It is not the purpose of this paper to delve into the reasons why the particular software being used may or may not be effective, although this is in itself an extremely important issue. Our purpose is to suggest a rationale as to why computer based simulations are not as helpful as we might suppose, and to propose an alternative path leading to statistical inference, which potentially avoids this problem.
The Bayesian approach shall serve us in this respect: which are the advantages and drawbacks of such a model, mainly with regard to a better understanding for stochastics education? This question refers to two different aspects: to both the exemplary use of such an approach in instruction, and to the benefits and more comprehensive knowledge resulting in principle from such a didactical way of phrasing the question. Accordingly, and from an educational perspective, this is not simply a matter of deciding whether the Bayesian approach is right or wrong - i.e. of contributing to the controversy about the subjective and the objective concept of probability - but rather this debate is intended to help us obtain new insights into the relationship between probability theory and statistics which are not confined to stating either a strict separation, or an identity, between probability theory and statistics.
In this paper, we will discuss the types of misconceptions that arise from students' responses to the five problems. Then we will consider the implications of these misconceptions for the teaching of probability and statistics, and suggest some approaches to probability that may be useful for confronting the misconceptions that our students possess.
There is a growing feeling in the statistical community that significant changes must be made in statistical education. Statistical education has traditionally focused on developing knowledge and skills and assumed that students would create value for the subject in the process. This approach hasn't worked. It is argued that we can help students better learn statistical thinking and methods and create value for its use by focusing both the content and delivery of statistical education on how people use statistical thinking and methods to learn, solve problems, and improve processes. Learning from your experiences, by using statistical thinking in real-life situations, is an effective way to create value for a subject and build knowledge and skills at both the graduate and undergraduate levels. The learnings from psychology and behavioral science are also shown to be helpful in improving the delivery of statistics education.
Over the past several years, we have been working on the Reasoning Under Uncertainty (RUU) project, whose goal has been to develop and test a computer-supported environment in which high school students could learn how to think in probabilistic and statistical terms. The central ideas of the project are to use the computer as a tool for data gathering, manipulation, and display, and to have students investigate questions that are meaningful to them. In contrast to the usual emphasis in statistics courses on formulas and computational procedures, RUU emphasizes reasoning about statistical problems. We believe that students should be able to engage in statistical reasoning about uncertainties that either they or society face. Such a course conforms well to the National Research Council's suggestion that "elementary statistics and probability should now be considered fundamental for all high school students" and to the new NCTM guidelines for including probability and statistics in the elementary and secondary curriculum.
Searle (1989) cited the need for caution when using statistical computing packages. He suggested that classroom time is best spent on learning the why and when of statistics and that the how is unworthy of academic credit. We must not let misplaced caution cause us to lose this additional opportunity to educate students in the proper use of statistical methods. Teaching portions of statistical computer packages can give students an appreciation of the knowledge and care that must go into using techniques that are not covered in the classroom. Equally important, we must not leave the teaching of statistical computer packages to nonstatisticians.
We statisticians have an opportunity to help our nation regain a leadership role in international markets, but we will have to change the way we teach statistics before we can do our part. I have some suggestions for changes in how we teach Statistics 101.
The "problem of three prisoners", a counterintuitive teaser, is analyzed. It is representative of a class of probability puzzles where the correct solution depends on explication of underlying assumptions. Spontaneous beliefs concerning the problem and intuitive heuristics are reviewed. The psychological background of these beliefs is explored. Several attempts to find a simple criterion to predict whether and how the probability of the target event will change as a result of obtaining evidence are examined. However, despite the psychological appeal of these attempts, none proves to be valid in general. A necessary and sufficient condition for change in the probability of the target event, following observation of new data, is proposed. That criterion is an extension of the likelihood-ratio principle (which holds in the case of only two complementary alternatives) to any number of alternatives. Some didactic implications concerning the significance of the chance set-up and reliance on analogies are discussed.
Rather than talking about interesting students I have met over the year, this talk centers instead on how we can interest students in statistics. Two possible aspects of this issue are: a. how we can get more students to take one or more courses in statistics, b. how we can get more students to go into graduate studies in statistics.
This article is concerned with a recent debate on the generality of utility theory. It has been argued by Lopes that decisions regarding preferences between gambles are different for unique and repeated gambles. The present article provides empirical support for the need to distinguish between these two. It is proposed that violations of utility theory obtained under unique conditions, cannot necessarily be generalized to repeated conditions.