Research

  • 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.

  • 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.

  • Those familiar with a statistical package are often surprised at how long it takes a novice to accomplish even a simple task. In a college environment, students often complain about the countless hours spent on a simple assignment. An examination of their computer printouts and written work often fails to reveal where the students spent their hours. Unfortunately, it is possible for students to understand conceptually what to do but still not be able to do it. In an effort to learn where students actually ran into difficulty and discover more about the types of mistakes they were making, we undertook a series of experiments at Babson College. These experiments involved two instructors each teaching two sections of an applied statistics course. There were 154 undergraduate students in these four sections. an extensive set of references dealing with this area may be found in Kopcso, McKenzie, and Rybolt (1985). References to our past work and another recent article are present at the end of this paper.

  • 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.

  • 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.

  • 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 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.

  • Since 1976 the authors have been engaged in a systematic investigation of the cognitive effects of games on mathematics learning. This investigation focused on identifying effective uses of games so that recommendations for appropriate incorporation of games into school practices can be made.

  • Statistics is not at present taught to French 11 to 15 year olds. Syllabuses do not require it and text books offer very few activities or exercises bearing on statistics. Very simple statistical sequences may be found in some books, in the sections on proportionality, percentages or reading graphs. This paper presents research supporting the development of the teaching of statistics in secondary schools.

  • Since 1976 the authors have been engaged in a systematic investigation of the cognitive effects of mathematics instructional games. From the outset the research has focused on identifying effective uses of games in order that recommendations for appropriate incorporation of games into mathematics instruction can be made. Three studies described indicated that games seem effective in improving student performance at cognitive levels. Suggestions for future research are offered.

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