“REINVENTING” TECHNIQUES FOR THE ESTIMATION OF THE AREA OF IRREGULAR PLANE FIGURES: FROM THE EIGHTEENTH CENTURY TO THE MODERN CLASSROOM

Abstract

The issue of the area of irregular shapes is absent from the modern mathematical textbooks in elementary education in Greece. However, there exists a collection of books written for educational purposes by famous Greek scholars dating from the eighteenth century, which propose certain techniques concerning the estimation of the area of such shapes. We claim that, when students deal for an adequate period with a succession of carefully designed tasks of the same conceptual basis—in our case that of the area of irregular shapes—then they “reinvent” problem-solving techniques for the estimation of their area, given that they have not been taught anything about these shapes. These techniques, in some cases, are almost the same as the abovementioned historical ones. In other cases, they could be considered to be an adaptation or extension of these.