3.4.0.8 Success of the Course: the Mathematics Learned.

By providing students with immediate access to authentic data, the web gives students a great sense of power. In addition, using spreadsheets to construct mathematical models forces students to think algebraically about the relationships between different quantities. It is impossible to get the cell references right without understanding the relationships, and it is impossible to enter the formulas correctly without knowing algebra. To make charts correctly, the student must understand the relationship between numerical data and its graphical representation. Thus, using spreadsheets provides a fresh way of reviewing algebra, percentages, and graphs. The student reports show that this review was well received.

In addition to strengthening the basics, IDD enabled students to explore some significant mathematics. As an illustration, two examples are described.

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In the lab on the Charles River water flow, students investigated rates of change and accumulated change - thereby receiving a discrete introduction to calculus. This lab was also useful in another important, though less deep, way. It ensured that students thought about how to change units - both linear and cubic units as well as the units of rate of change.

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In making their presentations, some students went to the UN website and downloaded data on the Human Development Index (HDI) of several countries. The HDI is a weighted average of several quantities such as per capita income, GNP, life expectancy, and adult literacy (all indexed so that they are percentages), and so on. One group's presentation, which showed the regression of HDI against GNP, set off a firestorm of argument. Students felt that it was not legitimate to fit a regression line to this data since HDI contained GNP as one of its components. This was an extraordinarily interesting and thought-provoking argument, which caused students to do a great deal of independent investigation.