Teaching geometry through didactical situations: the case of the triangle inequality

Abstract

This paper aims to discuss the use of Brousseau’s Theory of Didactical Situations in mathematics (TDS) for eighth-graders to explore the concept of triangle inequality in Euclidean geometry. Data sources included observation notes, video recordings of lessons, and students’ written work. Data analysis was done through a deductive content analysis approach that utilized the conceptual framework based on Brousseau’s notion of didactical situations. Findings revealed that student behaviors that were expected to take place through situations occurred at every phase as stated in the theory. Mathematical ideas leading up to the construction of new knowledge were gradually formulated and justified as stages progress. Students worked out different methods of evaluation to solve an open-ended exploratory task and defended them in a way that invited other students to implement their chosen strategies. They developed their implicit informal knowledge by building on their thinking and the thinking of others through situations. All these results highlight how important it is to use didactical situations to pave the way for learning to learn, as it not only facilitates the purposeful exchange of ideas through whole-class discussion that ensures a common understanding of mathematical ideas but also allows students to create their own learning adventures.