Statistics is one of the most important subjects in the undergraduate curriculum. However, the subject is conceptually difficult because inferential methods are based on probability theory, itself a difficult subject which cannot be adequately covered in the introductory course. Thus, many students finish the course having memorized some of the jargon and techniques, but with little real understanding. The undergraduate statistics course can be improved by adopting a rule of three, so that each major topic is explored from three points of view: 1. Mathematical. This term refers to the usual mathematical derivation and formulation of the statistical methods. 2. Data Analysis. This term refers to the application of the statistical methods to data, preferably from real problems, yielding numerical and graphical results. 3. Simulation. This term refers to simulations of the statistical methods that make the conceptual foundations clear in a way that words, static pictures, and even data analysis cannot. The mathematical and data analysis components are a well-established part of the course, with many excellent texts and statistical packages as teaching tools. The simulation component is not widely used throughout the course, in part because well- designed, customized simulation tools are not available. The purpose of this project is to develop a set of software modules that function as virtual laboratories, allowing a student to replicate a statistical procedure thousands of times in a matter of minutes with the output displayed in customized tables and graphs that create a rich learning environment. A special web site will be used to help with evaluation and dissemination. The third year of the project is devoted entirely to teacher preparation. The main activity will be a summer workshop to promote the "rule of three" in statistics education and to disseminate the software developed among the faculty who teach statistics, probability and technology courses to pre-service teachers.
