Source: http://revistas.pucsp.br/emp/article/view/39865
Timestamp: 2019-04-19 18:49:35+00:00

Document:
This paper is part of an investigation on the problem of knowledge infrastructure necessary for the development of school mathematical modeling on problems in context. For this, the research cycle of mathematical modeling is proposed as a device inspired by the five gestures that characterize a real research in the light of the anthropological theory of the didactic. Results obtained from the empirical analysis of a problem in context show the potential of the mathematical modeling research cycle for the acquisition of new useful knowledge, if not indispensable to teachers in formation, as well as forwards future research.
Ciclo Investigativo de Modelagem Matemática. Teoria Antropológica do Didático. PEP.
BARQUERO, B., BOSCH, M.; GASCÓN, J. The ecological dimension in the teaching of mathematical modeling at university. Recherches en Didactique de Mathématiques, v. 33, n. 3, p. 307-338, 2013.
BIEMBENGUT, M. S. Concepções e tendências de modelagem matemática na Educação Básica. Tópicos Educacionais, Recife, v. 18, n. 1-2, jun./dez. 2012.
BLOMHØJ, M.; JENSEN, T. H. Developing mathematical modeling competence: Conceptual clarification and educational planning. Teaching Mathematics and its Applications, 22(3), p. 123-139, 2003.
BLUM, W. Quality teaching of mathematical modelling: What do we know, what can we do? In: CHO, S. J. (Ed.). The Proceedings of the 12th International Congress on Mathematical Education. Cham: Springer International Publishing. 2015. p. 73-96.
BORROMEO FERRI, R. Mathematical modelling in European education. Journal of Mathematics Educational Teachers College, v. 4, n. 2, p. 18-24, 2013.
BORSSOI, A. H. e ALMEIDA, L. M. W. Percepções sobre o uso da Tecnologia para a Aprendizagem Significativa de alunos envolvidos com Atividades de Modelagem Matemática. Revista Electrónica de Investigación en Educación en Ciencias, Buenos Aires: Universidad Nacional del Centro de la Província de Buenos Aires, Argentina, v. 10, n. 2, p. 36-45, dez. 2015.
BOSCH, M.; GASCÓN, J. Las prácticas docentes del profesor de matemáticas. XIème École d'Été de Didactique des Mathématiques que se celebró en Agosto de 2001.
CHARLOT, B. O sujeito e a relação com o saber. In: BARBOSA, Raquel Lazzari Leite (Org.). Formação de educadores: desafios e perspectivas. São Paulo: Editora UNESP, 2003. p.23-33.
CHEVALLARD, Y. Teaching mathematics in tomorrow’s society: A case for an on coming counter paradigm. In: CHO, S. J. (Ed.). Proceedings of the 12th international congress on mathematical education. Berlin: Springer, 2015. p. 173-187.
______. Éléments de didactique du développement durable – Leçon 1: Enquête codisciplinaire & EDD. 2013a.
______. Las matemáticas en la escuela: Por una revolución epistemológica y didáctica. 1. ed. Cuidad Autónoma de Buenos Aires: Libros del Zorzal, 2013b.
______. La notion d´ingénieriedidactique, un concept à refonder. Questionnementetélémentos de réponses à partir de la TAD. In: MARGOLINAS et al. (Org.): Enamont et en aval desingénieriesdidactiques, XVª École d´Été de Didactique des Mathématiques – Clermont-Ferrand (Puy-de-Dôme). Recherches en Didactique des Mathématiques. Grenoble: La Pensée Sauvage, v. 1, p. 81-108, 2009.
______. L’Analise des pratiques enseignantes en theórie anthopologique du didactique. Recherches en Didactiques dês Mathematiques. Grenoble. La Pensé Sauvage Éditions, v. 19. 2, p. 221-265, 1999.
______. Fundamental concepts in didactics: Perspectives providedbyananthropological approach. In: DOUADY, R.; MERCIER, A. (Ed.). Research in Didactique of Mathematics, Selected Papers. La Pensée Sauvage, Grenoble, 1992. p. 131- 167.
