“When you find the right task, you'll know": design and validation of a geometric task - a case study

The design of a task entails a process in which several elements must be considered that play an active role in the choices that are made and address, in particular, the issue of the suitability of the task that is created. The aim of this article is to present an autoethnographic case study focused on the process followed by two teacher-researchers when designing a task for the assessment of learning related to a geometric object. In the analysis, tools of the Ontosemiotic Approach are used to identify and describe the knowledge produced in the processes of formulation, resolution and validation of the task. Adopting an ethnographic perspective, this paper presents the path followed from the genesis of an idea for a task to its validation, through a reflection on the choices made and focusing on the experience of the eureka moments identified as key in the whole process. As a result, elements of the eureka moments experienced and the trajectory followed by the teachers are described, since these elements are considered fundamental in the processes of problem solving and task design. Finally, as part of the discussion, the authors reflect on the importance of the choice or design of tasks and activities and their relationship with the affective dimension since the achievement of these types of moments creates positive beliefs and attitudes about mathematics, as well as about the students' abilities to do mathematics.