DISCUSSION AND CONCLUDING REMARKS
The data presented illustrate the diversity of ways of thinking and modes of action:
four groups of solvers, who certainly have very different learning experiences, attend
different schools and live in different places, realize and recognize the potential
relevance of a single tool, GeoGebra, in solving this problem. These four solutions
exemplify the kind of symbiosis described by Borba and Villarreal (2005) since the
problem solving strategies and representations they use are revealing of subjects in
action with a technological tool; so they can be identified as “students-with-media” or
perhaps more accurately as “students-with-GeoGebra”.
Still, it is possible to identify common aspects of their problem solving activity: they
all represent the rectangular lawn and the triangular flowerbed, they all use “dragging”
to check or verify, and they all analyse and conclude. But what each one takes out of
that activity is not entirely the same and seems to be closely related to their ability to
use, simultaneously, their mathematical competence and their technological fluency.