DIDATICAL ENGINEERING: SOME IMPLICATIONS FOR THE RESEARCH THE TEACHING COMPLEX ANALYSIS – CA

Francisco Regis Vieira Alves

Abstract


This article discusses and describes the two initial phases provided by a nominated research design of Didactical Engineering – DE. Thus, in view of an interest declared by the teachhing of Complex Analysis – CA, the work emphasizes the elements that hold the potential to constitute the two initial stages of an DE, nomitaded by preliminary and a priori analysis, with emphasis on description and conception of only two problems situations. So, in view of the long heritage of the French tradition in Didactics of Mathematics, also elects the Theory of Didactical Situations – TSD, in complementary character in other to ensure the reasonable control of the didactic mediation, as well as the predictive character of a theorical and conceptual framework for the research, structured for teaching of CA, reproductible and repeatable in any empirical situation of application in academic locus.

Keywords


Didatical Engineering. Teaching of Complex Analysis. Research. Technology. Visualization.

References


Alves, Francisco. R. V. (2015a). Visualização de Teoremas em Análise Complexa: exemplos no contexto da Transição Complexa do Cálculo TCC. Revista Sinergia, 16(1), 65 – 76.

Alves, Francisco. R. V. (2015b). Sobre a evolução do modelo de Fibonacci: a classe das funções hiperbólicas de Fibonacci. Revista VYDIA Educação, 35(1), 133 – 146.

Alves, Francisco. R. V. (2015c). Sequência Generalizada de Fibonacci e suas relações com o número de ouro. Boletim Cearense de Educação e História da Matemática. 2(6), 1 – 4.

Alves, Francisco. R. V. (2014a). Engenharia Didática para o Teorema da Função Implícita: análise preliminares e a priori. Revista Brasileira de Ensino de Ciência e Tecnologia, 7(3), 148 – 168.

Alves, Francisco. R. V. (2014b). Técnica Computacional para o Ensino de Matemática Computational Technique for Teaching Mathematics – . EM TEIA: Revista de Educação Matemática e Tecnológica Iberoamericana, 5(2), 1 – 9.

Alves, Francisco. R. V. (2014c). Aplicações no Ensino de Variável Complexa: uma discussão sobre o uso dos softwares Geogebra e CAS Maple. Revista do Instituto GeoGebra Internacional de Sáo Paulo, 3(2).

Alves, F. R. V. (2013). Reconhecimento de padrões com o apoio do software GeoGebra: os casos da convergência pontual e uniforme. Revista TEAR, 2(2), 1 – 20.

Alves, F. R. V. (2012). Insight: descrição e possibilidades no ensino do Cálculo. Vydia Educação, 32(2), 149 – 146.

Alves, Francisco. R. V. (2011). Aplicações da Sequência Fedathi na promoção das categorias intuitivas do Cálculo a Várias Variáveis (tese de doutorado). Fortaleza: Universidade Federal do Ceará – UFC, 339f.

Alves, Francisco. R. V. & Borges, Neto, H. (2012). Engenharia Didática para a exploração didática da tecnologia no ensino no caso da Regra de L`Hospital. Educação Matemática Pesquisa, 14(2), 337 – 367.

Alves, Francisco. R. V; Borges Neto, H. & Alves Dias, M. (2012). Implicações e aplicações da Teoria dos Registros de Representação Semiótica no ensino do Cálculo. Jornal Internacional de Estudos em Educação Matemática, 5(1), 54 – 84.

Almouloud, Ag Saddo. (2007). Fundamentos da Didática da Matemática. São Paulo: Editora UFPR.

Arsove, M. G. (1954). The Looman-Menchoff theorem and some subharmonic functions analoges. International Congress of Mathematicians. January, Washington, 94 – 105.

Artigue, M. (1984). Modélisation et Reproductibilité en Didactiques de Mathématiques. Em: Les Cahiers Rouge des Didactiques des Mathematiques, 8(1), 1 - 38.

Artigue, M. (1996). Ingénierie Didactiques. Brun, J. (org.). Didactiques de Mathématiques, 243 – 264.

