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Proceedings

  • The teaching of statistics from kindergarten to graduate university levels is of great importance, and everyone here is concerned with aspects of that teaching. The present talk deals with a less structured side of our statistical outreach: presenting statistical thinking to the several great publics that are out there beyond the classroom and beyond formal education. What of statistics can we transmit to nonstudents in legislatures, courts, factories, the military, the nursery, and so on? How to transmit it? That outreach is important not only for its own direct sake; it also is important indirectly, for, in one way or another, the broad publics out there strongly influence what is done statistically in schools and colleges. I have three broad themes. First, I discuss the natural desire of statisticians to be understood and encouraged by society at large. (Along with that, I discuss parallel natural desires by other groups.) Second, I make suggestions about kinds of statistical lessons for the public . . . which differ from statistical lessons in school. Third, I end with a speculative analysis of the unfortunate near-absence of song, story, and rousing myth that might underlie statistics.

  • This paper will concentrate on the role of statistics in the curriculum for the 5-11 age group. It is in the early years of schooling that the conceptual foundation is laid on which the secondary and tersary phases of a student's education are built. A brief overview of what and when certain topics are currently taught in the elementary schools in Britain, Canada, and the USA is presented.

  • In Italy 11 to 13 year old students go to the Lower Secondary School for a uniform scholastic program and to complete their compulsory education. After this students may choose to go to a variety of Upper Secondary Schools different in the length of their study programs (5, 4, or 3 years) as well as their study specializations (scientific/classical, technical, artistic, teacher training, professional training). Not all Upper Secondary Schools teach Statistics and Probability. Only technical and professional instruction provides, in some specializations and at different levels, for the study of Statistics and Probability in the last years of School (classes III, IV, V). Combinatorics and Probability when thought are always part of the mathematics program. Similarly Statistics can be found in the mathematics program, only if it includes Probability. Otherwise it is a part of the program of subjects concerned with economics, finance and so on. Reform projects have been under study in which mathematicians have proposed the introduction of Statistics and Probability into the mathematics program for all Upper Secondary Schools. At this moment the reform is still under discussion and it is not easy to predict how much time will be needed to reach an agreement. At this moment, apart from the contents of programs, the most serious problem for the teaching of Statistics in Italy is whether it is being effectively taught because of the limited preparation of teachers actively involved in the teaching of these programs.

  • Games are often used in teaching as a means of introducing and exploring probability concepts, since they provide familiar and practical instances of the notions in question. This paper describes a study in which two versions of a game are used as the setting in which students' understanding of probability is assessed. The subjects involved had received no formal instruction in probability prior to the experiment, but during it some of them used intuitions about chance as they developed their strategies for playing. There is also evidence that as they responded to the interviewer's questions and explained their strategies, subjects sometimes attended to previously unnoticed features of the situations and developed new strategies as a result.

  • 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.

  • It is important to develop children's mental images of numbers parallel to their acquisition of counting and calculating skills. This is achieved by various kinds of activities which reveal, in one way or the other, the underlying structures. In school mathematics numbers are closely connected with calculations, which are, in my opinion, too much emphasized. The emphasis should be shifted towards handling of numbers without calculations. The introduction of stem-and-leaf displays is a step towards that end. Being based on the fundamental idea of place value stem-and-leaf displays also help developing the children's understanding of number.

  • In England and Wales all pupils take major examinations at the age of 16. Until recently these were either the General Certificate of Education (GCE) for the more-able pupils and the Certificate of Secondary Education (CSE) for those not taking the GCE. As from courses starting this year there will be only one set of examinations, the GCSE, which are aimed at pupils of all abilities. Whilst combining the two systems the opportunity has been taken to rethink all the syllabuses and the purposes for which they are devised. This rethinking shows in published national criteria. All syllabuses have to conform to general criteria, many individual syllabuses have their own extra subject specific criteria (but statistics is not one of these).

  • The so-called operative method has its roots in the work of J. Piaget. His concept of the "operation", both concrete and formal operation, and the psychological approach. We have learned from psychology that the learning of operational concepts has to be linked with the attributes of the operative method above mentioned. It is the experience of many teachers that pupils accept and make use o the operative attributes when problems are posed according to the operative principles, that pupils deal - sometimes - consciously with these attributes of tasks or problems, and that a special sort of active behavior is developed during a long term learning process according to this didactical design. Pupils between 12 and 15 years of age - especially the "slow-learners" - have to solve a large number of assignments before they can begin and carry out a process of generalization. One of the goals is to concretize learning through discovery; therefore formal solutions remain somewhat in the background, whereas more emphasis is placed upon the activities of the pupils and their dealing with variation in situation and tasks.

  • The following paper will present some tentative ideas for the discussion on how the further evolution of curricula may react to changes in statistics which have become visible by the emergence of EDA. The emergence of Exploratory Data Analysis (EDA) presents a challenge to more traditional views, attitudes and value systems of statistics, which are often also the implicit basis of curricula and teaching approaches to statistics and probability. Simple examples, ideas and techniques of EDA are sometimes considered to be a new curriculum content, because it is hoped that they may replace the rather boring teaching of techniques of descriptive statistics by more interesting examples of real data analysis, where the students may become more actively involved in processes of discovering relevant features of the systems the data refer to.

  • The primary source of the material used in this presentation is The Art and Techniques of Simulation, a book from the Quantitative Literacy Series. These techniques are designed for use in middle school through senior high school. They feature statistical topics that are important to students, a wealth of hands-on activities, real data sets and active experiments which motivate student participation, and graphical methods instead of complicated formulas or abstract mathematical concepts. In particular, simulation is introduced as a technique for solving probability and statistics problems.

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