• Twenty-five years ago, the term "technology" had a rather different meaning than it does today. Anything other than chalk-and-talk or paper-and-pencil was considered technology for teaching. This might have included anything from fuzzy-felt boards to mechanical gadgets, as well as the multimedia of that period (i.e., television, tape recordings, films, and 35mm slides). The title of this Round Table talk refers to "technology"; however, the papers are concerned mainly with computers and software. The occasional reference to calculators is really only a variation on this theme, because they are essentially hand-held computers. This is merely an observation--not a criticism. The re-invention of the meaning of the term 'technology' is something to which we have all been a party.<br>The developments in computers and computing during the past quarter of a century have been so profound that it is not surprising that they replaced other technological teaching aids. This does not mean that we should forget such alternative aids altogether, nor the need to research their effective use. However, it is obvious that computers have significantly increased the range, sophistication, and complexity of possible classroom activities. Computer-based technology has also brought with it many new challenges for the teacher who seeks to determine what it has to offer and how that should be delivered to students.<br>Innovations in this area tend to be accompanied by a number of myths that have crept into our folklore and belief systems. Myths are not necessarily totally incorrect: They often have some valid foundation. However, if allowed to go unchallenged, a myth may influence our strategies in inappropriate ways. This Round Table conference provides a timely opportunity to recognize and examine the myths that govern innovations and implementations of technology in the classroom, and to establish the extent to which our approaches are justified.

  • The history and current nature of research in statistics education are outlined and some<br>suggestions for its future direction are made. It is claimed that research in statistics<br>education is a research discipline in its own right.

  • The present paper is intended to illustrate by means of examples what can be accomplished in an environment where students have access to statistical computing package and also where they are familiar with a simple computing language. The authors have identified three broad areas in which the computer is helpful: reducing the need at lengthy manual calculations, facilitating graphical data analysis, and illustrating statistical concepts by means of simulation experiments. The first two categories tend to be well supported in the available packages, and they present here some representative examples. The last category seems not to be well developed in the standard texts, and their treatment here is more extensive, including both manipulations with standard packages and programming exercises.

  • Evaluation, analysis and interpretation of data is an important task of all sciences. Students should be introduced to a critical relationship with numbers. As an example, the two aspects measurement of a single value and investigation of the functional interrelationship of two measured values are discussed. The current mathematical subject should be applied, practised and constantly repeated. The proposed examples are interesting experiments, which allow us to mix empirical and mathematical conclusions. (orig.)

  • This opening chapter presents the aims and rationale of the book within an appropriate theoretical framework. Initially, we provide the reader with an orientation of what the book intends to achieve. The next section highlights some important issues in mathematical education, establishing a framework against which ideas in the book have been developed. Partly, the research has been inspired by the first series on mathematical education: Freudenthal's Didactical Phenomenology of Mathematical Structures. Though he considers many topics in mathematics he excludes (perhaps surprisingly) probability. Finally, summaries of each of the chapters are related to these didactic approaches.

  • There are unusual features in the conceptual development of probability in comparison to other mathematical theories such as geometry or arithmetic. A mathematical approach only began to emerge rather late, about three centuries ago, long after man's first experiences of chance occurrences. A large number of paradoxes accompanied the emergence of concepts indicating the disparity between intuitions and formal approaches within the sometimes difficult conceptual development. A particular problem had been to abandon the endeavour to formalize one specific interpretation and concentrate on studying the structure of probability. Eventually, a sound mathematical foundation was only published in 1933 but this has not clarified the nature of probability. There are still a number of quite distinctive philosophical approaches which arouse controversy to this day. In this part of the book all these aspects are discussed in order to present a mathematical or probabilistic perspective. The scene is set by presenting the philosophical background in conjunction with historical development; the mathematical framework offers a current viewpoint while the paradoxes illuminate the probabilistic ideas.

  • The analysis of historical development and philosophical ideas has shown the multifaceted character of probability. Kolmogorov's axiomatic structure does not reflect the complexity of ideas. The abundance of paradoxes not only occurred in the historical development of the discipline, it is also apparent in the individual learning process. Misconceptions are obstacles to comprehending and accepting theoretical ideas. Empirical research on probabilistic thinking aims to clarify and classify such misconceptions from both the theoretical as well as the individual's perspective. We present major research ideas of psychology and didactics of mathematics from a critical perspective. Our method of interpreting subjects' responses to experimental situations will be a complementarity of intuitions and official mathematics which is especially helpful for transferring ideas to actual teaching.

  • This chapter presents an epistemological analysis of the nature of stochastical knowledge. In particular, the mutual relationship between the elementary concept of probability (in its empirical form of relative frequency and in its theoretical form of Laplace's approach) and the basic idea of chance is demonstrated. An important consequence for teaching elementary probability is that there cannot be a logical and deductive course for introducing the basic concepts and then constructing the theory upon them; developing stochastic knowledge in the classroom has to take into account a holistic and systematic perspective. The concept of task system is elaborated as an appropriate curricular means for treating the theoretical nature of stochastic knowledge in the classroom.

  • This chapter is concerned with the impact of computers on probability in general secondary education. Mathematics educators have been producing ideas for using computers and calculators in probability education for two decades. Although there are many teaching suggestions, empirical research on this topic is uncommon and critical reports of practical experience rarely go beyond an enthusiastic description. A critical review of ideas, software and experience which would be helpful for further research and development is the major objective of this chapter. We will deal with pedagogical aspects, the subject matter and its change, and the role of changing technology. Various approaches will be reviewed; computers used as general mathematical utilities, simulation as a scientific method, and simulation for providing an empirical background for probability. Graphical methods may enhance the idea of visualization. The emphasis is on general orientation in the field.

  • This chapter is devoted to the research on probability which may be found in the subject of psychology, and deals with various research paradigms. Salient experimental tasks and research issues on how individuals cope with probabilistic settings are discussed. The objective is to provide a substantiated and representative review of the large number of psychological investigations. We start by presenting an indicative sample of psychological studies on people's response to probabilistic problems. Critical dimensions for judging the educational relevance of paradigms and issues will be introduced. The few developmental theories which deal with the acquisition of probability in psychology will be discussed. Shortcomings and perspectives of the educational research are critically examined in the concluding sections.