TEACHING CONTEMPORARY STATISTICS WITH ACTIVE LEARNING

Data abound in everyday life as well as in most academic disciplines. No one can doubt the importance of helping students learn to gain insight from numbers. However, statistics instruction has not always been aligned with the practice of statistics, with research into how students learn statistics, or with students' needs and interests. One challenge has been that statistics is often taught by instructors whose primary training lies elsewhere. For example, statistics courses are often taught by mathematicians whose background may include only theoretical courses, if any, in statistics.

There have been numerous recent recommendations for improving the instruction of statistics. For example, recommendations of a joint committee of the American Statistical Association (ASA) and the Mathematical Association of America (MAA) with regard to the teaching of statistics are to:

(1) teach statistical thinking,
(2) emphasize data and concepts, not theory and recipes, and
(3) promote active learning.

Similar foci can also be seen in the recent NCTM Standards that call for teaching data analysis, probability, and statistics throughout the K-12 curriculum and the new Advanced Placement Statistics program. The Conference Board of Mathematical Sciences has issued Guidelines for Mathematical Preparation of Teachers that recognize the importance of statistics and call for more thorough preparation of instructors.

The "Teaching Contemporary Statistics with Active Learning" workshops, sponsored by the ASA since 1998, are designed to enable instructors to improve their teaching of statistics. The focus of the workshops is on demonstrating alternative instructional methods for promoting deeper understanding of fundamental statistical concepts by providing instructors with numerous example activities that can be directly implemented into the classroom. Secondary goals include enhancing use of technology and authentic assessment practices in statistics courses, while providing a myriad of print and electronic resources for teaching statistics. We have also been involved with similar faculty development workshops sponsored by the MAA and the College Board.

The website www.rossmanchance.com/pbs/activities.html provides five example activities from our workshop. We believe they illuminate some of the distinctions between statistics and mathematics and illustrate how one can teach statistical thinking with real data and active learning. The first activity reveals the important role played by context in statistics by having students explore patterns in weights of Olympic rowers; the second illustrates the importance of a study's motivating question through examination of reading level requirements of cancer pamphlets; the (in)famous 1970 draft lottery provides the context for the third example, through which students discover that numerical summaries can indeed illuminate patterns that are hard to see in raw data. The need to watch out for lurking variables is the moral developed by the fourth activity which explores the well-known Berkeley sex discrimination data, and the fifth activity uses data on televisions and life expectancy to lead students to recognize the crucial distinction between association and causation.

Most of the activities demonstrated in the workshops are drawn from Workshop Statistics, a series of coursebooks available from Key College Publishing that consists of activities through which students discover statistical concepts, explore statistical principles, and apply statistical methods. Other collections of activities include Activity-Based Statistics, also available from Key College Publishing, Interactive Statistics, from Prentice-Hall, and the Quantitative Literacy series from Dale Seymour. On-line resources for teaching statistics include Data and Story Library, Journal of Statistics Education, and Chance News. A very helpful site for organizing one's search for on-line resources is maintained by Robin Lock. A new collection of resources for teaching statistics is Teaching Statistics: Resources for Undergraduate Instructors, available from both the MAA and ASA.

In conclusion, this is a very exciting time to be involved in statistics instruction. New technologies allow increased focus on concepts rather than calculations, and numerous resources are now available that enable instructors to focus on (and assess) statistical thinking in an interactive, collaborative, and engaging environment.

Further Reading

For reading about the distinctions between statistics and mathematics, we recommend the article "Mathematics, Statistics, and Teaching" by George Cobb and David Moore, published in a 1997 issue of The American Mathematical Monthly.

The recommendations of the ASA/MAA committee are found in "Teaching Statistics" by George Cobb, an article in the collection Heeding the Call for Change, published by the MAA in 1992.

A summary of statistics education reform is provided in "New Pedagogy and New Content: The Case of Statistics" by David Moore (with discussion), published in a 1997 issue of the International Statistical Review.

A discussion of constructivism as it applies to teaching statistics is contained in "How Students Learn Statistics" by Joan Garfield, published in a 1995 issue of the International Statistical Review.

Allan Rossman is Associate Professor of Mathematics and Statistics at Dickinson College and chair of the ASA Section on Statistical Education. Beth Chance is Assistant Professor of Statistics at Cal Poly - San Luis Obispo. They are the primary authors of Workshop Statistics and have conducted numerous workshops for K-12 and undergraduate instructors.