In this article, we report how a geometric task based on the ACODESA methodology (collaborative learning, scientific debate and self-reflection) promotes the reformulation of the students' validations and allows revealing the students' aims in each of the stages of the methodology. To do so, we present the case of a team and, particularly, one of its members who expresses the intention of reformulating validations for a mathematical conjecture besides showing evolution in the form of justifying. [For complete proceedings, see ED581294.]