Laurie Snell, Tom Moore, and Peter Doyle
This project is a cooperative effort among six colleges -- Dartmouth, Grinnell, King, Middlebury, Princeton, and Spelman -- to develop and teach a new introductory mathematics course called CHANCE.
CHANCE treats issues that are reported in the news: statistical problems related to AIDS, the effects of lowering serum cholesterol on heart attacks, the use of DNA fingerprinting in the courts, maintaining quality of manufactured goods in the face of variation, informed patient decision making, reliability of political polls, and so forth. Students study the newspaper accounts of these topics, articles in general science journals, such as Chance, Science, Nature, and Scientific American, and finally the original research papers.
We propose to develop materials -- summary modules, student projects, classroom experiences, data sets, bibliographies -- based on our various CHANCE courses, and to disseminate these materials to both college and pre-college teachers. To this end, we will establish at Dartmouth a CHANCE center where we will continually update the materials developed, publish a regular newsletter, and maintain an electronic bulletin board. Each summer at Dartmouth we will conduct an evaluation session for those who have taught the course, and a workshop for others would like to teach the course.
The public has an increased need to understand chance issues such as testing for the HIV virus, new treatments for AIDS patients, the effects of lowering serum cholesterol on the prevention of heart disease, the undercount problem in the census, environmental influences on cancer rates, the use of DNA fingerprinting in court, and many others. Newspapers are responding to this need by increasing their coverage of scientific studies. Results that appear in the New England Journal of Medicine are often reported on the day the issue is released. The New York Times weekly Science section provides in depth coverage by first rate science reporters. While this increased coverage leads to a more informed public, it may also cause a public reaction, and at times even a government reaction, more extreme than is justified by the scientific facts. This is particularly true in the emotionally charged subject of AIDS.
Our educational system seems not to prepare our doctors, lawyers, politicians, or the general public to properly assess the results of scientific investigations involving chance. Colleges have long emphasized basic statistics and probability courses, but recent studies by psychologists in the Tversky school suggest that students do not come away with a clear idea of even the most basic probabilistic concepts. The quantitative requirement of the Harvard core curriculum, which insists that students demonstrate an ability to reason with chance data, is one school's recognition of the urgency of this problem. The problem is also recognized in the report Everyone Counts of the National Research Council:
Literacy is a moving target, increasing in level with the rising technological demands of society. Indeed, there is some evidence that the decline in reading comprehension scores over the last several decades is due in part to the growing mathematical content of what one is required to read. It is not just computer manuals or financial reports that require an understanding of mathematical ideas; so do reports of political polls, debates about AIDS testing, and arguments over the federal deficit. Even Supreme Court decisions resemble mathematical arguments whose subject matter is law rather than numbers; often, legal cases rest as much on probabilistic inferences (for example, DNA fingerprinting, fiber analysis) as on direct evidence.
The standard elementary mathematics course develops a body of mathematics in a systematic way and gives some highly simplified real-world examples in the hope of suggesting the importance of the subject. The examples are not the ones that the students deal with in their daily life, and so they do not feel the need for an understanding beyond that required for the final examination.
We are developing a course that will reverse this format: we will choose serious current applications of probability and statistics and make these the focus of our course called CHANCE. In this course we will develop concepts in probability and statistics only to the extent necessary to understand the applications. This will require at times also reversing the order in which one meets statistical topics. An orderly development of statistics such as you find in a typical first statistics book ends with a discussion of tests of significance; starting with a discussion of a serious application requires that we learn to use these tests right away.
Rather than lead the students to try immediately to guess the "correct test" when confronted with a real-world problem, we will encourage them to consider alternatives, and to use the new computer technology to carry out simulations and exploratory data analysis.
It is not our aim to systematically develop a canon of statistical tests or formulas; rather we intend to help the students learn how to think about statistics and probability, and how to seek out for themselves the tools appropriate for a particular problem. We hope that correctly applying probability and statistics to problems that they themselves consider important will lead students to continue to use sound quantitative thinking in their daily lives. In addition we hope that some will be motivated to do further study in mathematics in general and probability and statistics in particular.