Tarefas exploratório-investigativas para o ensino de álgebra na 6ª série do ensino fundamental : indícios de formação e desenvolvimento da linguagem e do pensamento algébricos
The following research, qualitative in nature, originated with the practice of teacher researcher, the challenges encountered in teaching algebra and studies undertaken in respect of investigations mathematical as a methodology potentially motivating and positive results in relation to the development of language and the algebraic thinking. With the main objective of identifying evidence of formation and development of language and algebraic thinking of students who are starting to learn this subject, were the dynamics and communications that occurred in the development of exploratory-investigative tasks into two classes of 6th grade of Education Essential in a private school in the city of Americana - SP. The research was done in partnership with a teacher, who has teaching experience, had already researched and worked with exploratory-investigative activities. Researcher and teacher partner built the tasks undertaken during the investigation with the cooperation of the participants in the Collaborative Group for Research in Mathematics Education (GCEEM), of which both are members. Given the data of the search, a second goal was set: to identify some strengths and limits the use of exploratoryinvestigative tasks in the current educational context. With the focus on the dynamics of the classroom, in the statement provided by exploratory-investigative tasks and the teaching of algebra, it was possible to analyze further the first task, in which students had to explore a situation and analyze a regular basis. In exchanges of ideas among students, with the teacher and the records made during the development of the task, it was possible to identify the signs of formation and development of language and algebraic thinking. The data were collected and analyzed, according to various benchmarks theoretical research on mathematics, communication and teaching of algebra. To build the analysis of the goals outlined, first trying to identify and analyze the communications of the students and teacher at both the oral and written, during the completion of the task. Data were grouped into three blocs: (1) The movement of classroom research and evidence of language and algebraic thinking. (2) The movement of the classroom that led to conflicts and difficulties. (3) The conflict between the thought and language. During the review it was noted that the difficulties encountered by students originated in the absence of concepts - particularly that of variable - and the different language used by the teacher. It was possible to see that students, even with the thought arithmetic, were induced to use symbolic language - used by the teacher - without first developing the concepts needed. We could still see some limits within the educational context, such as the time required to give meaning to the concepts. By identifying the evidence, it became clear that students need to feel that to use the algebra symbolic is necessary- think scientifically - to solve problems, in another words, to be encouraged so that the algebra has meaning.