As contribuições do ensino desenvolvimental de Davydov para o ensino de geometria euclidiana no curso de licenciatura em matemática

Abstract

The research presented is themed "The contributions of the developmental teaching of Davydov for teaching Euclidean geometry in a degree course in mathematics" and stems from the problem: what is the potential of the developmental teaching theory of Davydov in the teaching-learning processes of the Pythagorean theorem in a degree course in mathematics? The research, applying a qualitative approach, followed the dialectic-critical method, as suggested by Gamboa (2013) and Triviños (2013) and based on the cultural-historical theory of the following authors: Vygotsky (1991, 1993, 2001), Davydov (1987, 1988), Libâneo (1989, 1994, 2004, 2006, 2009, 2011), Freitas (2012, 2013, 2015), and Libâneo and Freitas (2013). The participants of the research were students from the 6th period of course degree in mathematics at the Pontifícia Universidade Católica de Goiás (Goiás) studying Euclidean geometry. Using the studies of Davydov, the research seeks alternative methodologies to teaching-learning of mathematics, therefore, a didactic training experiment was planned and applied between the months of April and May 2017. The data were collected using a socio-economic survey; a diagnostic evaluation at the beginning of the experiment, in addition to printed activities and audio recordings that were catalogued, transcribed and categorized according with the developmental teaching theory. An evaluative activity was applied at the end of the experiment in order to identify the student’s zone of actual development, after the developmental activities were applied. The analysis identifies that, regarding the diagnostic evaluation and the sociocultural context, the participants of the research have received a precarious education from a school that is not efficient at scientific education in the area of mathematics, carrying potential damage on the formation of the future mathematics teacher. Regarding the formative didactic experiment, the analysis concluded that the Davydovian approach, in this case, promoted activities that motivate and at the same time shape the student when he/she is directed by the teacher. The evaluation of the zone of actual development of the student, at the end of the survey, concluded that, although all the students took part of all the stages of the experiment, not all were able to interpret and solve the proposed problems about the theme presented, a fact regarded as signs of learning, concluding that there was no concept formation in its entirety. The observation is that the historical context and the generalization presented in the topic were not presented to the students participating in the survey in the period they were in high school, neither during the initial process of their course, it is considered that this approach was important to the student in order to understand the dialectical and historical development of the object. Regarding to non-appropriation of the content by some of the participants, this point out the need for further research, since the students lack understanding of essential concepts.