# Teaching

• ### Computer algorithms for the classical distribution functions

Access to a collection of computer programs for the classical distribution functions, particularly if these can be readily used interactively by any student, is an important teaching tool for teachers of probability and statistics. The availability of such a collection allows the teacher and student to concentrate on the concepts and development of probability and statistics with little if any emphasis on the details of determining probabilities from tables. Algorithms are presented that provide a useful array of methods for evaluating the classical distribution functions.

• ### Use of handheld programmable calculators in statistics courses for nontechnical students

The usefulness of stochastic models and statistical inferences in a wide range of disciplines has gradually led to the inclusion of probability and statistics courses in many academic curricula. Unfortunately, the required course in statistics is often the most disliked and feared course in a student's curriculum. This is especially the case for "nontechnical" students who generally have limited mathematical capabilities. Instructors of statistics courses for such students often feel they must devote a significant proportion of their instruction to improving the students' algebraic and computational skills. In what follows, I shall report on a program we have been using for Management Science students at the Naval Postgraduate School in Monterey, California. In this program, Texas Instruments T159 calculators are issued to all students entering the Management Science (MS) curriculum, and these personal calculators are used by the students throughout their six quarter program leading to a Master's degree in Management Science.

• ### Simulation of games studied in the seventeenth and eighteenth centuries

Today, I would like to present four simulations of games from the seventeenth and eighteenth centuries, realized on the screen of a micro-computer which will eventually provide numerical results.

• ### Case studies for an adequate understanding and interpretation of results by statistical inference

On the whole, case studies (and exemplary project studies) can permit the perception that not only knowledge of statistics (in the mathematical-technical sense) but especially expert knowledge in the field of application, of the problem at hand, and some "meta"-knowledge about possibilities and limitations of statistical methods in question will and should play a decisive role to compete in situations with uncertainty. The intuitive way to teach statistics should be by means of case studies. Case studies should have the same place in teaching statistics as simulation has in elementary probability.

• ### Is a scientific legend a comprehensive case study?

Students often perceive statistics as an overabundance of seemingly unconnected methods and problems. This problem could be eliminated if statistics were presented as a scientific investigation of a single comprehensive real-life case study, which we conditionally call a "scientific legend".

• ### The teaching of probability and statistics in schools: Issues for interdisciplinary reflection

In the following discussion several issues are presented for interdisciplinary reflection on the teaching of Probability and Statistics in preparatory school. they are set out according to a scheme which links this particular subject, with, in the first place, other disciplines - mathematics, physical-natural sciences, humanities and social sciences; secondly, with the variables of individual learning and modes of scholastic organization; and finally, with environmental variables (see scheme 1). The scheme is organized around problems and disciplines involved in the didactic complex and incorporates many features of the learning-teaching process. Some of the issues originate in the Italian reality; they may also be valid in other national contexts.

• ### The teaching of sample design to government statisticians from developing countries

This paper discusses the education and training given to participants specializing in Sampling and Statistical Methods at the ISPC. This education and training in survey sampling is conducted through linkage of sampling concepts with the various other survey-related skills and fields. This means, among other things, that it is not sufficient to merely offer a course on sampling theory when the objective is to train participants to be functioning sampling practitioners and technicians. While this paper primarily discusses the training in sampling conducted at the ISPC for statisticians from developing countries, it is nevertheless felt that most of the remarks are relevant to the teaching of survey sampling in general.

• ### Teaching of survey sampling

Sampling techniques may be considered as technology for information production needed for planning socio-economic development. In teaching the sampling course, a balance between sampling theory and its application is required to be maintained. This can be achieved only if a course on design follows practical exercises based on live data. Demonstrations of conduct of actual surveys by involving students from the initial stage of planning to the final stage of reporting the results may be considered as an integral part of the course. A proper sequence in planning the course may be helpful from the communication point of view. Adequate emphasis on the role of sampling and non-sampling errors in interpreting the survey results may be laid. To maximise the utilities of training and research in sampling techniques, there is a need of developing an integrated programme of teaching, research and extension.

• ### The design and analysis of experiments - What is it about?

Basic definitions are given. Then the subject is divided into six "components", which are discussed in turn: I: Planning, design and layout. II: Management of the experiment or experiments. III: Data recording. IV: Scrutiny and editing of the data. V: Computational analysis. VI: Interpreting and reporting the results. Over-theoretical, over-mathematical teaching of the subject is criticized. The importance of practical considerations is stressed.

• ### Probability games

There is considerable, good evidence that games can be effective tools in teaching mathematics and that all games are not equally effective. One key to effectiveness may be the degree to which the mathematics content is involved in the play of the game, since there would seem to be a corresponding involvement of the game players with that content. There is clear evidence that probability can be taught through games, but the role of students' strategy use may be important for understanding the effects of these games. Although only limited attention has in the past been given to identification of students' strategies, techniques have now been developed which may allow relating strategy use to learning.