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# Proceedings

• ### A practical approach to the central limit theorem

The most important aspect of the Central Limit Theorem is that no stipulation is made concerning the population from which one is sampling. From a pedagogical point of view, a student needs to draw a random sample from a population with a known distribution and then to compare the sample mean with the population mean to see "how close", he or she comes. Any student who does this will know the difference between the two. Students will also be led to understand the difference between the population mean and the mean of the sample means. It is not enough for a teacher to talk about these ideas - concrete experience with sampling is necessary for success. It is hoped that these experiments go some way towards enabling students to observe the central limit phenomenon operating, as well as providing empirical evidence of the truth of the theorem.

• ### Mutually exclusive and independence: Unraveling basic misconceptions in probability theory

Two central concepts in probability theory are those of "independence" and of "mutually exclusive" events and their alternatives. In this article we provide for the instructor suggestions that an be used to equip students with an intuitive, comprehensive understanding of these basic concepts. Let us examine each of these concepts in turn along with common student misunderstandings.

• ### A way of teaching significance testing

Nowadays increasingly many people are admitting and increasingly many people are claiming to be Bayesians. We have heard a lot already at this conference about Bayesian statistics. Our pupils are going to read many texts by non-Bayesians and they need to learn how to interpret the various terms involved. The concepts and methods to which those terms refer are rooted in common-sense. This emerges, I believe, when they are exposed (rather than taught) in the way I adopt and that I want to share with you. I am asking you to participate in a speeded-up version of what would take several sessions with pupils.

• ### The teaching of statistics and probability in the Italian junior high school

In 1979, the Italian Ministry of Education issued a new curriculum for the Junior High School. Among other innovations, the curriculum introduced the teaching of statistics and probability. In 1982, three years after the first decree, an exploratory survey for evaluating the reactions of teachers to the situation and the prospects for the so-called "mathematics of uncertainty and probability" was carried out in the Venetian district. A large survey was carried out in the remaining Italian districts in 1983. Examining the obtained responses, a profile of the teachers is sketched and some answers to questions we had in mind while we began the research are given: "Is statistics taught?", "Which parts of statistics and probability are taught?', "Why some teachers put off the teaching of statistics?" . In the last two paragraphs, comments on prospects for the teaching of statistics are presented together with suggestions that, if put into practice, might improve the situation described.

• ### A curriculum of probability and statistics in Italian secondary school (11-14)

No real introduction of statistics and probability into the classroom was really ever put into effect. The reasons for this are manifold. Teachers to whom the task of teaching statistics and probability is assigned, are in effect these who also have to teach mathematics, the natural sciences, physics and chemistry. In Italy there are no degree courses of a widely-varying subject matter ..., for which reason teachers come from degree courses of a much more specific nature such as mathematics, physics or chemistry. Thus we have tried to present the problem and bring the solution into prospect which, if clear and correct at the level of subject matter and didactics, would also in addition possess the characteristics for concrete realisation and hence generalisation for the greatest possible number of situations and teachers. Experimentation has also been carried out on the proposed curriculum in order to test not just certain aspects of content but also methodology and those aspects related to "time-linked resources".

• ### An exploratory survey of teachers of mathematics in the state upper secondary schools in Italy: Some results

In Italy the knowledge both of the environments in which the teachers work and of their attitudes towards the teaching of mathematics in general and of probability and statistics in particular, is in extremely short supply. The survey of which the broad outlines are presented here aims to fill this gap. The intention is to provide material for policies of reform for the school levels considered. The outstanding result is in the way it brings out the great differences, not only in basic knowledge and training of teachers, but also in their attitude towards the teaching of mathematics and in particular probability and statistics. This makes it particularly difficult to propose a standard syllabus for the subjects previously mentioned at the Upper Secondary School level., and yet this tendency of policy-makers, at least for the first to be reformed. It is quite clear that serious problems that arise at the level of teacher retraining derive from this.

• ### Behavioral statistics textbooks: Source of myths and misconceptions?

Numerous writers have argued quite forcefully that users of statistics in the behavioral sciences have been guilty of misunderstanding and misapplying even the most rudimentary concepts and procedures of applied statistics. Why is this the case when almost rudimentary concepts and procedures of applied statistics. Why is this the case when almost every university and college in America has several departments teaching applied statistics courses in the behavioral sciences? We are quick to hold researchers responsible for statistical abuses, but it may well be that researchers are only parroting what they have read or been taught. Since the most common element in almost all teaching of behavioral statistics is the textbook, could it not be that the textbook is a source of statistical "myths and misconceptions" so often denounced as misleading and inappropriate? A conceivable source of statistical misconceptions and errors occurring in the published literature, theses, and dissertations is the behavioral statistics textbook. To illustrate the nature and extent of myths and misconceptions found in some of the best-selling introductory behavioral statistics textbooks is the purpose of this paper.

• ### A national schools statistics competition

In the United Kingdom, the Statistics Prize is one of many school competitions catering to a wide range of disciplines and types of pupils. It therefore vies for interest in the schools and also among potential sponsors. This paper discusses the benefits, as well as the problems and misconceptions that have occurred since the establishment of the competition.

• ### The training of Brunel University undergraduates who intend to become statistics teachers

This paper deals with some experiences with an undergraduate course in Mathematical Studies with Education which has in recent years been offered at Brunel University, U.K. We confine ourselves in particular to a statistics input to a final year specialist module titled "Mathematical Education".

• ### Statistics and probability in the school mathematics curriculum: A review of the ASA-NCTM Quantitative Literacy Project

This paper discusses the NCTM Quantitative Literacy Project. Teachers, and then students, must be trained to make intelligent decisions based on numerical information if our society is to grow and prosper. Such training is the goal of the Quantitative Literacy Project, which is directed by a joint committee of the American Statistical Association and the National Council of Teachers of Mathematics. It is the intent of this three-year project to complete the following activities: 1. Provide guidelines on the teaching of statistics and probability within the mathematics curriculum; 2. Develop a model inservice program for training teachers in modern statistical concepts and in methods for teaching these concepts; 3. Produce curriculum materials to assist teachers in the proper presentation of statistical and probabilistic concepts, and encourage further development in natural and social sciences; and 4. Develop a mechanism to evaluate the effectiveness of the materials and the techniques for teaching statistics.