Um Outro Caso de Obstáculos Epistemológicos: o princípio de permanência Another Case of Epistemological Obstacles: the principle of permanence

dc.creator	Gert Schubring
dc.date	2008-08-01T00:00:00Z
dc.date.accessioned	2015-07-20T22:44:52Z
dc.date.available	2015-07-20T22:44:52Z
dc.identifier	0103-636X
dc.identifier	1980-4415
dc.identifier	https://doaj.org/article/a603da52d67f4799aea3f7bd66f0dcf3
dc.identifier.uri	http://evidence.thinkportal.org/handle/123456789/23549
dc.description	Os números negativos constituíram um problema conceitual para a matemática enquanto grandezas e números não foram separados epistemologicamente e a definição da matemática era a ciência das quantidades. A solução do problema conceitual aconteceu no século XIX numa parte da comunidadematemática, como componente do surgimento do novo paradigma da matemática, vencendo a ontologia substancialista e estabelecendo a visão relacionista, baseado na algebrização da matemática. Porém, o corpo professoral nas escolas secundárias não quis, na sua maioria, adotar o novo paradigma, o princípio de permanência, erigindo-se como obstáculo epistemológico para eles. Eles continuaram a aderir à visão platônica, baseando-se em justificações geométricas, sustentando que cada afirmação deve ser demonstrável. Pretendendo que os próprios obstáculos fossem o interesse dos alunos em achar na matemática nada de arbitrário mas sim absoluta conseqüência lógica, eles tornaram o princípio de permanência um obstáculo “didactogênico”, como chamou Brousseau os obstáculos causados pelas caraterísticas do ensino. Palavras-Chave: Números negativos, obstáculos epistemológicos, princípio de permanência<br>The negative numbers constituted a conceptual problem for mathematics as long as quantities and numbers had not been separated epistemologically and as mathematics was understood to be the science of quantities. The solution of the mathematical problem was achieved in the 19th century in a part of the mathematical community, as an element of the rise of the new paradigm of mathematics, overcoming the traditional substantialist ontology and establishing the relationist epistemology, based on the algebrisation of mathematics. The group of mathematics teachers at secondary schools was not prepared in its majority, however, to accept the new paradigm. It was in particular the principle of permanence, which proved to be an epistemological obstacle for them. They continued to adhere to the Platonist view, relying on geometrical justifications, maintaining that any mathematical statement should be capable of being demonstrated. Disguising their own obstacles to be those of the students who would accept nothing arbitrary in mathematics but rather absolute logical consistency, these teachers turned the principle of permanence to constitute an “obstacle didactogène” as Brousseau had called those obstacles caused by characteristics of teaching. Keywords: negative numbers, epistemological obstacles, principle of permanence
dc.language	Portuguese
dc.language	English
dc.publisher	UNESP - Campus de Rio Claro - Instituto de Geociências e Ciências Exatas
dc.relation	http://www.periodicos.rc.biblioteca.unesp.br/index.php/bolema/article/view/1527
dc.relation	https://doaj.org/toc/0103-636X
dc.relation	https://doaj.org/toc/1980-4415
dc.rights	CC BY-NC-ND
dc.source	Bolema : Boletim de Educação Matemática, Vol 20, Iss 28 (2008)
dc.subject	Special aspects of education
dc.subject	LC8-6691
dc.subject	Education
dc.subject	L
dc.subject	DOAJ:Education
dc.subject	DOAJ:Social Sciences
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.subject	DOAJ:Mathematics
dc.subject	DOAJ:Mathematics and Statistics
dc.subject	Special aspects of education
dc.subject	LC8-6691
dc.subject	Education
dc.subject	L
dc.subject	DOAJ:Education
dc.subject	DOAJ:Social Sciences
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.subject	DOAJ:Mathematics
dc.subject	DOAJ:Mathematics and Statistics
dc.subject	Special aspects of education
dc.subject	LC8-6691
dc.subject	Education
dc.subject	L
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.subject	Special aspects of education
dc.subject	LC8-6691
dc.subject	Education
dc.subject	L
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.subject	Special aspects of education
dc.subject	LC8-6691
dc.subject	Education
dc.subject	L
dc.subject	Mathematics
dc.subject	QA1-939
dc.subject	Science
dc.subject	Q
dc.title	Um Outro Caso de Obstáculos Epistemológicos: o princípio de permanência Another Case of Epistemological Obstacles: the principle of permanence
dc.type	article