Source: http://revistas.pucsp.br/emp/article/view/40140
Timestamp: 2019-04-19 18:55:05+00:00

Document:
This article addresses the indispensability of non-mathematical knowledge for the use of mathematical models on problems in concrete contexts based on the assumptions of the Anthropological Theory of the Didactic. The Mixed Praxeological Model is proposed as a methodological analysis device. The analysis of the model of the calculation of Personal Income Tax in situation demonstrates the potentiality of the device to emerge the non-mathematical knowledge that base the mathematical models on concrete contexts. Preliminary results indicate the indispensability of the non-mathematical knowledge of the situation for the pertinent use of mathematical models, and forward future research.
Modelagem Matemática. Teoria Antropológica do Didático. Modelo Praxeológico Estendido. Imposto de Renda Pessoa Física.
BLOMHØJ, M.; JENSEN, T. H. Developing mathematical modelling competence: Conceptual clarification and educational planning. In: Teaching Mathematics and its Applications v. 22, n. 3, p. 123-139, 2003.
BORSSOI, Adriana Helena; DE ALMEIDA, Lourdes Maria Werle. Percepções sobre o uso da Tecnologia para a Aprendizagem Significativa de alunos envolvidos com Atividades de Modelagem Matemática. In:Revista Electrónica de Investigación en Educación en Ciencias, v. 10, n. 2, p. 36-45, 2015.
BOSCH, Marianna; CHEVALLARD, Yves; GASCÓN, Josep. Science or magic? The use of models and theories in didactics of mathematics. Proceedings of the Fourth Congress of the European Society for Research in Mathematics Education, 2005.
BRASIL. Relatório Nacional PISA 2012: Resultados brasileiros. OCDE, 2012.
______. Constituição da República Federativa do Brasil. Brasília, 1988.
CASTELA, Corine. Cuando las praxeologías viajan de una institución a otra: una aproximación epistemológica del “boundarycrossing”. In: Educación Matemática, v. 28, n. 2, ago. 2016.
CASTELA, Corine; ROMO VÁSQUES, Avenilde. Des Mathematiques a L´automatique: etude des effets de transposition sur la transformee de Laplace dans la formation des ingénieurs. In : Recherches en Didactique des Mathématiques, Grenoble, France: La Pensée Sauvage, v. 31/1, n. 91, p. 79-130, 2011.
CHEVALLARD, Yves. La Transposición Didáctica: del saber sabio al saber enseñado. 3. ed. 3. reimp. Buenos Aires: Aique Grupo Editor, 2009.
______. La Transposición Didáctica: del saber sabio al saber enseñado. 2. ed. 3. reimp. Buenos Aires: Aique Grupo Editor, 2005.
______. L’Analise des pratiques enseignantes em theórie anthopologique du didactique, In : Recherches em Didactiques des Mathematiques. Grenoble. La Pensé Sauvage Éditions, v. 19.2, p. 221-265, 1999.
______. La Transposition Didactique. Grenoble: La Pensée Sauvage-Éditions, 1991.
______. La Transposition Didactique. Du Savoir savant au savoir enseigné. Grenoble: La Pensée Sauvage, 1985.
COÊLHO, Sacha Calmon Navarro. Curso de Direito Tributário Brasileiro. 9. ed. Rio de Janeiro: Forense, 2007.
ECO, U.El mago y el científico.El Pais,p. 13-14, 15 dez. 2002.
GRANDSARD, F. Mathematical modeling and the efficiency of our mathematics. 2005.Disponívelem: Acesso em: 02 jun. 2009.
JULIE, C.Mathematical literacy: Myths, further inclusions and exclusions. Pythagoras, v. 64, p. 62-69, 2006.
MALHEIROS, Ana Paula dos Santos. Modelagem em Aulas de Matemática: reflexos da formação inicial na Educação Básica. In: Perspectivas da Educação Matemática, v.9, n. 21, 2016.
OLIVEIRA, Alex da Silva.Monografia sobre o Imposto de Renda Pessoa Física. Publicado pela Faculdade Cearense (FAC). Curso de Ciências Contábeis, 2013.
SCHUKAJLOW, S.; KAISER, G.; STILLMAN, G. Empirical research on teaching and learning of mathematical modelling: a survey on the current state-of-the-art. In: ZDM - Mathematics Education, n. 50, v. 1-2, p. 5-18, 2018. Doi 10.1007/s11858-018-0933-5.
WHITNEY, H. The Mathematics of Physical Quantities: Part I: Mathematical Models for Measurement. In: The American Mathematical Monthly, v. 75, n. 2, p. 115-138, fev.1968.

References: v. 
 v. 
 v. 
 v. 
 v. 
 v. 
 v. 
 v.