Abstract:

The aim of this study is to analyse the performance of a group of students aged 10-11 in a construction of a table in a routine mathematical exercise and its impact in terms of transformations of representations. The methodology was qualitative (case study). The participants were 17 students who worked individually. The task consisted in a routine geometrical exercise with the statement in verbal language and with the drawing of six triangles. Students had to classify each triangle by their sides (scalene, isosceles and equilateral) and by their angles (right triangle, obtuse triangle and acute triangle). We asked them to organize their answer in a table. Data were collected by individual students’ written registers. All students constructed adequate tables. We verified that students of this age were autonomous and critics. They elaborated a table with the same information but organized it in different ways and with different degrees of abstraction. During the resolution of the task, the students made treatments and conversions. In the tables of C1 category, students classified each of the triangles in a simple way despite the information obtained could be related. In the tables of C2 category, students grouped the triangles in a different way, allowing students to make other comparison among the triangles. We concluded that the table make possible to increase the number and the quality of the transformations of representations. The answer organization in a table can improve a routine mathematical exercise because it ensures a variety of transformations of representations which develops their fluency among representations allowing the students an understanding of mathematical contents.

Keywords:

middle school, routine mathematical exercise, table, transformations of representations.