Abstract

Producing geometric constructions with a ruler and compass or using some dynamic software, as well as justifying and explaining the procedures used with a geometric language, are part of the knowledge necessary for the teaching of geometry in Chile. In this article, we analyze the learning of this knowledge from the objectification processes that occur when two future mathematics teachers and the teacher educator worked together to solve a task that required the construction with GeoGebra of a right triangle with certain properties. In the results, we observed that the contradictions inherent in the response of a student drove the actions of the participants towards the achievement of the objective of the activity. In addition, the coordinated use of words, gestures and geometric notation made it possible tomake the intentions and actions of the subjects apparent in search of an encounter with mobilized knowledge. Finally, we highlight the role of some participants in the learning reflected in the activity.