Constructing a Parabolas World Using Dynamic Software to Explore Properties and Meanings

Mathematical instruction scenarios should provide conditions for students to pose and reflect on questions that lead them to identify and discuss mathematical relationships. The use of dynamic software offers students the possibility to represent mathematical objects and examine their relationships from multiple perspectives. In this context, we discuss an example in which a simple geometric configuration, constructed through dynamic software, functions as a platform to generate mathematical relationships that need to be explored and presented in terms of their properties. Thus, we illustrate that dynamic representations of mathematical objects may help students reconstruct basic mathematical results and identify connections among those objects. In particular, we observe that analysing behaviours of triangles, rectangles, lines, segments, or perpendicular bisectors may guide students to search for properties and meaning associated with parabolas.