Análise do nível de raciocínio matemático e da conceitualização de conteúdos aritméticos e algébricos no ensino fundamental - considerações acerca de alunos do Sistema Telensino Cearense

Abstract

This study examined the level of mathematical reasoning and conceptualization of addition and algebraic structures in 8th grade tele-students, in view of the social and historical conditions prevailing in the Telensino system. The guidelines of the research were defined with a basis on the Theory of Activity, according to which the process of learning can only effectively occur departing from the activity of the learning subject mediated by another, through whom it is possible to apprehend patterns of insertion into reality, and through historically and culturally constructed objects of culture. Thus, in order to understand the elements of the learning process of the Telensino students it was necessary to examine the development of activity within the classroom, assessing both the subjects responsible for the social mediation and the textbooks - the Manuais de Apoio - through which the mediation of instruments takes place. In order to encompass all these aspects, different methodological steps were adopted: for classroom activity, the methodology was direct observation, for the students, semi-directed interviews and tests of mathematical conceptual domain, as well as tests of mathematical reasoning, were employed; as for the textbooks, these were analyzed against the background of MEC requirements and with reference to their approach to the concepts of addition structures and algebraic concepts. The study indicated that the students present a level of mathematical reasoning beiow expectations for 8th grade students: in general, they rank in the first of the four stages of mathematical reasoning development, as defined by Johannot, displaying a tendency to centralization and difficulty in symbolizing. As concerns mathematical and algebraic concepts, students demonstrate serious problems with addition structures, besides a very limited understanding of algebraic expressions and problems. These deficiencies were regarded as being reinforced by characteristics which are peculiar to Telensino: the presence, in the classroom, of a lay teacher, who is not required to be even a Mathematics graduate, the use of the Manuais de Apoio that reduce the student to a passive attitude and fragment the contents in order to fit the broadcasting system that brings them into the classroom, the impossibility of taking into consideration the conceptual domain of either student or class, prior to defining further challenges, since the broadcasting is unified for the whole of Ceará. It seems clear that the adoption of Telensino as a means to universalize the Ensino Fundamental has hindered the establishment of a personnel-qualifying policy to face the real needs of adolescents attending public schools in Ceara.