Sampling distributions for introductory statistics students using internet polling software

The topic of sampling distributions is the first source of considerable difficulty for introductory statistics students. In this article, an active learning idea for an introduction to sampling distributions is presented. The activity uses real data collected from the class, and the results are used to generate sampling distributions using electronic communication of sample statistics from student mobile telephones.     

概率论与数理统计课程改革的创新机制

针对课程改革的目的,结合教学实践,就概率统计课程建设和教学改革的必要性进行综合分析并主张：通过讲述概率统计理论发展史,引导学生明确学习重点;借助多媒体教学,整合教学大纲内容,系统教学;将理论与实际相联系,激发学生学习兴趣;立足基本理论,开设统计学软件实验课程．     

概率统计类课程多维立体教学的实践与认识

针对概率统计类课程不同于其它确定性数学的特点,作者从教学内容及教学方法两个方面进行了探索与实践.在教学内容上,强调点面结合,拓展一些现代的与本学科密切有关的面上知识.在教学方法上,强调多维立体教学方式,即结合多媒体课件,案例教学,软件演示,实验教学,实现以教师为主导,学生为主体的主客体相结合的教学思想,以期达到使学生受益最大化的目标.     

Developing statistical modelers and thinkers in an introductory, tertiary-level statistics course

While models are an important concept in statistics, few introductory statistics courses at the tertiary level put models at the core of the curriculum. This paper reports on a radically different approach to teaching statistics at the tertiary level, one that uses models and simulation as the organizing theme of the course. The focus on modeling and simulation??along with inference??was facilitated by having students use TinkerPlots? software for all modeling and analysis. Results from a 3-month teaching experiment suggest that a course focused on modeling and simulation through randomization and resampling methods in which students learn to think using a powerful and conceptual modeling tool can foster ways of thinking statistically. Furthermore, such an approach seems to help students develop experiences with and appreciation for the science and practice of statistics.     

Academics’ perceptions of the use and relevance of software in quantitative and financial disciplines

Software may be used in university teaching both to enhance student learning of discipline-content knowledge and skills, and to equip students with capabilities that will be useful in their future careers. Although research has indicated that software may be used as an effective way of engaging students and enhancing learning in certain scenarios, relatively little is known about academic practices with regard to the use of software more generally or about the extent to which this software is subsequently used by graduates in the workplace. This article reports on the results of a survey of academics in quantitative and financial disciplines, which is part of a broader study also encompassing recent graduates and employers. Results indicate that a variety of software packages are in widespread use in university programmes in quantitative and financial disciplines. Most surveyed academics believe that the use of software enhances learning and enables students to solve otherwise intractable problems. A majority also rate spreadsheet skills in particular as very important for the employability of graduates. A better understanding of the use of software in university teaching points the way to how curricula can be revised to enhance learning and prepare graduates for professional work.     

Toward Understanding the Role of Technological Tools in Statistical Learning

This article begins with some context setting on new views of statistics and statistical education. These views are reflected, in particular, in the introduction of exploratory data analysis (EDA) into the statistics curriculum. Then, a detailed example of EDA learning activity in the middle school is introduced, which makes use of the power of the spreadsheet to mediate students' construction of meanings for statistical conceptions. Through this example, I endeavor to illustrate how an attempt at serious integration of computers in teaching and learning statistics brings about a cascade of changes in curriculum materials, classroom praxis, and students' ways of learning. A theoretical discussion follows that underpins the impact of technological tools on teaching and learning statistics by emphasizing how the computer lends itself to supporting cognitive and sociocultural processes. Subsequently, I present a sample of educational technologies, which represents the sorts of software that have typically been used in statistics instruction: statistical packages (tools), microworlds, tutorials, resources (including Internet resources), and teachers' metatools. Finally, certain implications and recommendations for the use of computers in the statistical educational milieu are suggested.     

Toward Understanding the Role of Technological Tools in Statistical Learning

This article begins with some context setting on new views of statistics and statistical education. These views are reflected, in particular, in the introduction of exploratory data analysis (EDA) into the statistics curriculum. Then, a detailed example of EDA learning activity in the middle school is introduced, which makes use of the power of the spreadsheet to mediate students' construction of meanings for statistical conceptions. Through this example, I endeavor to illustrate how an attempt at serious integration of computers in teaching and learning statistics brings about a cascade of changes in curriculum materials, classroom praxis, and students' ways of learning. A theoretical discussion follows that underpins the impact of technological tools on teaching and learning statistics by emphasizing how the computer lends itself to supporting cognitive and sociocultural processes. Subsequently, I present a sample of educational technologies, which represents the sorts of software that have typically been used in statistics instruction: statistical packages (tools), microworlds, tutorials, resources (including Internet resources), and teachers' metatools. Finally, certain implications and recommendations for the use of computers in the statistical educational milieu are suggested.     

高级统计学的教学实践与思考

基于教学实践和调查问卷对研究生高级统计学的各个教学环节进行了探讨和分析.区别于本科生的统计学教育,在研究生的统计教学中,不仅要介绍统计方法,而且还要通过更加有效的手段加强研究生对统计分析方法的整体认识和应用能力.教学实践和对调查问卷的统计分析结果表明:将传统的解释性教学和演示性教学与现代的具有建构主义特征的发现学习相结合将有助于培养研究生的学习能力和科研能力.     

