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Previous issue date: 2017-02-24 / A pesquisa que originou este texto de tese de doutorado teve como objetivo examinar de
que forma as ideias de John Wallis, emergentes na obra Arithmetica Infinitorum, datada de
1656, apresentou inova??es que podem contribuir para o encaminhamento conceitual e
did?tico de no??es b?sicas da componente curricular de C?lculo Diferencial e Integral, no
curso de Licenciatura em Matem?tica. Nesse sentido, avaliamos o potencial pedag?gico da
referida obra para subsidiar o ensino de conceitos matem?ticos, em particular as no??es de
integrais, com vistas ao melhoramento do entendimento dos estudantes acerca dessas ideias
matem?ticas, tratadas nos Cursos de Forma??o de Professores de Matem?tica. Por
admitirmos que os alunos necessitam ampliar o n?mero de trajet?rias que levam ao
desenvolvimento de uma ideia Matem?tica ? que, neste trabalho, nos propusemos a
responder a seguinte quest?o: como a explora??o did?tica do exerc?cio criativo de um
matem?tico na hist?ria pode contribuir na abordagem pedag?gica para o ensino de
conte?dos de C?lculo e An?lise na Licenciatura em Matem?tica? Para tal, apoiamo-nos em
princ?pios de criatividade elaborados por Mihaly Csikszentmihalyi, que prop?s um modelo
para criatividade que leva em considera??o o contexto social e cultural. Por considerarmos
fundamental a explica??o do ciclo do pensamento referente ? inven??o matem?tica,
associamos a esses princ?pios os processos do Pensamento Matem?tico Avan?ado,
proposto por Tommy Dreyfus, de modo que destacamos como esses processos se conectam
com as no??es de criatividade. Assim, formulamos um modelo para examinarmos a obra
Arithmetica Infinitorum, indicando seus potenciais pedag?gicos para subsidiar o ensino de
conceitos matem?ticos baseado em um car?ter investigativo. De maneira que foi poss?vel
estabelecermos uma proposta de conex?o entre conhecimento matem?tico desenvolvido
historicamente por diferentes matem?ticos e seus potenciais conceituais epistemol?gicos,
com a possibilidade de ser implementada na a??o do professor de Matem?tica formador de
professores de Matem?tica, com vistas a desenvolver compet?ncias e habilidades para uma
futura atua??o do professor em forma??o. / The research which arose this doctorate?s thesis had as purpose examining in which ways
John Wallis? ideas, emerging in Arithmetica Infinitorum, dated 1656, has presented
contributing innovations for the didactic and conceptual guiding of Differential and
Integral Calculus? curricular components basic notions, in Mathematics Licentiate course.
For that matter, we evaluated the production?s pedagogical potential to subsidize
mathematical concepts? teaching, mainly integral notions, aiming theim provement of
students? understanding about these mathematical ideas, which are contemplated in the
Mathematics Teachers training course. Acknowledging that the students need to expand
the number of paths which lead to the development of a Mathematical idea, in this study
we propose to answer the following question: how can the didactic exploration of a
mathematician?s creative exercise contribute to the pedagogical approach for the Calculus
and Analysis teaching, in Mathematics Licentiate course? For that we leaned on the
creativity criteria discussed by Mihaly Csikszentmihalyi, due to considering it substantial
in the thinking cycle explanation regarding the Mathematics creation. We relate to these
principles the processes developed by Advanced Mathematical Thinking, suggested by
Tommy Dreyfus, in order to highlight how these processes attach to creativity notions.
Therefore, we formulated a model to examine the writing Arithmetica Infinitorum pointing
its pedagogical potential to subsidize mathematical concepts? teaching, based on
aninvestigative character. This way, it was possible to establish a connection proposal
between mathematical knowledge historically developed by different mathematicians and
their conceptual and epistemological potentials, with a possibility of being implemented in
Mathematics teacher?s actions, Mathematics teacher?s trainer, in order to grow expertise
and abilities for a forthcoming actuation of the training teacher.
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.ufrn.br:123456789/22700 |
| Date | 24 February 2017 |
| Creators | Lopes, Gabriela Lucheze de Oliveira |
| Contributors | 12432962249, http://lattes.cnpq.br/4490674057492872, Morey, Bernadete Barbosa, 59616571834, http://lattes.cnpq.br/7554818862651491, Silva, Carlos Aldemir Farias da, 49638033487, http://lattes.cnpq.br/7226908910873590, Noronha, Claudianny Amorim, 59388374215, http://lattes.cnpq.br/3258090174478169, Quaresma, Jo?o Cl?udio Brandemberg, 26425726253, http://lattes.cnpq.br/3873561463033176, Fossa, John Andrew, 13056476453, http://lattes.cnpq.br/2466525106349625, Sad, Ligia Arantes, http://lattes.cnpq.br/1714140036102231, 57957525768, Mendes, Iran Abreu |
| Publisher | PROGRAMA DE P?S-GRADUA??O EM EDUCA??O, UFRN, Brasil |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/doctoralThesis |
| Source | reponame:Repositório Institucional da UFRN, instname:Universidade Federal do Rio Grande do Norte, instacron:UFRN |
| Rights | info:eu-repo/semantics/openAccess |
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