Literature Index

This paper discusses the Illinois procedure for teaching the Monte Carlo method. Where there is limited time, or where students will not be able to grasp conventional methods firmly, we advocate teaching the Monte Carlo approach, and perhaps that only. Where there is more time, and where students will be able to well learn conventional methods, we advocate (a) teaching Monte Carlo methods at the very beginning as an introduction to statistical thinking and practice; and (b) afterwards teaching the Monte Carlo method with the conventional method as alternatives to the same problems, to help students learn analytic methods and to give them an alternative tools for their use.

The Chance and Probability Concepts Project, directed by the author at Loughborough University from 1978-81 (Green, 1982a) revealed the very limited understanding which 11-16 year old English School pupils have of probability concepts. A previous article in Teaching Statistics (Green, 1983) presented a general report of the research findings and made some recommendations. This article describes an attempt to follow up the research with practical class based activities using the computer to improve pupils' understanding.

A number of studies have reported that there is a strong tendency to ignore base-rate information in favor of individuating information, except when the former can readily be incorporated into a causal schema. In the present study, students in eight undergraduate classes were given problems in which the base-rate information was (1) either causal of noncausal and (2) either incongruent or congruent with the individuating information. In addition, twelve subjects were interviewed as they attempted to solve several versions of the one of the problems. We found (1) strong individual differences in the perceived importance of base-rate information and even in how the probability estimation task itself was interpreted, (2) little if any effect of the causality manipulations employed by Ajzen (1977) and Tversky and Kahneman (1980, and (3) greater use of base-rate information congruent with the individuating information than of base-rate information which is incongruent. The interview data indicate that it is difficult to determine from the answer alone whether or not the subject thought that the base-rate information was relevant. These data also suggest that subjects have different strategies for dealing with probability estimation problems. One of these we characterize as not only nonBayesian, but also nonprobabilistic.

Emphasis on problem solving in mathematics has gained considerable attention in recent years. While statistics teaching has always been problem driven, the same cannot be said for the teaching of probability where discrete examples involving coins and playing cards are often the norm. This article describes an application of simple probability distributions to a practical problem involving a carÕs approach to a red traffic light, and draws on the ideas of density functions, expected value and conditional distributions. It provides a valuable exercise in applying theory in a practical context.