A Narrative Approach to Foster the Construction of Recursive Thinking in High School Students

Abstract

In this paper, we will explain the development of a mathematical activity involving narrative and short stories in particular, with the aim of investigating whether it is possible to use the narrative approach to promote the construction of recursive thinking in high school students from a four-year scientific high school (Grades 11 and 12). We present qualitative research based on the networking of two theoretical frameworks used to analyze students’ protocols and the issues surfacing during class discussion: Abstraction in Context (AiC) and Documenting Collective Activity (DCA). In our research, the students, divided into small groups, dealt with a highly immersive “story problem” with the Sierpinski Triangle as its central element. The task was designed to ensure consistency with the story and involved the construction, with GeoGebra 6.0 software, of a fractal city, Fractlandia, with squares and sinkholes. The preliminary results show that the story proposed functioned as a motivation to solve the problem, and the last questions of the task proved the most engaging for the students, mainly because of the connection with the story, and also because they involved some reflection about the behavior to the infinity of the perimeter and the area of the Sierpinski Triangle.