Estimating Tanks - Communication in Mathematical Statistics

In this chapter we present a model for using case studies for the core of an undergraduate theoretical statistics course. These case studies have more depth than most examples found in typical mathematical statistics texts. Each case study provides a real-world question to be addressed as well as background information on the question, data to address the problem, and suggestions for investigating the problem. An important goal is to encourage and develop statistical thinking. This chapter provides both a sample case study on quality control and analysis of variance and a directed project on experimental design that includes a discussion of how we have changed the class to fit these activities into the course. In essence, the case studies become the centerpiece of the course, and as a result, the curriculum, lectures, and assignments are significantly different from a traditional mathematical statistics course.

We should stick to the demand for traction the principle of probability theory and mathematical statistics course, keep the course of sustainable development, adhere to the quality as the core principles, and ensure the coordinated development of curriculum construction. There are many problems in the construction of curriculum system for the probability theory and mathematical statis tics course, such as, the practical features need to strengthen, the structure of curriculum content should be expanded, the teaching quality of teachers need to strengthen, the teaching methods need to reform and other issues. Aiming at the above problems, put forward the reform of the following measures: around the goal of innovation training on talents, strengthen the practical characteristics of course system; facing the transformation of new challenges, broaden the structure content of the curriculum system in universities; facing the transformation of new challenges, improved the tea chers' ability and quality cultivation; facing the transformation of new challenges, improved method in the course teaching mode. And these measures will be applied to the actual teaching, must pay much effort to the probability theory and mathematical statistics course construction, make contribution to promote transformation and development pattern of innovation talent training.

With the rapid development of higher education in China, colleges and universities are facing new challenges and impacts in talent training. Probability Theory and Mathematical Statistics is one of the important courses in higher education for science and engineering majors and economics and management majors. Its critical role in cultivating students’ thinking skills and improving their problem-solving skills is self-evident. Course ideological and political education construction is an important link in college talent training work. Combining ideological and political education with course teaching can help students establish correct value concepts and play a certain role in improving their comprehensive ability and quality. At present, the construction of ideological and political education in the Probability Theory and Mathematical Statistics course still faces some problems, mainly manifested in the lack of attention paid by teachers to course ideological and political education, insufficient exploitation of ideological and political elements, and the simplification of ideological and political education implementation methods. In order to comprehensively deepen the construction of course ideological and political education in line with the actual needs of Probability Theory and Mathematical Statistics course teaching, we should strengthen the construction of teacher teams, improve teachers’ ability to carry out course ideological and political education, integrate educational resources, develop educational resources for ideological and political education, and innovate teaching methods to improve the overall effect of ideological and political education integration.

In the United States, a course in mathematical statistics is a part of the undergraduate curriculum in many departments of mathematics. The traditional course in mathematical statistics, it seems, has not really ‘caught on’ with large numbers of students enrolled in it. In this paper an alternative approach to the course is presented. The approach was implemented in an experimental course at Salisbury State College. Observations concerning the advantages and disadvantages of the method are given. Instructors of courses in mathematical statistics might find the approach appropriate for clarifying concepts in the subject.

In this department The American Statistician publishes articles, reviews, and notes of interest to teachers of the first mathematical statistics course and of applied statistics courses. The department includes the Accent on Teaching Materials section; suitable contents for the section are described under the section heading. Articles and notes for the department, but not intended specifically for the section, should be useful to a substantial number of teachers of the indicated types of courses or should have the potential for fundamentally affecting the way in which a course is taught. In this department The American Statistician publishes articles, reviews, and notes of interest to teachers of the first mathematical statistics course and of applied statistics courses. The department includes the Accent on Teaching Materials section; suitable contents for the section are described under the section heading. Articles and notes for the department, but not intended specifically for the section, should be useful to a substantial number of teachers of the indicated types of courses or should have the potential for fundamentally affecting the way in which a course is taught.

Under the background of the large-scale popularization of “Internet + Education”, personalized education mode based on artificial intelligence and other information technologies has become the trend of teaching reform development. In this paper, we have collected and pre-processed students’ learning behaviors during the teaching of Probability Theory and Mathematical Statistics courses, and established a large biological database based on these behaviors. The features of learning behaviors are extracted using the SHAP method, and the features are fused and processed by the MFCNN module. The Bi-LSTM method is used to warn students of academic risks. Finally, we construct a visualization system to assist in teaching Probability Theory and Mathematical Statistics. The results of practical application show that with the assistance of the system, the average grade of the students’ Probability Theory and Mathematical Statistics course progresses quite obviously, the post-test grade is significantly higher than the pre-test grade, and the student’s ability of critical reflection also improves. In addition, a significant difference (p<0.05) was observed between the students of the experimental class and those of the control class in the learning motivation posttest. This paper provides new ideas for research related to the big database of biology and academic early warning in teaching, which contributes to the further promotion of teaching reform.

