A organização do ensino de funções em um curso de licenciatura em matemática de uma universidade tecnológica: contribuições da teoria da atividade e da abordagem CTS para a aprendizagem da docência

Abstract

The research had as its objective to scope the teaching of the function concept in a discipline of “Elementary Mathematics Fundamentals: Numbers and Functions”, within the Mathematics Teaching Graduation Course in the Pato Branco Campus of the Federal Technological University of Paraná, on the direction of the learning process in teaching by future Mathematics teachers in Graduation courses. Based upon the proposed objective, the research problem adopted was: How does the organization of the teaching process of a concept in a discipline of “Elementary Mathematics Fundamentals: Numbers and Functions” can favor the learning of the teaching activity in the ambit of a technological university? To answer this question, the research takes on the theoretical presuppositions of Vygostsky’s Cultural-Historic Theory and the Activity Theory, beginning from the activity concept developed by Leontiev and the concept of Teach-Orienting Activity (AOE, translated) brought by Moura. For the development of the camp research, it was utilized the elaboration of Learn-Prompting Activities (SDAs, translated), founded on the AOE principles. Because it is a Graduation Course in a technological university, taking institutional policies as the parameter, a CTS approach was recurred to in the teaching situations, in order for the students to develop a scientific and technological alphabetization and to act within society to improve it. The situations that prompt learning were elaborated to the teaching of functions in the context of the discipline of “Elementary Mathematics Fundamentals: Numbers and Functions” and considering the thematic proposition about the production of conventional organic tobacco, which is related to the students’ background. It was applied to a first period class in the Mathematics Teaching Graduation Course of UTFPR – Pato Branco Campus, with the participation of 14 students in 8 meetings. The instruments used to collect data were: observation logbooks, writings from the participants, the recording of the interventions and talks with the class. The analysis of the data was done by using Caraça’s concept of “Isolated”, with the construction of episodes that consist of selected scenes within the data collected in reality. In the analysis process, two “Isolated” were determined: “Indications of the appropriation of the function concept” and “The teacher formation and the CTS approach in a technological university”. The data analysis evidences that this form of organizing the teaching of a concept can help students comprehend the essence of the concept itself, leading them to activity, can contribute for them to act in society in a critic manner, with the condition to make scientific and technological choices, and also collaborate for a Mathematics teaching linked to reality, where students reflect on the subjects and participate in a more collaborative way. Moreover, if employed in the initial formation of teacher, it can contribute to the formation of teachers with experiences as students in the CTS approach and the concept of teachorienting activity, só that they can utilize these references in their teaching activity.Keywords: initial teacher training; teaching guiding activity; STS; functions; mathematics education.