Breaking the didactic contract in solving a geometry problem with high school students

Apolo Castañeda
Juan Arturo Hernández-Morales
Rosa Isela González-Polo

Abstract: This study reports the results of the implementation of an experimental design in a high school mathematics classroom (students 12-14 years old) aimed at the construction of triangles, given three segments. Within the experimental design, there is a problem of calculation of area and perimeter where the ruptura and establishment of didactical contract is analysed. For the design of the sequence, theoretical reflections on the concept of didactical contract of Brousseau were considered, as well as the problem solving model of (Lester, 2013: 258), this allowed the design of activities regarding triangles construction using paper strips. These activities served as a prelude to address a problem of calculation of area and perimeter of a triangle with wrong measures. The results show that students get into contradictions, because despite finding certain conditions for the measure of the segments of a triangle and working previously with unsolvable problems, they cannot recognize a triangle with wrong measures and even claim that it is possible to obtain the perimeter of three segments of a figure which is not closed.

Key words: Didactical Contract, problem solving, geometry, high school students.


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