Using what we (Wilfried Herget and myself) refer to as picture mathematics, we can introduce younger children to the skills inherent in mathematical modeling. In this exercise the students must approximate the volume of this balloon in cubic meters. In order to do this, an appropriate yardstick must first be chosen, which in most cases is the average height of a male (the figure on top of the balloon). Next the students choose appropriate geometrically model(s) whose volumes can be easily found out. In some cases, even students as young as 9th graders used the regression

feature of the calculator to obtain functions defining the curvature of the balloon and found out through research that through the process of rotating the function(s) on an axis, i.e., obtaining the integral between two parameters of the square of the function multiplied by π, they could approximate the volume. Of course, they did not at this point have the formal understanding of the algorithms involved or why they work, but they knew that this would assist them in solving the problem. This is using the technology as a black box.

Beware: Some clever students realized that the number on the balloon is a telephone number (in Austria) so they called to find out the “official” answer!






							COMPUTER ALGEBRA SYSTEMS - TECHNOLOGY IN MATHEMATICS EDUCATION