A conceptual pathway to confidence intervals

Finding ways for the majority of students to better understand conventional normal theory-based statistical inference seems to be an intractable problem area for researchers. In this paper we propose a conceptual pathway for developing confidence interval ideas for the one-sample situation only from an intuitive sense to bootstrapping for students from about age 14 to first-year university. We make the case that conceptual development should start early; that probability and statistical instruction should change so that both orientate students towards interconnected stochastic conceptions; and that the use of visual imagery has the potential to stimulate students towards such a perspective. We analyse our conceptual pathway based on a theoretical framework for a stochastic conception of statistical inference based on imagery and some research evidence. Our analysis suggests that the pathway has the potential for students to become conversant with the concepts underpinning inference, to view statistics probabilistically and to integrate concepts into a coherent comprehension of inference.     

Every rose has its thorn: secondary teachers’ reasoning about statistical models

Statistical modeling is a core component of statistical thinking and has been identified by several countries as a curricular goal for secondary education. However, many secondary teachers have minimal preparation for teaching this topic. The goal of this research study is to learn about teachers’ perceptions of the role statistical models play in statistical inference and how these perceived purposes affect their reasoning about statistical models and inference. Problem-solving interviews were conducted with four in-service teachers who had recently taught a modeling and simulation-based introductory statistics course. Teachers’ responses suggest they may not see modeling variation as the primary purpose of statistical modeling and instead substitute two other purposes: making a decision and replicating the data collection process. Suggestions for how to build on teachers’ transitional conceptions and refocus attention on modeling variation are discussed.     

浅谈蒙特卡罗法在概率统计教学中的应用

在概率统计教学中利用蒙特卡罗法设计适当的模拟实验,结合多媒体在课堂教学中实时演示,能很好地加深学生对概率统计概念、思想的理解,进而培养学生的统计思维能力.     

The incoming statistical knowledge of undergraduate majors in a department of mathematics and statistics

Studies have shown that at the end of an introductory statistics course, students struggle with building block concepts, such as mean and standard deviation, and rely on procedural understandings of the concepts. This study aims to investigate the understandings entering freshman of a department of mathematics and statistics (including mathematics education), students who are presumably better prepared in terms of mathematics and statistics than the average university student, have of introductory statistics. This case study found that these students enter college with common statistical misunderstandings, lack of knowledge, and idiosyncratic collections of correct statistical knowledge. Moreover, they also have a wide range of beliefs about their knowledge with some of the students who believe that they have the strongest knowledge also having significant misconceptions. More attention to these statistical building blocks may be required in a university introduction statistics course.     

Toward a Common Framework for Statistical Analysis and Development

We develop a general ontology of statistical methods and use it to propose a common framework for statistical analysis and software development built on and within the R language, including R's numerous existing packages. This framework offers a simple unified structure and syntax that can encompass a large fraction of existing statistical procedures. We conjecture that it can be used to encompass and present simply a vast majority of existing statistical methods, without requiring changes in existing approaches, and regardless of the theory of inference on which they are based, notation with which they were developed, and programming syntax with which they have been implemented. This development enabled us, and should enable others, to design statistical software with a single, simple, and unified user interface that helps overcome the conflicting notation, syntax, jargon, and statistical methods existing across the methods subfields of numerous academic disciplines. The approach also enables one to build a graphical user interface that automatically includes any method encompassed within the framework. We hope that the result of this line of research will greatly reduce the time from the creation of a new statistical innovation to its widespread use by applied researchers whether or not they use or program in R.     

Problems and Possibilities with Teaching Introductory Statistics to Social Scientists

As undergraduates, many social scientists take only one introductory course in statistics, and this paper concentrates mainly on the various issues involved in teaching such a course. Among the topics discussed are: the aims of the course; the problem of students’ varying mathematical backgrounds and abilities, and in particular the very low level of mathematics of a significant number of them; the question of a common course for all social sciences, and the differing needs of the various subjects; who should teach introductory statistics; the problem of developing students’ motivation to study statistics; the use of practical work; the possibilities of the computer; the utility of programmed texts and teaching machines. The intention of the paper is to provide a framework for the seminar by a broad review of the topics, a number of which are discussed in detail in subsequent sessions.     

Examination of the dynamic software-supported learning environment in data analysis

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.     

Identification and definition of lexically ambiguous words in statistics by tutors and students

Lexical ambiguity arises when a word from everyday English is used differently in a particular discipline, such as statistics. This paper reports on a project that begins by identifying tutors’ perceptions of words that are potentially lexically ambiguous to students, in two different ways. Students’ definitions of nine lexically ambiguous words are also collected at the beginning and end of a semester of introductory statistics study, in a complex design taking account of multiple tutors and multiple words in multiple contexts. Tutor perceptions and actual student difficulties at the beginning of a semester are compared. The lexical ambiguity associated with the word ‘significance’ is shown to be evident in students even after completing an introductory statistics course.     

Use of Demonstrations and Experiments in Teaching Business Statistics

The aim of a business statistics course should be to help students think statistically and to interpret and understand data, rather than to focus on mathematical detail and computation. To achieve this students must be thoroughly involved in the learning process, and encouraged to discover for themselves the meaning, importance and relevance of statistical concepts. In this paper we advocate the use of experiments and demonstrations as aids to achieving these goals. A number of demonstrations are given which can be used to illustrate and explain some key statistical ideas.     

From Classroom to Online Teaching: Experiences in Improving Statistics Education

This study used reflective practitioner methodology to investigate how to improve the quality of statistical education. During the study, this methodology, curricula, pedagogical practices, assessment and a framework for learning to learn statistics were all developed as means of improving the quality of statistical education. Also documented was the move from being a classroom teacher of statistics to a teacher who is developing learning resources for online delivery to students. For a classroom teacher, flexible delivery has meant drawing on the sights, sounds, movement, quiet and live shows. By contrast, the online teacher feels the constraints of translating activity based programs to technologically based programs. As more students have chosen to rely on online materials rather than classroom activities, the focus of improving quality has been extended to the enrichment of online resources, so that the learning experience is not second to that of the classroom.