Research on misconceptions of probability indicates that students' conceptions are difficult to change. A recent review of concept learning in science points to the role of contradiction in achieving conceptual change. A software program and evaluation activity were developed to challenge students' misconceptions of probability. Support was found for the effectiveness of the intervention, but results also indicate that some misconceptions are highly resistant to change.
This paper is a follow-up of a report given by Stout and Smeltz (1982) at last year's conference. Together, these two reports examine the extent that non-traditional teaching techniques in statistics are being utilized in colleges and universities as well as the perceived effectiveness of these techniques by the individuals using them. This report focuses on the specific advantages and disadvantages of each nontraditional technique as outlined by survey respondents. The information obtained in this report will provide an indication of the overall impression of each technique. It should also be useful to prospective users as they analyze the costs and benefits of adopting these new techniques. Finally, it should provide a basis of knowledge for innovators as they attempt to improve the operationalization of each technique.
The Statistical Anxiety Rating Scale (STARS) was developed to measure statistical anxiety. Statistical anxiety is defined as the feelings of anxiety encountered when taking a statistics course or doing statistical analyses. Eighty-nine items were generated and presented to a sample of 1150 statistics students. STARS can be used by statistics teachers to help diagnose areas of high anxiety.
Probabilistic judgments made by researchers in psychology were investigated in statistical prediction situations. From these situations, it is possible to test the "representativeness hypothesis" (Tversky and Kahneman, 1971), and the "significance hypothesis" (Oakes, 1986). The predictive judgments concerned both an elementary descriptive statistic and a significance test statistic. In the first case, the predictive judgments were generally coherent, and fit comparatively well to Bayesian standard predictive probabilities. In the second case, they were generally incoherent, and fit poorly to Bayesian standard predictive probabilities. As for the two hypotheses tested, our findings are compatible with the significance hypothesis, but go against the representativeness hypothesis.
This paper discusses the Illinois procedure for teaching the Monte Carlo method. Where there is limited time, or where students will not be able to grasp conventional methods firmly, we advocate teaching the Monte Carlo approach, and perhaps that only. Where there is more time, and where students will be able to well learn conventional methods, we advocate (a) teaching Monte Carlo methods at the very beginning as an introduction to statistical thinking and practice; and (b) afterwards teaching the Monte Carlo method with the conventional method as alternatives to the same problems, to help students learn analytic methods and to give them an alternative tools for their use.
As part of a study of students' constructions of the idea of "average," teachers were also interviewed using the same problems and format as used with the students.
Recent survey data demonstrate an acute need for curricular resources in statistics. The first half of this paper summarizes and compares a dozen current or recent NSF projects, most of which are developing such resources. The second half of the paper develops four themes from the conference.
Many high school and college statistics courses, however, do not teach statistical reasoning effectively. Rather than helping students understand how to interpret the statistical statements they encounter, these courses focus upon statistical formulas and tests. We believe that the conventional approach not only leaves students confused about fundamental statistical concepts, but also makes the mathematics involved in statistics more rather than less obscure.
This paper reports on a clinical study of students' productive understanding of database record/field structures. Using a data analysis tool with which they were familiar, students were asked to create a database structure that would allow them to produce a desired graph. A recurring pattern was observed in which subjects produced a set-based structure instead of the required property-based structure.
We explore challenges in achieving authentic inquiry with data in classrooms from the fifth through the eighth grade. We present the Tabletop, a prototype computer-based data analysis tool based on animated visual representations, and reports on clinical and classroom trials of this tool. Vignettes from clinical sessions illustrate students' understanding of the software interface as well as interacting subtleties of data creation and data analysis. One year of classroom trials is summarized in terms of three important categories of conceptual and cultural prerequisites for successful implementation: a) reasoning about the aggregate, b) the objectification of knowledge, and c) the pragmatic structure of classroom projects.