概念图——概率统计教学的新途径

简述了概念图的起源、国内外发展现状,介绍了概念图的三个组成部分:结点、连线和连接语词,指出了相对于传统教学的概念图教学,在概率统计教学中的突出之处:概念图可作为教师教学的先行组织者;可作为学生复习时整理知识的工具;可作为教师检测学生学习的工具,提出了概率统计知识概念图制作的策略,并用实例说明了概念图应用于概率统计教学中的良好效果.     

关于事件域教学上的一些思考

事件域是概率论与数理统计中一个非常重要的定义，事件域的引入有利于规范概率论的理论．本文对事件域做了详细的分析，阐述了事件域引入的含义，解决了在教师教学和学生学习事件域时的一些疑惑．     

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.     

Students’ construction and use of statistical models: a socio-critical perspective

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

Some Thoughts on Computers and Introductory Statistics

Examination of results of an extensive project in the use of computers in undergraduate statistics reveals that the use is frequently unsuccessful because of insufficient maturity on the part of students. Nevertheless, even when students are not sufficiently mature to warrant hands‐on use, computers may still be used effectively. Indeed, when measured against the possible capabilities, instructor controlled computer usage can be just as effective as student use. An added bonus is economy of operation. Several suggestions for instructor controlled usage include graphical and numerical demonstrations, computer generated problem books with solutions, computer generated visual aids and loose‐leaf files of illustrations, examples and solutions.     

Introducing the Emerging Discipline of Statistics Education

Increasing attention has been given over the last decade by the statistics, mathematics and science education communities to the development of statistical literacy and numeracy skills of all citizens and the enhancement of statistics education at all levels. This paper introduces the emerging discipline of statistics education and considers its role in the development of these important skills. The paper begins with information on the growing importance of statistics in today's society, schools and colleges, summarizes unique challenges students face as they learn statistics, and makes a case for the importance of collaboration between mathematicians and statisticians in preparing teachers to teach students how to understand and reason about data. We discuss the differences and interrelations between statistics and mathematics, recognizing that mathematics is the discipline that has traditionally included instruction in statistics. We conclude with an argument that statistics should be viewed as a bridge between mathematics and science and should be taught in both disciplines.     

An evaluation of continuous assessment in statistics courses for social scientists

This paper reports on the use of continuous assessment in a statistics course for social scientists, in which assignments are open‐ended and use real data. The students' performance in the assignments and a formal examination are compared, and it is found that when students are assessed by a combination of continuous assessment and examination, those students who carry out the majority of the assignments score higher examination marks than do the rest.     

Generalized Cramér-von Mises tests of goodness of fit for doubly censored data

We generalize Cramér-von Mises statistics to test the goodness of fit of a lifetime distribution when the data are doubly censored. We derive the limiting distributions of our test statistics under the null hypothesis and the alternative hypothesis, respectively. We also give a strong consistent estimator for the asymptotic covariance of the self-consistent estimator for the survival function with doubly censored data. Thereby, a method, called the Fredholm Integral Equation method, is proposed to estimate the null distribution of test statistics. In this work, the perturbation theory for linear operators plays an important role, and some numerical examples are included.The author's research was supported by a Faculty Fellowship of University of Nebraska-Lincoln.     

Attitudes and perceived usefulness of statistics among health sciences students

A questionnaire was completed at the cessation of semester 2 in November 1989 by 102 postgraduate and 58 undergraduate health sciences students studying introductory statistics units. The questionnaire measured; (i) the student's attitude towards statistics, (ii) the way in which they learned statistics, (iii) the student's intention to pursue further statistics training, and (iv) the perceived usefulness of statistics in their professions. It was found that the learning of statistics would be enhanced by smaller tutorial groups, and more exposure to computer printouts to assist in interpretation of results. An emphasis on the understanding of statistics presented in journal articles should be a priority. It was also apparent that the more computer and research experience the student had prior to commencing the course, the greater the likelihood of a positive attitude towards statistics. However, both undergraduate and postgraduate students indicated that they would not enrol in an advanced biostatistics course, but would rather consult a statistician when necessary. Suggestions for more effective statistical teaching for health sciences students are also discussed.     

科学思维、科学方法在概率论与数理统计教学中的应用研究

根据我们的教学体会,讨论了在高等教育成为大众化教育的今天,在阐述科学思维、科学方法与数学思维、数学方法之间关系的基础上,如何在概率论与数理统计教学中培养大学生的科学思维和科学方法,并结合实例进行了探讨.     

Technological Tools in the Introductory Statistics Classroom: Effects on Student Understanding of Inferential Statistics

While technology has become an integral part of introductory statistics courses, the programs typically employed are professional packages designed primarily for data analysis rather than for learning. Findings from several studies suggest that use of such software in the introductory statistics classroom may not be very effective in helping students to build intuitions about the fundamental statistical ideas of sampling distribution and inferential statistics. The paper describes an instructional experiment which explored the capabilities of Fathom, one of several recently-developed packages explicitly designed to enhance learning. Findings from the study indicate that use of Fathom led students to the construction of a fairly coherent mental model of sampling distributions and other key concepts related to statistical inference. The insights gained point to a number of critical ingredients that statistics educators should consider when choosing statistical software. They also provide suggestions about how to approach the particularly challenging topic of statistical inference. This revised version was published online in July 2006 with corrections to the Cover Date.     

Perspective Functions: Properties,Constructions, and Examples

Many functions encountered in applied mathematics and in statistical data analysis can be expressed in terms of perspective functions. One of the earliest examples is the Fisher information, which appeared in statistics in the 1920s. We analyze various algebraic and convex-analytical properties of perspective functions and provide general schemes to construct lower semicontinuous convex functions from them. Several new examples are presented and existing instances are featured as special cases.     

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.     

对于工学硕士的《数理统计》教学的研究

工学硕士的《数理统计》教学 ,要根据工学硕士的培养目标和数理统计课程的特点编写教材、确定讲授内容和授课方式 .力求使学员掌握处理随机数据的思考方法 ,培养解决问题、分析问题和善于应用知识的能力 .改革《数理统计》教学 ,实现和普及多媒体教学是时代发展的趋势 .     

漫谈统计学的应用与发展(1)

本文分两部分:第一部分通过20多个实际案例说明统计学在各个领域的广泛应用,希望使更多的人对统计学有更全面、更深切的了解;第二部分简要介绍统计学在国内外的发展概况,并通过其发展进程的介绍,进一步阐明统计学的意义与价值。同时列举更多的论据说明近代统计学是当今最重要的科学技术之一。     

漫谈统计学的应用与发展(2)

本文分两部分:第一部分通过20多个实际案例说明统计学在各个领域的广泛应用,希望使更多的人对统计学有更全面、更深切的了解;第二部分简要介绍统计学在国内外的发展概况,并通过其发展进程的介绍,进一步阐明统计学的意义与价值。同时列举更多的论据说明近代统计学是当今最重要的科学技术之一。