Conference Paper

  • This is a collection of eleven full-length research papers presented at the Third International Conference on Teaching Statistics. The papers are: 1. A Complemetarity Between Intuitions and Mathematics, by Manfred Borovnik 2. What's Typical? children's Ideas About Average, by Janice R. Mokros, Susan Jo Russell, Amy Shulman Weinberg and Lynne L. Goldsmith 3. The Loss of Intuition - A Lesson for the School Teacher?, by F. R. Jolliffe 4. Assessment of the Understanding of Statistical Concepts, by F. R. Jolliffe 5. Exploring the Stability of Students' Conceptions of Probability, by Joan Garfield and Robert delMas 6.The Use of Multiple Items to Identify Misconceptions in Probabilistic Reasoning, by Robert delMas and Joan Garfield 7. Use of the Arithmetic Mean: An Investigation of Four Properties, by Marjorie Roth Lean and Judith Zawojewski 8. The Origin of Inconsistencies in Probabilistic Reasoning of Novices, by Clifford Konold, Alexander Pollatsek, Arnold Well and Jill Hendrickson 9. A Longitudinal Study of Pupils' Probability concepts, by David Green 10. The Use of Chance - Concept in Everyday Teaching - Aspects of a Socially 10. Constituted Epistemology of Mathematical Knowledge, by Heinz Steinbring 11. Learning About Sampling: Trouble at the Core of Statistics, by Andree Rubin, Bertram Bruce and Yvette Tenney

  • In this short presentation we describe the experimental results obtained from a group of university students who were asked about the interpretation given to the significance level in a test of hypothesis. From the analysis of students' arguments, interesting conclusions about the students' understanding and use of the concept are deduced and a wide variety of misconceptions which extend the results from Falk and White are shown. We think these conclusions constitute a first step towards the identification of obstacles in the learning of the aforementioned concept and can contribute to an improvement in the teaching and application of statistics.

  • The preliminary results of a systematic study of the difficulties and errors in solving a sample of combinatorial problems in two groups of pupils of secondary education are presented in this work. The analysis of the task variables of the problems constitutes a first approximation to the classification of the simple combinatorial problems and likewise enables the attribution of a content validity to the instrument developed, in order to assess the capacity to solve this kind of problems.

  • Three experiments were conducted with college age beginning statistics students to assess the validity of six popular beliefs about factors related to statistics achievement. Mathematics background and ability, logical reasoning ability, attitude toward statistics, and anxiety were all found to have some relationship to statistics achievement. Differences between graduates and undergraduates, and men and women, were also explored. No significant differences were found between the groups on any single factor related to statistics achievement. There were, however, differences in how those factors combined to affect achievement for the different groups. It was concluded that no one variable explored here is singularly necessary for achievement in beginning statistics.

  • Proposed reforms in the K-12 mathematics included incorporating data analysis and probability into the mathematics curriculum. It was proposed that elementary school students engage in experiences to: a) collect, organize, and describe data; b) construct, read and interpret displays of data; and c) formulate and solve problems that involve collecting and analyzing data. However, the research literature contains few studies about the teaching and learning of statistical concepts, especially for elementary school students and teachers.

  • Performance on problems included in the fourth administration of NAEP suggest that roughly half of secondary students believe in the independence of random events. In the study reported here about half of the subjects who appeared to be reasoning normatively on a question concerning the most likely outcome of five flips of a fair coin gave a logically inconsistent answer on a follow-up question about the least likely outcome. In a second study, subjects were interviewed about various aspects of coin flipping. Many gave contradictory answers to closely related questions. We offer two explanations for inconsistent responses: a) switching among incompatible perspectives of uncertainty, including the outcome approach, judgment heuristics, and normative theory, and b) reasoning via basic beliefs about coin flipping. As an example of the latter explanation, people believe both that a coin is unpredictable and also that certain outcomes of coin flipping are more likely that others. Logically, these beliefs are not contradictory; they are, however, incomplete. Thus, contradictory statements appear when these beliefs are applied beyond their appropriate domain.

  • The ability to seek out data, organize it, and interpret it is an empowering skill, and that a person who truly understands data has a source of power to use in influencing the direction of important decisions. The goal of education in statistics and probability should be to impart this sense of power to students, Learning statistics does not mean merely mastering the fomulaic transformations that yield mean, standard deviation, and P value. A true understanding of statistics includes knowing how to use data to discover and evaluate important associations and to communicate these associations to others. It requires learning how to evaluate other people's use of data and to augment or challenge them with additional data. There are NCTM Teaching Standards (NCTM, 1991), which include a new view of pedagogy in mathematics teaching - a focus on understanding the underlying concepts of our number system rather than on memorizing addition and multiplication facts, on facility in spatial visualization rather than on learning formulas for the area of polygons, and on planning and on carrying out data analysis projects rather than on knowing the difference between mean and median. Integrated with these two major changes, researchers and practitioners are looking more to technology to support new approaches to mathematics learning, as "tools for enhancing [mathematical] discourse." (NCTM, 1991, p.52) How does the computer fit into the developing view of statistics education? At first glance, the answer seems obvious: computers free students (and teachers) from the tedious computations that are required to calculate means, standard deviations, confidence intervals, etc. They draw graphs quickly and accurately. They generate multitudes of samples in a single bound. But this list of accomplishments leaves two crucial questions unanswered: 1) Are there other more powerful ways in which computers can facilitate students' learning of statistics? 2) Are there any drawbacks to uses of computers in statistics classes? The remainder of this paper will address both of these questions.

  • This study describes the development of a new instrument entitled Attitudes Toward Statistics (ATS), to be used in the measurement of attitude change in introductory statistics students. Two ATS subscales are identified, labeled Attitude Toward Course, and Attitude Toward the Field, respectively. These subscales are shown to have both high internal consistency and test-retest reliability. It is further shown that each ATS subscale provides distinctly different information about the attitudes of introductory statistics students.

  • In this work an analysis of some task variables of statistical problems which can be proposed to the students to be solved on the computer, are presented. The objective of this didactical-mathematical analysis is to provide criteria of selection of the said problems, directed to guiding the students' learning towards the adequate meanings of the statistical notions and to the development of their ability to solve problems.

  • This study was conducted to determine the effect of previous mathematics, statistics, and computer science coursework; attitudes toward statistics and computers; and mathematics ability on statistics achievement. A secondary purpose of this study was to determine the effect of the computer laboratory component of an inferential statistics class on the end of course attitudes toward statistics and computers controlling for precourse attitudes.