Fong and Nisbett (1991) argued that, within the domain of statistics, people possess abstract rules; that the use of these rules can be improved by training; and that these training effects are largely independent of the training domain. Although their results indicate that there is a statisically significant improvement in performance due to training, they also indicate that, even after training, most college students do not apply that training to example problems.
Research in the areas of psychology, statistical education, and mathematics education is reviewed and the results applied to the teaching of college-level statistics courses. The argument is made that statistics educators need to determine what it is they really want students to learn, to modify their teaching according to suggestions from the research literature, and to use assessment to determine if their teaching is effective and if students are developing statistical understanding and competence.
Ten subjects were asked to think aloud while solving two statistical problems. Ten subjects were instructed after each substep of his/her problem solving, to check in various ways the solution of the previous substep. The subjects detected 25 out of a total of 56 errors when they solved the problems. About half of the detected errors were computational errors. Nine errors were eliminated in response to the checking instructions. The think aloud data indicated that subjects' most common way of detecting their own errors was by noting that computations resulted in extreme values. Subjects also detected errors by (a) "spontaneous discovery"; (b) discontent with other aspects of a solution than the numerical value of the answer; (c) repeating a solution. The last mentioned type of error detection only occurred when subjects responded to the checking instructions. Finally it was found that subjects had a strong tendency to respond to the checking instructions either in a routinized or in a non-elaborated way. It was discussed how the formulation of checking instructions can be improved in order to avoid this effect.
The authors stress that graphical techniques are powerful analytic tools. To illustrate this point, the following techniques are presented in the context of regression analysis: a) stem-and-leaf plots; b) schematic plots; c) time-order plots; d) scatterplots; and e) probability plots. According to the authors, it is important that analysis be tailored to the data in instruction. This provides learners with opportunities to see that real life data analysis has its unique aspects and problems. To illustrate this point, the authors used data about "Old Faithful" in Yellowstone Park. Various plotting techniques were used in order to detect anomalies and to outline causes. This process allowed the researchers to determine the appropriate model for the data- autoregressive model.
People's intuitive conceptions of randomness have been found to depart systematically from the laws of chance. This is illustrated in the game of basketball. Players and fans have been found to believe in "streak shooting," a phenomenon involving the belief that players have a better chance to get a basket after a few successful attempts despite the statistical odds against such an occurrence. This misconception seems to affect how the game is played as well since many coaches and players believe that it is important to pass the basketball to a player that has successfully attempted most shots. This finding is consistent with "gambler's fallacy." It is suggested that the belief in the law of small numbers could be due to performance heuristics since strings of successful shots are more memorable than mixed ones.
The authors state the view that many intuitive judgements, right and wrong, are produced by the application of heuristics such as the representativeness and availability. Moreover, observed errors of judgement have two kinds of implications: they may illustrate a judgement heuristic or they may indicate a failure to correct the error once the intuition was articulated.
In statistical problems, the differential effects on training performance, transfer performance, and cognitive load were studied for 3 computer-based training strategies. The conventional, worked, and completion conditions emphasized, respectively, the solving of conventional problems, the study of worked-out problems, and the completion of partly worked-out problems. The relation between practice-problem type and transfer was expected to be mediated by cognitive load. It was hypothesized that practice with conventional problems would require more time and more effort during training and result in lower and more effort-demanding transfer performance than practice with worked-out or partly worked-out problems. With the exception of time and effort during training, the results supported the hypotheses. The completion strategy and, in particular, the worked strategy proved to be superior to the conventional strategy for attaining transfer.
Two reasons are given for the lack of adequate teaching in statistics: the newness of the field and students' lack of conceptual background. The author discusses the importance of the Schools Council Project for making significant progress in this area. The aim of this project is to produce appropriate teaching materials that are consistent with the teaching principles developed by the committee. The curriculum is divided into eight units, each lasting 4 to 5 hours. Students are grouped into four levels corresponding to ages 11-12, 12-13, 13-14, and 14-15. Units were well-constructed and designed for the general student with each topic carefully broken down and developed. The teachers' notes were carefully constructed and an integral part of each unit. These contained description of aims, objectives, prerequisites, equipment, and planning.
The authors state that athletics in general can be used to demonstrate probabilistic concepts and that these may be reinforced due to the motivational aspects of the examples. In this article, the planification of the NCAA Regional Basketball tournaments is examined as a probability problem (e.g. what is the probability of team #3 winning the regionals?). In calculating the probability of any team winning, the students must: 1) evaluate the probability of each game played; 2) assume independence of each contest; and 3) incorporate the relative strength of each team in the model. Three probability models are considered, the third being the most adequate. It seems to provide a good fit to the data and is considered interesting to students without requiring a strong mathematical background. The key point in this article is that these models demonstrate the multiplication principle and the additive property of mutually exclusive events in addition to the motivation provided by the topic itself.
This paper simply contains a long list of teaching aids that are available for sale from various companies such as transparencies, audio tapes, film strips, slides, films, video tapes, course packages, and probability devices.