# Chapter

• ### Some publications on teaching statistics in Japan

This short review lists some literature on the Japanese statistical education.

• ### Teaching statistics

This report on teaching statistics will present the Statistics Focus Group's recommendations under three headings, corresponding to statistics, mathematics, and teaching. A fourth section illustrates ways these recommendations can be put into practice, and a final section offers two meta-recommendations about implementation.

• ### Uncertainty

The task of this essay is not to urge attention to data and chance in the school curriculum- they are already attracting attention- but to develop this strand of mathematical ideas in a way that makes clear the overall themes and strategies within which individual topics find their natural place.

• ### Use of the arithmetic mean: An investigation of four properties issues and preliminary results

Our investigation utilised Strauss and Bichler's conceptual organisation of the properties of the mean, and had three purposes: (1) to investigate what happens developmentally to those statistical properties that were not mastered by age 12-14; (2) to examine the qualities of the statistical properties, including their relative conceptual difficulty and their relative ability to evoke the concept of the mean; and (3) to determine the relative effectiveness of different testing formats in assessing subjects' knowledge about the component properties of the mean.

• ### A new field of applied mathematics

This chapter deals with Exploratory Data Analysis (EDA) and is based on a detailed theoretical analysis of the latter.

• ### The base rate fallacy in attribution and prediction

This chapter focuses on the intuitive scientist's ability to use base rate or distributional information in two of these inferential tasks: causal analysis and prediction. It will be argued that essentially the same characteristics of human inference are implicated in these tasks.

• ### Understanding Students' Beliefs About Probability

Although I don't want here to defend my point of view, it will serve my purposes to exemplify what I regard as a contrary one. My assumption is that students have intuitions about probability and that they can't check these in at the classroom door. The success of the teacher depends on large part on how these notions are treated in relation of those the teacher would like the student to acquire. Additionally, I think it is a myth that mathematics, either as a discipline or in the mind of a mathematician, develops independently from concerns about objects and relations that are believed to have real-world referents. This was certainly not so in the case of the development of probability theory.

• ### A general education requirement

Learning and applying the statistical thinking theories and techniques of the Deming management philosophy of Quality Improvement in introductory statistics courses can produce quality general education graduates for the 21st century. Advantages for the graduate who experiences a statistics course with emphasis using the Statistical Process Control (SPC) methodology include: a) replacing fear of mathematics with statistical critical thinking, team problem solving, and writing and communication skills that enable learning for a life time, b) statistical interpretations and analysis of data using reasoning skills that are imperative survival skills necessary for the competitive job market, c) statistical foundations with the Quality Improvement (QI) philosophy which can contribute to improving disciplines and attitudes. The implementation of this new paradigm for statistics courses will require new attitudes for both students and teachers, new methodology of management and teaching, and new context for the course.

• ### Using "Consumer Reports" as a resource for data analysis in the statistics classroom

The author discusses the potential of the magazine "Consumer Reports" as a source of data for Shopping Statistics. This magazine provides alot of data on prices and various aspects of product quality for many different makes and brands for all sorts of products. Such a data source can allow students to learn about statistics using information found in every day life. Real world data can serve to contextualize student learning.

• ### Primary and secondary intuitions in the introduction of probability

The main objective of our research has been to study the intuitive biases corresponding to certain fundamental concepts and methods of the theory of probability. This is not simply a question of the general concepts of chance, or randomness, on which there are data already available. Research which has already been done by psychologists indicates the existence of a natural intuition of chance, or even of probability (cf. Fischbein et al., 1967, 1970a, b). However, A. Engel, a mathematician, has written: "...we have a natural geometric intuition but no probabilistic intuition". In order to elucidate this problem, we decided to go beyond the notion of chance, and try to follow the course of what, in fact, happens during the systematic teaching of certain concepts in the theory of probability. We therefore decided to study the intuitive responses of subjects to certain concepts and calculational precedures which were introduced during some experimental lessons on probability, viz. chance, and probability as a metric of chance; the multiplication of probabilities in the case of an intersection of independent events, and the addition of probabilities in the case of mutually exclusive events. Reprinted from Educational Studies in Mathematics 4 (1971), 264 - 280.