Submitted by Celso Magalhaes (celsomagalhaes@ufrrj.br) on 2018-09-25T18:27:49Z No. of bitstreams: 1 2017 - Sarai Oliveira Silva.pdf: 2076016 bytes, checksum: 4439b4d16ef8bd453bd30cbb53b93014 (MD5) / Made available in DSpace on 2018-09-25T18:27:50Z (GMT). No. of bitstreams: 1 2017 - Sarai Oliveira Silva.pdf: 2076016 bytes, checksum: 4439b4d16ef8bd453bd30cbb53b93014 (MD5) Previous issue date: 2017-08-31 / This research analyzes answers given by students of the first grade of High School about the elaboration of tables with prototypical examples of functions in a collaborative environment in which the students worked in pairs or groups of no more than three members. The development of this research was based on the Design Experiment on which we established the Theoretical Methodological foundation that also served to establish a framework of teaching and learning of functions for this group. The starting point was the preconceived ideas about the concept of function and about operations on the set of integers, Z. The set of familiar, but unconventional tasks to introduce the theme originated from this central idea, operations in Z. These tasks and the recording of students' written responses are our instrument of data collection and analysis. That is, the students needed to explain or justify the procedures used. The analysis of the answers has revealed that many students come to High School without knowing that the term function is also used to designate a mathematical concept; that the notion of function for them becomes the idea of "making calculations" and that for some students, function is the calculation itself. Based on the considerations above, we believe that the challenge is to think how to intervene in the classroom so that the student is given the opportunity to review his notions and broaden his vision of the concept of function. As a result of this research, we present a didactic guide for teachers containing suggestions of tasks for the study of functions starting from some of the preconceived ideas / Esta pesquisa analisa as respostas dadas por estudantes da 1? s?rie do Ensino M?dio acerca da elabora??o de tabelas, com exemplos protot?picos de fun??es, em um ambiente colaborativo, em que os estudantes trabalhavam em duplas ou em grupos de no m?ximo tr?s integrantes. Para o desenvolvimento desta pesquisa nos apoiamos no Experimento de Design, sobre o qual estabelecemos um quadro de ensino e de aprendizagem de fun??es para esse grupo. O ponto de partida foram ideias preconcebidas sobre o conceito de fun??o e sobre as opera??es no conjunto dos n?meros inteiros, Z. O conjunto de tarefas familiares e n?o convencionais, elaboradas para introdu??o do tema, partiu de opera??es em Z. Estas tarefas e o registro das respostas escritas dos estudantes s?o o nosso instrumento de coleta e an?lise de dados. A an?lise das respostas nos revelou que muitos estudantes chegam ao Ensino M?dio sem conhecimento de que o termo fun??o ? tamb?m usado para designar um conceito matem?tico, que a no??o de fun??o dos estudantes est? associada ? ideia de fazer contas e que para alguns, fun??o ? a pr?pria conta. Como produto resultante desta pesquisa, apresentamos um guia did?tico para o professor, contendo sugest?es de tarefas para o estudo de fun??es, cujo ponto de partida s?o algumas das ideias preconcebidas dos estudantes sobre fun??o