The following discusses the need to include real data sets in today's statistical education.
The following discusses the need to include real data sets in today's statistical education.
The subject of this paper is the approach to teaching statistics by combining theory and simulation.
In this paper, some difficulties of learning of the students, in the environment of a small liberal arts college, are listed.
We shall present four important areas in teaching data analysis: the selection of problems and data sets; the critical concepts underlying the process of data analysis; the development of pupils' facility with a range of representations, including the role of technology; and the management of data analysis activities in the classroom.
The first part of the presentation will describe an interactive self-paced instructional program developed on the Apple Macintosh computer. A demonstration version of the program will provide illustrations of the program. Illustrations of how students' concepts of chance are solicited and challenged by the program will also be demonstrated.
This article describes a lesson that exemplifies an alternative approach to teaching introductory probability. In this approach, students learn to apply probability models to real-life situations and estimate probabilities through conducting simulations. (See NCTM [1981] for several articles on using simulations in teaching probability.) The particular activity described in this article has been used in high school and introductory college courses for which Macintosh laboratories and the simulation tool Pro Sim (1992) were available. However, it could be done using other software, or without computers, by having students model the problem by flipping coins and pooling the class's data.
Brief description of a course using computers and data examples.
Computer scientists have been designing and experimenting with interactive, graphical interfaces for several years now. Recently, educational technologists have begun to take advantage of these advances. With funding from the Applications of Advanced Technologies program in the Division of Science and Engineering Education at the National Science Foundation of group of researchers at BBN are designing and developing interactive, graphical mini-laboratories to help students develop a qualitative understanding of statistics. These Macintosh-based mini-labs allow students to explore statistical concepts and processes by manipulating graphical objects.
While solving stochastical problems one often notices a certain discrepancy between the intuitive reasoning of the person involved, and the "objective" causes given by the mathematical theory. So, the paths to follow in either direction will usually turn out to be different ones and will not always lead to the same final answer.We have the greatest difficulties to grasp the origins and effects of chance and randomness. Also, the history of probability reports some problems and paradoxical examples which support the suspicion that stochastics is a rather exceptional science even within the mathematical fields. I shall introduce and discuss a small collection of problems of that kind i.e. problems which carry certain counterintuitive aspects. My objections here are manifold. First of all, the discussion of such problems, especially in the classroom, helps (i) to clarify ambiguous stochastical situations, (ii) to understand basic concepts on this field, (iii) to interpret formulations and results. Then, we, the teachers and professionals, can use them to test our own intuitive level of understanding. Finally, as those "paradoxes" and teasers have an entertaining aspect too, we should make use of this to increase the motivation of the students occasionally. Six of these problems were chosen to be discussed in the sequel. Here, I have tried to present them in a unique form. First, the problem will be formulated, an illustration included. Then, a "hint" is given, which adds (or stresses) some information about hidden processes or about strategies, which I recommend to follow. Thirdly, one solution is outlined, although very often several different approaches are known. Where possible I have chosen the one which follows a general idea. Finally, some variations, comments and references are added.
Statistics becomes interesting to non-methodologists only when taught in a research context that is relevant to them. Real data sets supplemented by sufficient background information provide just such a context. Despite this, many textbook authors and instructors of applied statistics rely on artificial data sets to illustrate statistical techniques. In this paper, we argue that artificial data sets should be eliminated from the curriculum and that they should be replaced with real data sets. Towards this end, we describe the rationale for using real data sets and describe the characteristics that we have found make data sets particularly good for instructional use. Having learned that real data sets can present problems for instructors, we discuss the difficulties that we have encountered when using real data and some of our strategies for compensating for these drawbacks. We conclude by presenting two authentic data sets and an annotated bibliography of dozens of primary and secondary data sources.