Recent research on probability judgment indicates that people's ability to estimate probabilities is very limited. It is argued that people may lack the cognitive apparatus necessary for processing probabilistic information, in so far as probability judgments play an unimportant role in everyday life. When probability judgments occasionally are made in everyday life it is argued that they are not based on frequency data but on some more or less well grounded theory.
The study tested whether improving students' knowledge of balance rules through experience with a balance beam promotes understanding of the mean. The study consisted of three sessions. In the pretest session, subjects' levels of balance knowledge and abilities to calculate the solutions to a variety of problems dealing with the mean were assessed. Subjects were classified as nonbalancers if they performed at a a level below Siegler's Rule IV and as noncalculators if they were unable to calculate solutions to weighted mean problems. In the second session, half the nonbalancers were given balance training and the other half were asked to solve unrelated control problems. In the transfer session, subjects were given a set of five problems to assess their understanding of the mean. Significant transfer was found: Subjects classified as nonbalancers on the pretest performed significantly better on the transfer problems if they had been given balance training rather than assigned to the control condition.
In the past two decades several influential organizations, including the national Council of Supervisors of Mathematics, NACOME, UNESCO, CEEB, and the Cambridge Conference on School Mathematics, have acknowledged the role that probability and statistics play in our society. Consequently, each has recommended that probability and statistics be included as part of the modern mathematics curriculum. Probabilistic reasoning may not be an easily acquired skill for most students, however. Several recent studies have reported that even after instruction, many students have difficulties developing an intuition about the fundamental ideas of probability. Without this intuition they fail miserably when forced to reason about probable events.
Some understanding of statistics is needed at all levels in society from the individual in his or her personal life to the professional statistician in the university or research institute, in Government or in business. Simple statistical and experimental principles underlie the understanding and interpretation of many everyday phenomena. There is a very strong case for improving the level of numeracy and statistical understanding at all levels in our society.
There is no doubt that statistics should be an important part of the secondary mathematics curriculum. A single classroom microcomputer can be valuable for work in both descriptive and inferential statistics. This article presents a framework for integrating a microcomputer into a statistics unit and includes descriptions of some programs suitable for the Apple microcomputer and ideas for lessons. Three functions that a microcomputer can perform within a statistics unit are illustrated: the easy generation of attractive graphs; the illustration of concepts; and the performing of tedious calculations. These three functions will frequently overlap within a specific program. Simulations are important but will not be discussed here.
This study evaluates the effect of participation in three computer simulation exercises on performance of students enrolled in an introductory statistics class. One-half of the students were required to participate in three computer exercises: means, normal curve, and correlation coefficient estimation. At a later date all students were given a paper-and-pencil test of their ability to quickly estimate statistics. Results demonstrated that the students who participated in the exercises attempted significantly more exercises with greater success than those who did not. Questionnaire results indicated that the students felt that the exercises were useful.
Recent evidence indicates that people's intuitive judgments are sometimes affected by systematic biases that can lead to bad decisions. Much of the value of this research depends on its applicability, i.e., showing people when and how their judgments are wrong and how they can be improved. This article describes one step toward that goal, i.e., the development of a curriculum for junior high school students aimed at improving thought processes, specifically, those necessary in uncertain situations (probabilistic thinking). The relevant psychological literature is summarized and the main guidelines in the curriculum development are specified: (a) encouraging students to introspect and examine their own (and other's) thought processes consciously, (b) indicating the circumstances in which common modes of thinking may cause fallacies, and (c) providing better tools for coping with the problems that emerge. Two detailed examples are given. In addition, the problem of training teachers is briefly discussed and a small-scale evaluation effort is described.
"Forty-eight sutdents with no previous exposure to probability or statistics read one of three texts that varied in the emphasis placed on rote and conceptual learning of basic concepts of elementary probability. A qualitative analysis of errors on a postinstruction test employed a model of problem solving whose stages were categorization of the problem, retrieval of the appropriate formula, and translation of values from the problem into the formula. Variations in performance on problems requiring the same formula for solution were largely attributable to surface features that affected the ease of categorization and translation. Students who read a text that emphasized conceptual learning tended to be less sensitive to surface features, which parallels results regarding novices and experts in various content domains."
The profession of statistics has adopted too narrow a definition of itself. As a consequence, both statistics and statisticians play too narrow a role in policy formation and execution. Broadening that role will require statisticians to change the curriculum they use to train and develop their own professionals and what they teach nonstatisticians about statistics. Playing a proper role will require new research from statisticians that combines our skills in methods with other techniques of social scientists.
According to the representativeness heuristic, the probability that an element is an exemplar of a given class is judged to be high to the extent that the element is representative of the class with respect to its salient features. In three experiments involving situations previously called upon in support of representativeness theory, questionnaire responses from 265 university students demonstrated systematic biases that deviated sharply from the obvious predictions of the theory. One such bias, the students' misinterpretation of proportion information as absolute-number information, is comparable to Piaget's concrete operations. The implications for representativeness theory are discussed in terms of the theory's relationship to concrete thinking, the importance of task characteristics, and the difficulty of a priori specification of the salient features with respect to which representativeness is assessed.