“Whiteboxing” the Content of a Formal Mathematical Text in a Dynamic Geometry Environment

Abstract

In this article, we provide an empirical example of how digital technology; in this case, GeoGebra may assist students in uncovering—or whiteboxing—the content of a mathematical proof, in this case that of Proposition 41 from Euclid’s Elements. In the discussion of the example, we look into the impact of GeoGebra’s “dragging” functionality on students’ interactions and the possession and development of students’ proof schemes. The study and accompanying analysis illustrate that, despite the positive whiteboxing effects in relation to the mathematical content of the proposition, whiteboxing through dragging calls for caution in relation to students’ work with proof and proving—in particular, in relation to students seeing the necessity for formal proof. Moreover, caution must be paid, e.g., by teachers, so that students do not jump to conclusions and in the process develop inexpedient mathematical proof schemes upon which they may stumble in their future mathematical work.