I - 100 Course Description: Helps students recognize, evaluate, and use forms of quantitative argument. Introduces basic concepts from statistics and calculus through three case studies: witchcraft in seventeenth-century New England; education, occupation, salary, gender, race, and ethnicity in the United States; global population and resources. Using real data in a Macintosh computer laboratory, students observe and summarize relationships, formulate and test hypotheses, and study connections among hypotheses, formal models, predictions, and actual results. Laboratory reports on each case study culminate in a paper.
SYLLABUS for I - 100, CASE STUDIES IN QUANTITATIVE REASONING
This course is offered every semester, and there are no prerequisites. It is divided roughly into three parts. For 1996-97 the three case studies are the following.
I. Narrative and Numbers: Salem Village Witchcraft
Witchcraft in seventeenth-century New England forms the central problem for investigation. The major project is to write a paper formulating and discussing a hypothesis about the relationship between wealth and power as reflected in the historical records for Salem Village during the 17th century.
This first section concentrates on what can be called "exploratory data analysis," that is, the search for meaningful patterns in numerical data. There is heavy emphasis on graphical and other methods as tools for finding and presenting patterns. The overall goal is to assign meaning to a set of data, stressing the process of translation between quantitative patterns and plausible explanations. Hypothesis testing is one method studied to safeguard against building up a theory on the basis of numerical coincidence or mere chance.
II. Earnings and Discrimination: What Determines How Much Is Earned?
Information on education, occupation, salary, gender race and ethnicity in the U.S. from the National Longitudinal Study of Youth provides a rich data set for investigation. Students formulate and test hypotheses and study the relationships between hypotheses, predications, and actual results.
This section concentrates on hypothesis testing and modeling. The ideas and techniques of measuring differences, the identification of critical and missing variables, and the role of disconfirming evidence in the construction of an argument are emphasized. Important statistical concepts such as distributions, averages, variation, correlation and regression are introduced.
III. Rates of Change: Population and Resources
The rate at which a quantity changes is the focus of this section. The relationships between growth rates of human populations and of resources are explored, beginning with the 18th century writings of Malthus and working toward modeling populations and resources in particular countries at the end of the 20th century. In the laboratory students use real data to design their own models to describe both the status quo and possible future realities.
Rate of change is a concept that is usually covered in calculus courses, but its usefulness in understanding a variety of situations makes it a natural topic of study. As in the two earlier sections of the course, the formulation of hypotheses, the translation of data into argument and the construction of models are used to further understanding.
Further remarks on QR:
The course described above teaches quantitative methods in the context of how they are used. Since it is unlike most college courses, here is some background information on it.
The course is distinctive in a number of ways. For instance, it has been designed and is taught by members of many departments: Biological Sciences, Economics, Geology, History, Mathematics and Statistics, Music, Philosophy, Physics, Psychology and Education, and Sociology. The course was developed in discussions among diverse faculty over several years. Its structure differs from that of a "regular math course" in that it includes lectures, labs and small discussion sections. A Macintosh computer facility is used by Quantitative Reasoning (QR) students for doing data analyses simulations and creating graphical displays. The primary difference, though, is one of approach. The course, which has no prerequisites, is designed to appeal to students with a broad range of academic interests and widely differing mathematical backgrounds -- from math-phobes to calculus-philes. It is not a simple presentation of technical methods followed by practice problems. Instead, case studies from a variety of disciplines form the subject matter of the course. Different quantitative methods are introduced and used in the attempt to develop understanding of these examples. The emphasis is not on rote computation, but on reasoning; not on formulas, but on ways to construct and evaluate arguments. The goals are to help students strengthen their analytical skills and acquire a more confident understanding of the meaning of numbers, graphs and the other quantitative materials that they will encounter in many subsequent courses, no matter what their majors.