Equações quadráticas : articulando suas formas algébricas e geométrica via um aplicativo ad hoc

Abstract

The main aim of this paper is doing a research in order to have a better understanding of the reasons that shows how the students from the 12th grade in the secondary education (two groups: ten in the first phase and six in the second) articulate algebra records and the quadratic equation formula, as well as, defining and developing a computational tool which could be helpful to this articulation. Once seen as fragmented, the articulation between these two records has been labeled as ordinary, however, many studies have shown that it’s not entirely true, since the students themselves don’t understand the articulation, even those who are in the last term of secondary school. As a means to find answers to these doubts, we’ve developed our research focusing on Duval Semiotic Representation Theory (2005). Having Balacheff Computational Transposition Theory (1993) as an example, we’ve developed an application called Formas, mentioning the importance of linking equations and graphics at the same time, considering the global learning and attesting visual variables which match to symbolic units. The investigation of the difficulties made us classify them by four types, initially identified in the phase one and once again attested in the first activity of the second phase. We’ve noticed that the application is efficient as a tool, especially when articulating in the graphic with the equations, when analyzing the procedures taken in the second activity, which were compared to the first activity. They made the students think more about their actions when identifying such difficulties and understanding their causes. Besides, it allowed the surge of further questions about software developing ad hoc to apply them in scientific researches, in the classroom, as well as, the necessity of a more specific, extending very far project about the articulation of algebra and geometry when teaching mathematics.