Submitted by PPG Educa??o em Ci?ncias e Matem?tica (educem-pg@pucrs.br) on 2018-11-27T18:59:25Z No. of bitstreams: 1 Tese vers?o final ok-homologada-27-11-18-Jeronimo-Becker.pdf: 2687389 bytes, checksum: a925730cf70384b2d14e62893fe74aec (MD5) / Approved for entry into archive by Sheila Dias (sheila.dias@pucrs.br) on 2018-11-28T14:06:20Z (GMT) No. of bitstreams: 1 Tese vers?o final ok-homologada-27-11-18-Jeronimo-Becker.pdf: 2687389 bytes, checksum: a925730cf70384b2d14e62893fe74aec (MD5) / Made available in DSpace on 2018-11-28T15:59:29Z (GMT). No. of bitstreams: 1 Tese vers?o final ok-homologada-27-11-18-Jeronimo-Becker.pdf: 2687389 bytes, checksum: a925730cf70384b2d14e62893fe74aec (MD5) Previous issue date: 2018-10-11 / In this doctoral thesis we seek for an understanding of how learning Calculus takes place in a context with instructors assisting professors, from two theoretical axes: Vygotsky?s social interactivity and David Tall?s three worlds of Mathematics. The investigation was carried out with a qualitative approach, as a case study, and the corpus was analyzed from the methodological perspective of Discourse Textual Analysis. The thesis we support here is that the tutoring Calculus?s can make a significant contribution for the learning of the Mathematics if the pedagogical proposal is guided by the theory of Three Worlds of Mathematics and supported in social relationships established between the peers. In that search, a study was carried out in 2 phases at Higher Education Institutions in the state of Rio Grande do Sul. On phase 1, we contacted the institutions in the state that have Calculus as a subject in their programs and who have instructors to assist professors and qualify learning. The most representative institution regarding the presence of interactive movements and of the theory of 3 worlds of Mathematics, participated in Phase 2, which was a return to the research field, and where we could dedicate a more specific look to the case. Professors and their instructors were interviewed. From the results obtained, we highlight the social relationship among subjects as a significant factor in learning Calculus. Team work can contribute for that to occur and the institution has to organize instructors? activity so as to make that action possible. We also identified that proximity between the instructor and the student can provide a tension-free environment, where communication takes place easily with a closer language, enhancing chances of building mathematical knowledge. Another finding was the fact that acting as an instructor can contribute to form a future teacher, incentivating students who are not in a teaching major and promoting articulation between learning theories discussed in classes with practical situations for those in a teaching major. The relevance of analyzing the mistakes students make and the need of mapping what has already been found to trace educational actions is another finding. In addition to that, we realize that digital technological resources can be allies for the instructor, favoring the path through the three worlds due to the possibilities of manipulating, visualizing and exploring, and their use is necessary in line with pedagogical practices aiming at autonomy and criticism. / Nesta tese, buscamos compreens?es relacionadas ? aprendizagem de C?lculo no contexto das monitorias, a partir de dois eixos te?ricos: a sociointeratividade de Vygotsky e a teoria dos tr?s mundos da Matem?tica de David Tall. Nessa busca, desenvolvemos uma investiga??o com uma abordagem qualitativa, do tipo estudo de caso, cujo corpus foi analisado a partir da perspectiva metodol?gica da An?lise Textual Discursiva (ATD). A tese defendida ? as monitorias de C?lculo podem colaborar significativamente para a aprendizagem de Matem?tica se a proposta pedag?gica desenvolvida for orientada pela teoria dos Tr?s Mundos da Matem?tica e fundamentada nas rela??es sociais estabelecidas entre os pares. Na busca por esses entendimentos, realizamos um estudo em Institui??es de Ensino Superior (IES) do Rio Grande do Sul, composto por duas fases. Na Fase 1, estabelecemos contato com IES ga?chas que realizam cursos com a disciplina de C?lculo e buscam qualificar a aprendizagem a partir da monitoria. A IES mais representativa em rela??o a ind?cios da presen?a de movimentos interativos e da teoria dos tr?s mundos da Matem?tica, participou da Fase 2, que foi um retorno ao campo de pesquisa, no qual dedicamos um olhar mais espec?fico para o caso. Foram entrevistados os professores respons?veis e os monitores. Dentre os resultados obtidos, destacamos a rela??o social entre os sujeitos como um fator significativo para a aprendizagem de C?lculo. O trabalho em equipe se constitui em uma possibilidade vi?vel para que isso ocorra, havendo a necessidade de que a institui??o organize a monitoria de forma a possibilitar esse tipo de a??o. Tamb?m identificamos que a proximidade entre monitor e estudante fomenta um ambiente livre de tens?es, em que a comunica??o ocorre de maneira facilitada em fun??o de uma linguagem mais pr?xima, aumentando as chances de constru??o do conhecimento matem?tico. Outra constata??o foi o fato de a monitoria ser um ambiente de forma??o para o futuro professor, incentivando a doc?ncia para estudantes que n?o cursam licenciatura e para aqueles que a cursam, promovendo articula??o entre teorias de aprendizagem vistas em aula com situa??es pr?ticas. A relev?ncia de analisarmos os erros que os estudantes cometem e a necessidade do mapeamento dos j? encontrados para o tra?ar de a??es educacionais foi outra constata??o. Al?m disso, percebemos que os recursos tecnol?gicos digitais podem se constituir em aliados do monitor, favorecendo o percurso pelos tr?s mundos em fun??o das possibilidades de manipula??o, visualiza??o e explora??o, sendo necess?rio o seu uso em conson?ncia com pr?ticas pedag?gicas voltadas ? autonomia e ? criticidade.