# Report

• ### Simulations in mathematics - Probability and computing: Learning probability concepts and modeling with computer simulations

"Simulations in Mathematics-Probability and Computing", (SIM-PAC), is a three year project funded by the United States' National Science Foundation's Materials Research and Development program. This paper describes the background and rationale for the project, its goals and objectives and the instructional strategy utilized by SIM-PAC. An example of a typical learning activity and the capabilities of the software are illustrated.

• ### Children's concepts of average and representativeness

This paper addresses two major questions about children's understanding of average. The first question deals with children's own understanding of representativeness within the context of data sets. When asked to describe a data set, how do children construct and interpret representativeness? The second question focuses on how children think about the mean as a particular mathematical definition and relationship. It deals with the underlying issue of how children develop mathematical definitions and how they connect these definitions with their informal mathematical understanding. This question, which has been considered by other researchers primarily in the context of experimental research designs, is addressed here in an open-ended, descriptive manner.

• ### A radically different approach to introductory statistics

This paper describes a new approach to a one semester introductory statistics course. This approach has been used by three instructors, including the author, at Madison. My primary goal is to enable students to discover that statistics can be an important tool in daily life. This is achieved by showing students that they are scientists, in a broad sense, and that statistics is an essential tool for doing science. The focus through the course is on scientific questions and how statistical thinking can shed light on their solutions. In short, data are preeminent and methods achieve importance through their ability to illuminate data sets. This is the reversal of the common practice of methods being the focal point and data sets being reduced to illustrating methods. This paper also describes the author's successes with early (in the semester) use of student projects.

• ### Using cooperative learning to teach statistics

Mosteller noted the paucity of studies on "how to improve collegiate or university teaching in a behavioral way," and offered examples of techniques that he had found effective in the classroom. Stimulated by Mosteller's suggestions and by research results on "cooperative learning", I adopted new procedures for teaching an introductory undergraduate course in psychological statistics and compared results with those from the course that I had taught by more conventional methods in prior years. A Letter to the Editor in The American Statistician provides a summary of findings. That letter is reproduced (with the permission of the publisher) on the facing page. The present report provides a more complete description of the methods employed, with the intent that it may facilitate their use by others.