Students’ Epistemological Framings When Solving an Area Problem of a Degenerate Triangle: The Influence of Presence and Absence of a Drawing

Abstract

This study explores the epistemological framings of undergraduate students when solving an area problem of a degenerate triangle, without or with a triangle drawing. Through mixed research with a triangulation design, the resolution processes and responses of students were analyzed. The aim was to analyze how students’ epistemological framing changes during the problem-solving process depending on whether the task contains the drawing of the triangle or not. Quantitative results show significant differences between students who solve the problem without a triangle drawing and those who do. Qualitative results evidence that students who solved the problem with the drawing established an initial epistemological framing that contained an “obvious fact”: the non-zero area of the triangle. They hardly modified this epistemological framing during the solving process, forcing the response to be a positive number. In contrast, students who solved the problem without the drawing easily modified their initial epistemological framing by observing that the area of the triangle was zero. Students’ perceptions of the level of difficulty of the problem are discussed, too.