História da matemática e produção de significado: proposta de tarefas didáticas para o ensino do teorema de Tales

Abstract

This field research has a qualitative approach and was developed in a class of students of the second year of high school of a public school in the city of São Raimundo das Mangabeiras - Maranhão. It is a dissertation work of Professional Master in Science and Mathematics Education and consists in the elaboration, application and validation of an educational product presented to the students of this class. Its general objective is to analyze the production of mathematical meaning of students in the resolution of didactic tasks under the epistemological support of the semantic fields model (MCS). Under the influence of the notions of meaning and knowledge expressed in the MCS, an alliance between the epistemological notion and the history of mathematics resource was provided through the construction of an episode of history of mathematics based on traditional accounts dealing with the structuring of Tales, starting from the problem of calculating the height of a pyramid and proposing the resolution of didactic tasks to the students. Five meetings were held with the class during the math class schedule for the application of the math history episode and didactic tasks. The work used field research and the aid of images and audio recording with transcription. It presents the students 'resolutions through written records, gestures and speeches, which in the authors' conception produced meaning according to the notions-categories pointed out in the MCS. It is noteworthy that it was established a reading of the production of the meaning of these subjects in the proposed tasks and that in another situation could be different productions. The MCS develops in the field of action and, at that moment, the perception brought is not that of error, but of the process, in which one can know where the student legitimizes what he speaks and as a teacher should go where student is cognitively talking to him. However, it is understood the feasibility of applying the tasks developed for real classrooms. The students' productions went in the direction that was intended, promoting the validation of the sequence of tasks developed in the research. The educational product, Teaching Tasks Using Mathematics History Episodes to Produce Meaning on the Tales Theorem is able to become an instrument that incorporates the strategies adopted by mathematics teachers in the use of mathematics history in the classroom. , enabling a rapprochement between students and teacher and between students and students, since MCS allows and envisions this approach between individuals in the context of the teaching and learning process.