• The purpose was to investigate the development of probabilistic thinking as outlined by Piaget and Inhelder, to clarify interrelations of different probabilistic tasks, and to examine the effects of IQ and gender on probabilistic thinking from 5 to 12 years. There were 240 subjects, boys and girls, medium in socio-economic status (SES) and IQ, of two cultural backgrounds, and of three age groups: 5 to 6 years, 8 to 9 years, and 11 to 12 years. Each subject was administered individually the Stanford- Binet and four Piagetian tasks assessing randomization, distribution of multiple discrete elements, odds estimation and permutations. The responses were evaluated globally and in terms of specific measures. The results showed an increase in probabilistic performance that was mostly larger between the first two groups than the last two, positive interrelations among the tasks, partly different factorial structures in each age group with increasing factorial differentiation, more interrelations of IQ with global than specific measures and more in older than younger children, and more differences in favor of boys in older than younger groups. Discussion focuses on the degree of support for Piaget's claims and implication concerning the structure and development of probabilistic cognition.

  • The lack of literature-based guidance for conducting evaluations of statistics texts has likely contributed to some disturbing patterns in published evaluations and studies of statistical texts. Similar patterns probably exist in unpublished evaluations, such as the evaluation (and possible adoption) of a test by an instructor. A critical failing in this area is that published evaluations almost invariably employ criteria for conducting the review that lack any literature-based rationale, being, apparently, experientially based, a failing which is compounded by a lack of empirical evidence supporting the usefulness of the criteria employed in the evaluation. The purpose of these (symposium) papers is to continue and extend the research exemplified by Cobb (1987), Hubety and Barton (1990), Brogan (1980), and others by attempting to construct and pilot criteria for evaluating statistics texts that are grounded in the statistical education and text evaluation literatures. This study is an initial step in a line of research which may result in the establishment, maintenance, and updating of a database containing evaluations of introductory statistical texts similar to (but much smaller in scale) that maintained for educational and psychological tests (e.g., Mental Measurements Yearbooks). Evaluative information of this kind should benefit the direct consumers of these texts, students and instructors.

  • This report presents research, materials development, and dissemination activities conducted in year 2 of the Project (May 1, 1991, to May 1, 1992). In general, most efforts in year 2 were devoted to research activities in accordance with the original Project plan. This plan called for completion of data-collection for the research component of the Project by the end of year 2, with year 3 expected to be devoted to writing of research reports and development of training materials. [Research activities in year 2 were for the most part a direct continuation of work done in year 1. To enable the reader to understand the current status of the Project (as opposed to what was done in year 2 only), we have chosen, wherever appropriate, to combine descriptions of year 1 and year 2 activities]

  • A quasi-experimental design with two experimental groups and one control group was used to evaluate the use of two books in the Quantitative Literacy Series, Exploring Data and Exploring Probability. Group X teachers were those who had attended a workshop on the use of the materials and were using the materials during the 1986-1987 school year. Group Y teachers were those who were trained by the Group X teachers and were using the materials during the 1986-1987 school year. Teachers of Group Z, the control group, were teaching similar classes from the same schools as teachers of Groups X and Y. A pretest was administered to all three groups in November 1986. A March Test was administered to the two experimental groups. A May Test, posttest, was administered to all three groups. In addition, teachers maintained daily logs of the amount of instructional time allocated to mathematics and the amount of instructional time allocated to the Quantitative Literacy materials. All teachers were requested to complete a questionnaire at the end of the study. A total of sixty teachers from two states, Wisconsin and Connecticut, agreed to participate in the study. A complete set of data was received from 42 teachers--7 in Group X, 25 in Group Y, and 10 in Group Z. The results indicate that using the Quantitative Literacy materials resulted in students learning approaches and techniques for describing data sets and means of computing probabilities. On the May Test, the scores of the Quantitative Literacy classes, Groups X + Y, were significantly higher than those of the control group. There were no significant differences in the student scores between Group X and Group Y. Thus, the form of training that a teacher had received did not affect student test scores. Teachers varied in the amount of time allocated to the materials and how that time was distributed. Some used the materials over an extended period of time and integrated the Quantitative Literacy materials with their regular content. Other teachers taught the materials as a unit over a relatively short period of time, one or two months. Teachers felt the materials were fairly easy to use. However, there did not seem to be significant differences in teacher beliefs that could be attributed to group membership.

  • 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.

  • A project goal was to affect change in the secondary mathematics curriculum and the styles and methods of instruction. The project was based on three fundamental assumptions: (1) The prevailing style of presentation in the secondary mathematics curriculum is too narrow and formalized. We must broaden the curriculum and encourage active learning styles which stress experimental and exploratory approaches to learning. (2) The role of the teacher is absolutely crucial to affect change in the curriculum and styles of instruction. The teacher's attitude about what is important and how it should be taught is the most important factor. (3) Statistics should be presented in a coherent fashion and must be approached through problems, not just techniques. The role of statistics in society and statistics across the curriculum are important objectives of statistical education.

  • This study focused on the relations between performance on a three-choice probability-learning task and conceptions of probability as outlined by Piaget concerning mixture, normal distribution, random selection, odds estimation, and permutations. The probability-learning task and four Piagetian tasks were administered randomly to 100 male and 100 female, middle SES, average IQ children in three age groups (5 to 6, 8 to 9, and 11 to 12 years old) from different schools. Half the children were from Middle Eastern backgrounds, and half were from European or American backgrounds. As predicted, developmental level of probability thinking was related to performance on the probability-learning task. The more advanced the child's probability thinking, the higher his or her level of maximization and hypothesis formulation and testing and the lower his or her level of systematically patterned responses. The results suggest that the probability-learning and Piagetian tasks assess similar cognitive skills and that performance on the probability-learning task reflects a variety of probability concepts.

  • The likelihood of a statement is often derived by generating an explanation for it and evaluating the plausibility of the explanation. The explanation discounting principle states that people tend to focus on a single explanation; alternative explanations compete with the effect of reducing one another's credibility. Two experiments tested the hypothesis that this principle applies to inductive inferences concerning the properties of everyday categories. In both experiments, subjects estimated the probability of a series of statements (conclusions) and the conditional probabilities of those conclusions given other related facts. For example, given that most lawyers make good sales people, what is the probability that most psychologists make good sales people? The result showed that when the fact and the conclusion had the same explanation the fact increased people's willingness to believe the conclusion, but when they had different explanations the fact decreased the conclusion's credibility. This decrease is attributed to explanation discounting; the explanation for the fact had the effect of reducing the plausibility of the explanation for the conclusion.

  • 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.