______. La transposition didactique. Du savoir savant au savoir enseigné. Grenoble: La Pensée Sauvage. [Traducción en español de Claudia Gilman (1997). La transposición didáctica. Del saber sabio al saber enseñado. Buenos Aires: Aique, 1991.
______. Arithmétique, algèbre, modélisation, étapes d’une recherche. Publication de l’IREM d’Aix-Marseille. 1989.
FONSECA, Cecilio; GASCÓN, Josep; OLIVEIRA, Catarina. Desarrollo de un modelo epistemológico de referencia en torno a la modelización funcional. Revista Latinoamericana de Investigación en Matemática Educativa, v. 17, n. 3, p. 289-318, nov. 2014.
FREJD, P.; ÄRLEBÄCK, J. First results from a study investigating Swedish Upper secondary students’ mathematical modelling competencies. In: KAISER, G. et al. (Ed.). Trends in Teaching and Learning of Mathematical Modelling (ICTMA 14). Dordrecht: Springer, 407416, 2011.
GARCIA, F.; GASCÓN, J.; HIGUERAS, L.; BOSCH, M. Mathematical modelling as a tool for the connection of school mathematics. ZDM Mathematics Education, v. 38, n. 3, p. 226-246, 2006.
GRANDSARD, Francine. Mathematical modelling and the efficiency of our Mathematics. 2005.
GREEFRATH, G., & VORHÖLTER, K. (2016). Teaching and learning mathematical modelling: Approaches and developments from German speaking countries. ICME-13 topical survey. Cham: Springer.
HOUSTON, K.; NEILL, N. Assessingmodellingskills. In: LAMON, S. J.; PARKER, W. A.; HOUSTON, S. K. (Ed.). Mathematical modelling: a way of life – ICTMA 11. Chichester: Horwood, 2003. p. 155-164.
IVERSEN, Steffen M.; LARSON, Christine J. Simple Thinking using ComplexMath vs. Complex Thinking using Simple Math: a study using Model Eliciting Activities to compare students’ abilities in standardized tests to their modeling abilities. ZDM, v. 38, n. 3, p. 281-292, June 2006.
KAISER, G.; BLOMHØJ, M.; SRIRAMAN, B. Towards a didactical theory for mathematical modelling. ZDM Mathematics Education, v. 38, n. 2, p. 82-85, 2006.
KAISER, G.; SRIRAMAN, B. A global survey of international perspectives on modelling mathematics education. Zentralblatt für Didaktik der Mathematik, v. 38, n. 3, 2006.
NISS, M. Prescriptive modeling - challenges and opportunities. In: STILLMAN, G. A.; BLUM, W.; BIEMBENGUT, M. S. (Ed.). Mathematical modelling in education research and practice: cultural, social and cognitive influences. Cham: Springer, 2015. p. 67-79.
PERRENET, J.; ZWANEVEL, D. The many faces of the mathematical modeling cycle. Journal of Mathematical Modelling and Application, v. 1, n. 6, p. 3-21, 2012.
REVUZ, A. The Position of Geometry in Mathematical Education. Educational Studies in Mathematics, v. 4, p.48-52, 1971.
SCHUKAJLOW, S.; KAISER, G.; STILLMAN, G. Empirical research on teaching and learning of mathematical modelling: a survey on the current state-of-the-art. ZDM – Mathematics Education, v. 50, n. 1-2, p. 5-18, 2018. Doi 10.1007/s11858-018-0933-5.
SILVA, Denivaldo Pantoja da. A invariável prática da regra de três na escola. 2017. Tese (Doutorado em Educação em Ciências e Matemáticas) - Instituto de Educação Matemática e Científica, Universidade Federal do Pará, Belém, 2017.
TREFFERS, A. Three dimensions. A model of goal and theory description in mathematics instruction - The Wiskobas project. Dordrecht: D. Reidel,1987.

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