Literature Index

Students in a small experimental design class obtained information about statistical and research applications concerning a variety of products advertised by different companies. The resulting data were perceived to have several advantages for the students: (a) it made collecting and interpreting data more interesting and less mysterious, (b) it helped them to understand how research design and statistics are used in real-life situations, and (c) it helped them to make more discerning judgments about advertisers' claims for their products.

This article describes the virtual manufacturing environment Watfactory (freely available at http://services03.student.math.uwaterloo.ca:8080/~stat435/login.htm) and discusses its use in teaching process improvement. Watfactory provides a rich and realistic simulation of a manufacturing process and is accessed through a website requiring no software other than a Web browser. With Watfactory, students select, plan, and analyze the data from a sequence of empirical investigations of many different types, with the ultimate goal of reducing variation in the process output. We have found that using Watfactory addresses many shortcomings in traditional teaching methods for both undergraduate and industrial short courses.

In this paper we report the results from a major UK government-funded project, started in 2005, to review statistics and handling data within the school mathematics curriculum for students up to age 16. As a result of a survey of teachers we developed new teaching materials that explicitly use a problem-solving approach for the teaching and learning of statistics through real contexts. We also report the development of a corresponding assessment regime and how this works in the classroom.<br><br>Controversially, in September 2006 the UK government announced that coursework was to be dropped for mathematics exams sat by 16-year-olds. A consequence of this decision is that areas of the curriculum previously only assessed via this method will no longer be assessed. These include the stages of design, collection of data, analysis and reporting which are essential components of a statistical investigation. The mechanism outlined here could provide some new and useful ways of coupling new teaching methods with learning and doing assessment - in short, they could go some way towards making up for the educational loss of not doing coursework. Also, our findings have implications for teaching, learning and assessing statistics for students of the subject at all ages.

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.