With the massive emergence of new technologies empowered by big data and technology, the four original disciplines of engineering, agriculture, medicine and liberal arts have to keep up with the times and integrate big data, artificial intelligence and other related contents. New engineering, new agriculture, new medicine and new liberal arts came into being, the four new disciplines focus on professional cross-cutting practical [1], but also to improve the quality of talent training creative exploration, in the near future the layout of higher education disciplines or a major reshuffle will come. Industrial transformation and upgrading in the context of the national development of the economy is often heard by us, people need to study, digest, reform and innovate their own technology system on the basis of the introduction of advanced technology. Similarly the transformation and upgrading of disciplines in the context of the big data era is also imperative, various disciplines will develop in the direction of convergence and intersection, and disciplines can no longer be siloed disciplines, they all need to cross-fertilise with new big data-related knowledge to keep up with the times. Probability Theory and Mathematical Statistics is one of the required courses for undergraduates of statistics, big data and computer science majors, which are all related engineering and science majors under the construction of new engineering disciplines, while computers, the Internet, and artificial intelligence are driving educational changes and innovations, so the probability theory and mathematical statistics course should be integrated into the theories of the new engineering discipline to carry out innovation and reform. Through the restructuring of the teaching content to add the big data background of some of the methods to deal with the problem, so that students can use the idea of statistical modelling to analyze the economic and social stochastic phenomena, and can develop a pragmatic spirit based on data [3]. This paper will be from the reform of the teaching mode, teaching content innovation and restructuring, reform of the assessment method and the promotion of the four aspects of the teaching model to develop the probability theory and mathematical statistics in the four new disciplines under the background of the reform and innovation of the curriculum research.

Considerable research suggests that traditional assessments in higher education are outdated, and newer, more authentic assessment strategies should be pursued. One such form of authentic assessment is a portfolio of learning evidence, and another is the oral interview or oral assessment. However, the portfolio and interview are not only methods of assessment, but also primary drivers of learning and creative thinking. In statistics and data science education, the portfolio of learning evidence and interview assessment have not been implemented widely, although some authors have explored the implications of assessments. This mixed-methods study examines the interplay between the use of portfolios and interview assessments in a mathematical statistics course and Fink’s framework for significant learning. The study finds that there are indeed numerous advantages that can be gained from using these novel methods instead of traditional learning and teaching methods.

The purpose of this study was to identify Higher Order Thinking Skills (HOTS) in mathematics education study program students in the Mathematical statistics course. HOTS in this study is based on the Revised Bloom Taxonomy which includes analyzing, evaluating and creating, especially in the dimensions of factual knowledge and conceptual knowledge. This research is a qualitative descriptive study. The research subjects were 35 students of the fourth semester mathematics education study program of Al Asyariah Mandar University. The data collection techniques such as essay test and each of which consisted of 3 items of dimension of procedural knowledge and conceptual knowledge, which was C4 (analyzing), C5 (evaluating), C6 (creative) level. HOTS data were obtained from test answers given to students and then analyzed descriptively. HOTS criteria include low, medium, and high. The results of the research on the factual knowledge dimension with a C4 level (analyzing) of 6.7 (medium), a C5 level (evaluating) of 4.6 (low), and a C6 level (creating) of 4.3 (low). Whereas in the conceptual knowledge dimension with a C4 level (analyzing) of 6.9 (medium), a C5 level (evaluating) of 4.7 (low), and a C6 level (creating) of 4.1 (low). In general, students’ HOTS are in low criteria.

Taking the online teaching of probability theory and mathematical statistics course as example, this paper systematically analyzes the development background and process of the network teaching platform based on Android. Firstly, this paper introduces the software development environment and system function requirements, and provides the core technology and backbone architecture of the system. Then, it introduces the overall design architecture of the software, system function module design, database design, as well as the software interface function and implementation process. The main technical realization includes the development of Android system application software, the development and application of Ajax, OAuth authentication, SQLite application, etc. Finally, through the design and test of the interactive communication platform based on Android system, the implementation of the mobile learning platform is explained and tested in technical details. The test results show that the prototype design of the mobile learning platform achieves the expected goals.

