# Proceedings

• ### Didactical phenomenology of probability

This research is inspired by the first book in the series launched by Reidel on mathematical education. Freudenthal (1983) expounds his philosophical approach in great detail considering many topics in mathematics but excluding (perhaps surprisingly) probability. The paper is presented in three parts which are kept succinct. After showing the relevance of didactical phenomenology, a perspective on approaches to probability is given as a framework for the experimental research which has been undertaken.

• ### Appropriate teaching and learning of stochastics in the middle grades (5-10)

We will present and discuss the outlines of a curriculum for stochastics instruction in the middle grades. Four criteria for a sequence of study are analyzed, and six phases of learning are described.

• ### Difficulties in learning probability and statistics

In the literature on education in probability and statistics, different issues of difficulty have been addressed rather independently by individuals from three different disciplines: college statistics faculty, specialists in pre-college mathematics education, and psychologists. The main contributions of the literature in these three disciplines are described, and a list of areas of difficulty students have in learning probability and statistics is provided, based on this literature. Implications are suggested for teaching and for future research.

• ### Teaching statistics through data analysis

In what follows I will summarize the pros and cons of three approaches to the use of data analysis in teaching introductory level statistics courses. Using data analysis as a learning tool to lead students to an understanding of the statistical principles on which various analytic techniqwues are based is important. This paper summarizes the pros and cons of three approaches to the use of data analysis in teaching introductory level statistics courses. These approaches involve the use of large batch-oriented statistical packages, interactive analysis programs, or simulations based on spreadsheets.

• ### The use of counterexamples in learning probability and statistics

Many of the lectures here expressed their opinion that the primary task of statistics departments is to produce truly professional statisticians. However at least a part of the statisticians must have a serious mathematical background especially in probability theory, stochastic processes and mathematical statistics. The new term stochastics is very suitable for these three disciplines. Scientists working in the field of stochastics will be called stochasticians. It is obvious that the stochasticians are educated at the mathematics departments of universities. So, the main problem is how to organize the teaching process for the students in order to produce good statisticians and stochasticians who would be able to solve problems arising in the real world as well as other purely theoretical problems.

• ### Children's understanding of randomness: Report of a survey of 1600 children aged 7-11 years

This paper reports on some aspects of research carried out in 1986 using 1600 Primary school children in mixed ability classes in state schools in a small Leicestershire town. The subjects, aged between 7:9 and 11:9 were give two untimed class tests which together took from 40 to 55 minutes to administer. All questions were read out to the subjects. The first test was concerned with concepts of randomness, the second with comparison of odds. Results indicate that young children do have a sound conceptual awareness of randomness.

• ### Conditional probabilities: Insights and difficulties

Conditional probabilities play a central role in the process of inferring about the uncertain world. The formal definition of P ( A / B ) is easy and poses no problems. However, upon careful probing into students' ideas of conditional probabilities, some misconceptions and fallacies are uncovered. In this paper I wish to discuss three issues involving conditional probabilities that I believe require serious consideration and clarification by students and by teachers of probability. These issues are: Interpreting conditionality as causality, problems with defining the conditioning event, and confusion of the inverse.

• ### Revising probabilities according to new information: A fundamental stochastic intuition

In what follows I will try to sketch some phenomena of misunderstanding ideas of probability, and give some comments on the interplay between mathematics and intuitions which I think represents the origin of lack of comprehension. A brief overview of the favor concept should enable the impression that by way of teaching this concept probabilistic reasoning could be improved.

• ### Stochastics at the school level in the age of the computer

In this paper, two examples will be used to demonstrate the flavor of a computer oriented approach to the teaching of stochastics at the school level.

• ### Optimum balance between statistical theory and applications in teaching

As Director of Research and Training at the Indian Statistical Institute for over 35 years, I had the opportunity to develop and institute a wide variety of educational and training programs in statistics at various levels: - Pre-college, undergraduate and graduate courses leading to bachelor's, master's and Ph.D. degrees. - Applied courses for research scientists working in basic disciplines like biology, psychology, sociology and economics. - Refresher and advanced courses for statisticians employed in government offices, business, industry and research organizations. - Short courses for factory workers to help in the implementation of quality control programs. - Workshops for field workers who gather information by interviewing people or by direct observation. I shall describe the efforts we have made in formulating these varied types of educational and training programs and in implementing them. I hope my experience will be of some use to others engaged in these endeavours.