education at a general science university. The education method introduced as the development of active learning is to impose a report preparation on each student according to their interests. The purpose of this method is for students to understand through experience the way of thinking of the statistics by connecting deduction and induction when they will integrate, without being conscious, a thorough explanation about deductive content in classroom and an inductive thorough by the voluntary activity at the time of making the report. This method promotes positive activity of students, enables them to obtain a deeper understanding of statistics by analyzing familiar data about themselves, and improves their satisfaction level.

Key words: University statistics education, active learning, deduction and induction.

## An Estimation of Minimum Class Size for an Effective Classroom Experiment on the Central Limit Theorem Using Clickers

We examined a classroom activity in which learners perform sampling and validate the central limit theorem using clickers or a classroom response system. In this activity, learners are motivated by a dataset that they generate themselves. The effectiveness of the activity, however, depends on the sample size, which is equal to the number of learners in the class. The required size is estimated from questionnaire data by making use of item response theory. It turns out that in classes that consist of 80 learners, no more than half could convince themselves that the theorem is reliable. Therefore, it is important to seek an activity design for which a larger sample is available.

Key words: Clicker, classroom response system, classroom experiment, central limit theorem, statistics education, item response theory.

## Prospects for Statistics Education through JINSE

In this article, we describe the structure of the original JINSE (Japanese Inter-university Network for Statistical Education) founded in 2012, followed by an introduction to extended JINSE (Japanese Inter-organizational Network for Statistics Education), founded in 2017.

Key words: Statistics education, quality assessment.