This paper takes Probability Theory and Mathematical Statistics course as an example, and takes WeChat public platform as the carrier, discusses the blended ratio of time between online learning and face-to-face teaching, and makes a study on teaching effect by using group comparison method. The results show that blended ratio 2: 6 is significantly better than 1: 6, 3: 6 and 0: 6 for online learning and face-to-face teaching. The results have some significance for improving the utilization rate of existing educational resources, allocating teaching time rationally and improving teaching quality.

The purpose of this research is to analyze the difficulty of students in solving problems related to mathematical creative thinking ability comprehensively as a result of the implementation of PACE (Project, Activity, Cooperative learning, Exercise) model and conventional learning in Mathematical Statistics Course. This research was a qualitative research. The subjects in this research were students of Mathematics Education Program who took Mathematical Statistics Course at one of the private universities in East Jakarta. This research used purposive sampling and various instruments. They were test of mathematical prior knowledge (MPK), test of mathematical creative thinking ability (MCTA), observation sheet, interview sheet, and researcher. The data of this research was collected using triangulation techniques. The result of this research show that students are still experiencing difficulties based on MPK level and overall in solving problems related to mathematical creative thinking ability in both learning (PACE model and conventional). However, the difficulty of students who have obtained PACE Model learning is lower than students who have obtained conventional learning. The most of difficulty of students in both learning (PACE model and conventional) is in indicator of ‘originality’. Keywords: mathematical creative thinking ability, Mathematical Statistics, PACE model

Alternative grading methods, such as standards-based grading, provide students multiple opportunities to demonstrate their understanding of the learning outcomes in a course. These grading methods allow for more flexibility and help promote a growth mindset by embracing constructive failure for students. Implementation of these alternative grading methods requires developing specific, transparent, and assessable standards. Moving away from traditional methods also requires a mindset shift for how both students and instructors approach assessment. While providing multiple opportunities is important for learning in any course, these methods are particularly relevant to an upper level mathematical statistics course where topics covered often provide an additional challenge for students as they lie at the intersection of both theory and application. By providing multiple opportunities, students have the space for constructive failure as they tackle learning both a conceptual understanding of statistics and the supporting mathematical theory. In this article we share our experiences—including both challenges and benefits for students and instructors—in implementing standards-based grading in the first semester of a mathematical statistics course (i.e., focus primarily on probability). Supplementary materials for this article are available online.

Purpose of the study: Mathematical problem-solving ability is a crucial skill influenced by various factors, including personality types. This study aims to analyze students' mathematical problem-solving abilities based on extrovert and introvert personality types in the MBTI framework. Methodology: This research was descriptive qualitative research. Data were collected through an MBTI questionnaire to determine students' personality types and a mathematical problem-solving test to assess their abilities. The participants consisted of 11 undergraduate students from the Mathematics Education Department at Institut Agama Islam Negeri Kerinci, who were enrolled in the Mathematical Statistics course. Main Findings: Extroverted students tend to excel in understanding problems and planning solutions; however, they are more likely to overlook careful execution. In contrast, introverted students struggle with planning and do not always review the solutions they have produced. It can be concluded that extroverted students have better mathematical problem-solving abilities than introverted students in the mathematical statistics course. These results highlight the role of personality in cognitive strategies and error patterns during problem-solving. Tailored instructional approaches could help both extroverted and introverted students optimize their problem-solving abilities. The small sample size and single-institution context may limit the generalizability of these findings. Future research is recommended to expand on these insights. Novelty/Originality of this study: This study fills the gap by conducting an in-depth analysis of specific problem-solving behaviors, cognitive strategies, and error tendencies associated with extroverted and introverted students based on the MBTI framework, thereby offering a richer understanding of how personality types affect problem-solving ability.

Statistical power is an important topic taught in most graduate-level and undergraduate-level mathematical statistics courses, but it is often difficult to understand conceptually. Visualizing the power curve, sampling distributions, and how they interact can help students more easily conceptualize power, but the creation of such visuals can be difficult and time-consuming. Interactive web applications provide a way for students to dynamically visualize power, and many web applications for understanding power exist. However, most of these applications assume samples are drawn from a Normal population, concern only the sample mean, and/or were created for introductory classes. In this paper, we describe a web application suitable for undergraduate-level and graduate-level mathematical statistics courses that was created to allow users to visualize the complex relationships underlying power for multiple different statistics and population distributions (available at https://powerapp.shinyapps.io/powerapp/); source code is provided for instructors who wish to modify the application. Our experience implementing this application across two different semesters is also discussed, and example activities are provided in the appendix.