Submitted by Automa??o e Estat?stica (sst@bczm.ufrn.br) on 2017-04-17T22:47:12Z No. of bitstreams: 1 GabrielaLuchezeDeOliveiraLopes_TESE.pdf: 6049374 bytes, checksum: 3515f5da06487f76c77ce277db17c307 (MD5) / Approved for entry into archive by Arlan Eloi Leite Silva (eloihistoriador@yahoo.com.br) on 2017-04-19T23:33:36Z (GMT) No. of bitstreams: 1 GabrielaLuchezeDeOliveiraLopes_TESE.pdf: 6049374 bytes, checksum: 3515f5da06487f76c77ce277db17c307 (MD5) / Made available in DSpace on 2017-04-19T23:33:36Z (GMT). No. of bitstreams: 1 GabrielaLuchezeDeOliveiraLopes_TESE.pdf: 6049374 bytes, checksum: 3515f5da06487f76c77ce277db17c307 (MD5) 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.

Auteur romain du 6ème siècle connu pour ses traductions en latin des textes en grec d’Aristote, Boèce a aussi rédigé une traduction-adaptation d’un texte de Nicomaque de Gérase sur l’arithmétique. La première partie de ce mémoire de maîtrise est consacrée à l’étude de Boèce en tant que passeur de savoir. Sa relation avec son père adoptif est mise en valeur afin de soutenir l’hypothèse selon laquelle Boèce aurait acquis sa connaissance du grec et son éducation tout en restant à Rome, sans avoir séjourné dans les écoles athéniennes ou alexandriennes. La deuxième partie porte sur le contenu mathématique du De institutione arithmetica. Après avoir montré comment le De arithmetica était relié à l’oeuvre de traduction par Boèce des philosophes grecs, le choix de l’Introduction à l’Arithmétique de Nicomaque comme point de départ du traité d’arithmétique de Boèce est étudié. Un catalogue raisonné des concepts mathématiques présentés est ensuite proposé, organisé autour des notions de quantité en soi et quantité relative qui conservent l’opposition entre le Même et l’Autre et rappellent l’opposition fondamentale entre Limité et Illimité, si chère aux pythagoriciens. Ce mémoire se termine par une analyse de la transmission du De institutione arithmetica et de son influence sur les mathématiques et l’enseignement du quadrivium au Moyen-Âge. / Roman author of the 6th century known for his Latin translations of Aristotle’s Greek texts, Boethius has also composed a translation-adaptation of a treatise on arithmetics written by Nicomachus of Gerasa. The first section of this master’s thesis focuses on characterizing Boethius as a intermediary, transferring Greek knowledge to the Latin West. His relationship with Symmachus is highlighted in order to argue that Boethius had been able to learn Greek and reach such a high level of learning in Rome, without the need to study in the Athenian or Alexandrian schools of his time. The mathematical content of the De institutione arithmetica is the main topic of the second section. After showing how the De arithmetica is related to Boethius’ magnum opus – the Latin translation of the Greek philosophers – the choice of Nicomachus of Gerasa’ Introduction to Arithmetics as the source of Boethius’ treaty on arithmetics is studied. Then, a catalogue raisonné of the mathematical concepts showcased is provided, organized around the notions of quantity constant of itself and relative quantity which retain the opposition between the Same and the Other and stems from the pythagoricians’ fondamental opposition between the Limited and the Unlimited. This masters’ thesis ends with an analysis of the medieval transmission of the De institutione arithmetica and of its influence on medieval mathematics and education through the quadrivium.