# Book

• ### Teaching Statistical Concepts

With the increasing recognition that statistics should be a part of the core curriculum for the compulsory years of schooling for all children, there is now an urgent need for teachers to be trained in both statistical content and appropriate teaching methods. this is a world-wide problem which is exacerbated because of the many changes which are currently taking place in the way in which statistics is practiced. This book lays the foundation for teachers' responses to these changes, exploring how best to teach those applied skills which are now seen to be a more relevant part of the content of statistics courses. It includes consideration of: changes taking place in statistics itself, for example in the areas of Exploratory Data Analysis, statistical computing and graphics; conceptual difficulties which face teachers and students of statistics and probability; research into statistical education; management of statistical project work; developments in teaching methods and materials; use and evaluation of teaching resources, including computer hardware and software, audio-visual aids and textbooks; assessment of statistical skills and understanding. Although teachers of advanced statistics courses will find the book of great interest, its main focus is on how to provide for the needs of the majority of students, namely those students who (although studying the subject in its own right, or combined with mathematics or other disciplines) do not intend to become specialist statisticians. Based on the authors' wide experiences of teaching statistics and statistical computing and their extensive knowledge of the related literature and research, the book provides a synthesis of ideas on the practicalities of teaching statistics, with a critical overview of relevant research into statistical education.

• ### Misconceptions of probability: From systematic errors to systematic experiments and decisions

Some of our misconceptions of probability may occur just because we haven't studied much probability. However, there is considerable recent evidence to suggest that some misconceptions of probability are of a psychological sort. Mere exposure to the theoretical laws of probability may not be sufficient to overcome misconceptions of probability. Cohen and Hansel [20], Edwards [29], and Kahneman and Tversky [63-66] are among those psychologists who have investigated the understanding of probability from a psychological point of view. The work of Daniel Kahneman and Amos Tversky is especially fascinating, for the attempt to categorize certain types of misconceptions of probability which they believe are systematic and even predictable. Kahneman and Tversky claim that people estimate complicated probabilities by relying on certain simplifying techniques. Two of the techniques they have identified are called representativeness and availability. We shall explore these two techniques in more detail and discuss some implications for teaching probability and statistics in the schools.

• ### Teaching Data Handling within the Northern Ireland Mathematics Curriculum

This publication provides a historical background to the development of statistics and probability and an analysis of current research into the pedagogical issues associated with this area of mathematics. The final section contains information about resources of all types.

• ### Dynamic visual experiments with random phenomena

This paper will describe one approach to using visualization in learning statistics. The approach uses the ability of computers to perform statistical experiments (with the parameters determined by the learner) and display the results dynamically (as they occur). We will refer to the method as dynamic visual experimentation. We will use the term random phenomena to refer to the broad class of situations whose mathematical analysis requires statistical or probabilistic concepts or methods.

• ### The Teaching of Probability &amp; Statistics: Proceedings of the first CSMP International Conference

Under the sponsorship of the Central Midwestern Regional Educational Laboratory (CEMREL) and Southern Illinois University, the first international CSMP (Comprehensive School Mathematics Program) conference was held in Carbondale, Illinois, USA, from March 18 to 27, 1969. The subject of the conference was the teaching of probability and statistics at the pre-college level. In this volume are contained all the papers presented at the conference, background information about CEMREL and CSMP, the recommendations of the conference and a bibliography on the teaching of probability and statistics.

• ### Cognitive Strategies in Stochastic Thinking

Stochastic thinking denotes a person's cognitive activity when coping with stochastic problems, and/or the process of conceptualization, of understanding, and of information processing in situations of problem coping, when the chance or probability concept is referred to, or stochastic models are applied. In accordance with our view on stochastic thinking in decision making under uncertainty, three different aspects may be emphasized in psychological research: (1) the behavioral analysis, which may focus on analyzing or improving the product of the decision process. (2) The procedural analysis, which may, for instance, attempt to identify cognitive strategies of heuristics when tracing the process of thinking; and (3) the semantic or conceptual side, for instance, when analyzing the individuals's knowledge about probability or his/her use of probability to conceptualize uncertainty. Chapters: 1. Toward an understanding of individual decision making under uncertainty 2. The "Base-Rate Fallacy" - heuristics and/or the modeling of judgmental biases by information weights 3. A conceptualization of the multitude of strategies on base-rate problems 4. Modes of thought and problem framing in the stochastic thinking of students and experts (sophisticated decision makers) 5. Stochastic thinking, models of thought, and a framework for the process and structure of human information processing

• ### Learning and Testing Mathematics in Context; The case: Data visualization

This monograph describes a teaching experiment related to the NCTM Curriculum and evaluation Standards (1989).

• ### Visualization in Teaching and Learning Mathematics

This volume explores the role of visualization in mathematics education, especially undergraduate education.

• ### The Intuitive Sources of Probabilistic Thinking in Children

Productive reasoning of any kind is achieved through heuristics, and motivated by an anticipatory approach structured as intuition. This recognition has had important consequences in thinking about probability, since the intuitive substrate available in this domain is relatively inconsistent and ambiguous. A proper curriculum of probability learning should, then, take into account this primary intuitive substrate, and concern itself with improving it and with finding methods of building new intuitions which are readily compatible with it. Two main directions of research have been taken in relation to the formation of the concept of probability. The first originated by Tolman and Brunswick, concerns what has been termed probability learning. The second main line of research concerns the organisation of conceptual schemas in the domain of probability: the development of concepts such as chance, proportion, and the estimation of odds, and the development on children of the concepts and procedures of combinatorial analysis. These two directions of research are focussed on rather different problems, and the techniques they use are, consequently, different. Yet, as will be seen in the following chapters, their findings can be successfully combined in an effort to reach a unified view of this area.

• ### Decision Making Under Uncertainty (Advances in Psychology 16)

The topics discussed in this volume are of interest for several disciplines. The impact of the contributions presented in this volume on DECISION RESEARCH (FISCHHOFF), COGNITIVE PSYCHOLOGY (ZIMMER), DEVELOPMENTAL PSYCHOLOGY (WALLER), SOCIAL PSYCHOLOGY (BORCHERDING), ECONOMIC THEORY (SELTEN), and MATHEMATICS EDUCATION (STEINER) is outlined by researchers from these disciplines who were present at the Symposium. Of course, other disciplines, e.g. medicine, social sciences, mathematics, that were not represented, might also affected or challenged by the results and propositions documented in this volume. Naturally, the representatives of the different disciplines emphasize different aspects. Although from a decision theoretical perspective, methodological problems and questions of research strategies (e.g. top down vs. bottom up) seem to be most significant, conceptual issues about the nature of human knowledge are regarded as creating important research problems in other fields. The comments made by the mathematics educational view show the innovative power of a growing discipline. The methodology of mathematization is shown to be inextricably connected with the social dimensions of learning and instruction. Mathematics in general (and not only statistics and probability theory) is loosing its unique feature of always being either right or wrong when put into a social context (e.g. the classroom). Furthermore, as several of the papers point out, if the dynamic views were to be emphasized, we may not only expect decision research to have an impact on mathematics research but also the other way round.