Proposal for Idaho Teaching Economics Conference



Teaching Theory via Concrete Examples in Excel Workbooks: The Algebra of Expectations

Frank M. Howland

Wabash College

1 November 2000

This paper explores the uses of spreadsheet software to teach abstract ideas by employing flexible, concrete examples. I present the specific case of teaching the algebra of expectations. Excel workbooks demonstrate the fundamental facts about computing expectations for random variables and linear functions of random variables in univariate and bivariate distributions. Using Visual Basic macros, I illustrate the application of the rules for computing expectations via Monte Carlo sampling experiments which students can set up and control. In the illustrations, I deal with discrete and continuous distributions. The workbooks also include applications of the algebra of expectations to two important topics in the economics curriculum: the mean and variance of the ordinary least squares estimator in the standard econometric model, and the basics of the theory of expected utility.

The advantages of my approach include: the graphs are alive—change a parameter and the graph changes; the workbooks present the material from multiple perspectives; workbooks enable students to visualize the computations involved; the software does the tedious work of calculation; examples using real-world data can be readily incorporated into the lessons; instructors can easily vary the depth and breadth of the presentation; exercises testing student understanding are contained in the workbooks; and the software is very easy for students to use.

The particular example of the algebra of expectations supports the following general arguments:

(1) Well-written computer software can enable students to better understand complicated, abstract ideas via specific applications of those ideas.

(2) More specifically, spreadsheets, augmented by Visual Basic macros, are a powerful tool for teaching abstract ideas via example, despite their limited charting capabilities and their lack of tools for solving problems analytically. This power derives from the flexibility of Visual Basic and its ability to control the appearance and working of the spreadsheets, the visual character of spreadsheets, and students' familiarity with spreadsheets.

(3) Active learning is crucial; students must be guided to perform specific inquiries and to reflect on the results of those inquiries.

(4) There is no substitute for hard work by students and teachers. Most students will only truly understand abstract ideas by seeing the way they operate in a variety of contexts and by then being required to distill the common structure behind the examples. Teachers must read student answers in order to ascertain whether the point has been absorbed.

In my presentation I will demonstrate the workings of the spreadsheets using a laptop and projector. I will show how the material is used in Econometrics and Corporate Finance courses at Wabash College and will make the code available to interested parties, provided they agree to properly cite the work. This paper is based on ideas arising out of a long-standing collaboration with my colleague Humberto Barreto. A web site containing relevant material for this presentation can be reached by clicking on the "Proposal for 2001 Economics and the Classroom Conference" link at wabash.edu/econometrics.

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