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TALK ABOUT TEACHING


Teaching Quantitative Skills: How Some Faculty Have Responded

by Jonathan Baron

The College of Arts and Sciences has instituted a quantitative skills requirement, beginning with this year's freshmen. The idea is to encourage students to become "numerate." The modern world requires understanding of how people make inferences from numbers, particularly empirical data. In the last 100 years, statistical and numerical methods have spread to all levels of government, the world of commerce, medicine, and even law. In academia, the natural and social sciences have used these methods all along, and they are spreading to the humanities. The new requirement is not just about statistics or mathematics. It is about the promise and pitfalls of drawing conclusions from numbers, so it is also about scientific thinking, degrees of confidence, alternative explanations, plausibility, error, and also about the advantages of data over unaided intuition.

The nature of our requirement is different from that of any other college we know. It emphasizes hands-on experience with real data, rather than canned exercises (although we recognize that those are sometimes helpful too). Real data are important, because students can raise real questions about them. Was the sample biased with respect to the question? Was the sample big enough? How confidently could we extend the conclusion to other samples? What other ways might we answer this question?

Several courses have now been approved as meeting the requirement, and we have given small grants for the development of other courses. All the approved courses are listed in the quantitative skills web page, www.sas.upenn.edu/college/quantitative_skills/, with links to many syllabi.

Some are statistics courses. We have approved these as meeting the requirement only when they involve analysis of real data. Other courses are more traditional laboratory courses in the natural sciences. We approve these when exercises are open-ended enough so that students can raise real questions about interpretation, when it isn't just a matter of getting the right answer. Here are some examples of assignments in other kinds of courses, with particular attention to the projects that provide experience with real data.

History 188: Global Issues in Local Perspectives: Markets, Health, and Hunger
Among other things, students search the Web for data sets on poverty and deprivation. They use these data sets and others, provided for them, to carry out analyses using Systat (a statistics package now widely available on campus). They ask such questions as, "What is the relationship between the level of urbanism and national wealth?" and "What is the relationship between family income levels and child poverty?" They compare rates of growth among countries over two separate historical periods, examining graphs as well as descriptive statistics.
 
Linguistics 102: Introduction to Sociolinguistics
Students engage in four field projects, in which they make individual observations or field experiments on language change and variation in the Philadelphia area. They then upload their data into a class spreadsheet on a server at the Linguistics Lab, following a standard format. Then they are given an assignment for the analysis of the class data as a whole, which involves statistical tests on those relations that appear to them significant between the dependent linguistic variables and the various independent variables: age, neighborhood, gender, social class, etc. The course is taught in a room with computer projection connected to the net.
 
Political Science 215: Political Institutions and Economic Performance
Students define and carry out a project that involves replicating at least one important analysis dealing with the relationship between political regimes and economic performance, using the original data. The purpose is to help them understand the steps involved in the empirical examination of scientific propositions and, most importantly, to grasp how inferences are made on the basis of the data examined. They are encouraged both to understand the original analysis and to experiment with alternative approaches. The course has no prerequisite, but students are introduced to multiple regression, the main method used in the studies examined.
 
Psychology 453
Not all of the courses involve statistical analysis. This course is about decision analysis, particularly the elicitation of judgments of utility (or goodness, or value) of the sort used in cost-effectiveness analysis. Students elicit their own utilities for hypothetical medical conditions. Next, they carry out a decision analysis using several attributes, such as choosing a method for birth control. These methods emphasize that the relative value of attributes (e.g., price, probability of failure, or inconvenience) depends on the ranges in question, and raw judgments of "importance" are typically meaningless. Students also do an exercise on "conjoint analysis," in which the subject makes holistic ratings of various combinations of attributes, and they do a project in groups. Data are collected on the Web and analyzed using Systat. Last year, one of the projects, done on the web, used conjoint analysis to compare the values of those who owned (or preferred) sport utility vehicles and those who liked ordinary cars.
 
Sociology 4: The Family
Students complete a questionnaire concerning their own families. The questionnaire concerns attitudes ("Living together before marriage makes good sense"), experiences ("How many of your friends have had sexual intercourse?"), and background information ("Did your mother work full-time while you were under 6?"). Students then propose hypotheses to test, concerning correlations among various answers, and they discuss and test these hypotheses. They use Stata (a statistics package). Each student writes a 5-7 page paper.

The committee invites other faculty to develop courses along these lines and others. We would be happy to discuss ideas you have for introducing exercises or assignments in your courses specifically designed to teach quantitative skills (especially in Arts and Sciences). We have also made a statistics package, Systat, widely available around campus, for use in such courses.


With this essay, the Talk About Teaching series enters its fifth year as a project of the College of Arts and Sciences and the Lindback Society for Distinguished Teaching. Dr. Baron is Professor of Psychology and Chair of the College's Quantitative Skills Committee. The committee's web page may be found at www.sas.upenn.edu/college/quantitative_skills


Almanac, Vol. 45, No. 8, October 20, 1998

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