EJMT Abstract

A common response to new educational technology is to suggest banning it, arguing that it could replace the development of certain skills and knowledge with the capabilities of the new tool. To counter this argument, it is essential to provide examples demonstrating how the wise use of new instruments can enhance the teaching and learning of mathematical competencies. In our present contribution, we address the situation described above through an example in Geometry which incorporates the following elements:

1. the automated reasoning tools of GeoGebra Discovery, an experimental version of the mathematical software GeoGebra;
2. the development of mathematical reasoning and proof competencies through elementary geometry problems, such as loci computation; and
3. a concrete geometric construction as triggering event: given a triangle ABC, find the locus of points P such that ∠ABP and ∠ACP are congruent.

This construction can be quickly done using GeoGebra Discovery, but what does “finding” mean here? Is it just creating a visual image or finding an equation with coefficients based on the positions of A, B, and C? Our goal is to understand the geometric locus both symbolically and geometrically. As we explore with the help of algebra and geometry software, we’ll discover various connections to geometric concepts that will deepen our understanding of elementary geometry. In summary, our goal is to describe the challenges that arise in this elementary, yet highly inspiring and intriguing context, as an example of the methodological protocols and clear advantages associated with new technologies in mathematics education.