Artigue, M. (2009). Didactical design in Mathematics Education. Carl Winslow (eds). NORMA08, Copenhaguen: Sense Publishers, Denmark, 7 – 16.

Artigue, M. (2012). L´éducation mathématiques comme champ de recherché et champ de pratique: resultats et défis. EM TEIA: Revista de Educação Matemática e Tecnológica Iberoamericana, 3(3), 1 – 18.

Artigue, M. (2013). L´impact curriculaire des Technologies sur L´Éducation Mathématiques. EM TEIA: Revista de Educação Matemática e Tecnológica Iberoamericana, 4(1), 1 – 15.

Ávila, G. (2002). O ensino de Cálculo e da Análise. In: Matemática Universitária, 33(1), 83-94.

Balacheff, N. & Gaudin, N. (2002). Students conceptions: an introduction to a formal characterization. Les Cahier du Laboratoire Leibniz. 65, December, 1 – 25.

Bottazzini, U. (1986). The Higher Calculus: a history of real and complex analysis from Euler to Weierstrass. New York: Springer-Verlag.

Brousseau, G. (1976). Les obstacles épistemologiques et les problèmes en mathématiques. Revue Française de Pédagogie, INRP, 2(1), 101 - 116.

Brousseau, G. (1978). L’observation des activités Didactiques. Revue Française de Pédagogie, INRP, 1(1), 130-140.

Brousseau, G. (1986a). Théorisation des phénomènes d´enseignement des Mathématiques (these de doctorat). Bourdeaux: Université Bourdeaux I, 905f.

Brousseau, G. (1986b). Fondements et methodes de la Didactiques des Mathématiques. Recherche en Didactiques des Mathématiques. 7(2), 33 – 115.

Brousseau, G. (1986c). Obstacle épistémologiques, conflit socio-cognitifs et ingénierie didactique. Canadá, Otawa: Édition CIRADE agence d´Arc, 277 – 285.

Brousseau, G. (1988). Le contrat didactique: le milieu. Recherche en Didactiques des Mathematiques, 9(2), 309 – 336.

Brousseau, G. (1998). Les obstacles épistémologiques, problèmes et ingénierie didactique. G. Brousseau, (org.) (1998). Théorie des situations didactiques. Grenoble La Pensée Sauvage, 115 – 160.

Brousseau, G. (2004). L´Émergence d’une science de la Didactique des Mathématiques. Repères IREM, 55(1), 19-34.

Cecília, S. F. & Bernadez, N. C. (2008). Introdução às funções de uma variável complexa. Rio de Janeiro: SBM.

Chavez, E. (2014). Teaching Complex Numbers in High School. (dissertation in Natural Sciences). Louisiana: Louisiana State University. 66f.

Conway, J. B. (1978). Functions of One Complex Variable. Second Edition. New York: Springer Verlag.

Chevallard. Y. (1991). La Transposition didactique. Paris: La Pensée Sauvage Édition.

Danenhower, P. (2000). Teaching and Learning Complex Analysis in at two British Columbia Universities. (doctoral thesis). Canadá: Simon Fraser University. 308f.

Debnath, L. (2015). A brief history of the most remarkable numbers e, i and γ in mathematical sciences with applications. International Journal of Mathematical Education in Science and Technology. 46(6), March, 853 – 878.

Duval, Raymond. (1995). Sémiosis et Pensée Humaine: registres sémiotiques et apprentissages intellectuels, Editeur: Peter Lang.

Ferguson, D. C. (1958). A theorem of Looman 0 Menchoff (thesis of Master in Arts). Quebec: McGill University.

Flanigan, F. J. (1972). Complex Variables: harmonic and analytic functions. California: San Diego State University.

Gong, S. (2001). Concise Complex Analysis. New Jersey: World Scientific.

Gray, J. D. & Morris, S. A. (1978). When is a Function that Satisfies the Cauchy-Riemann Equations Analytic? The American Mathematical Monthly, 85(4), April, 246 - 256.

Greene, R. O. & Krantz, S. G. (2006). Function Theory of One Complex Variable. Third Edition, Graduate Studies in Mathematics, nº 40, Providence: American Mathematical Society.

Lima, E. L. (2010). Um curso de Análise. v. 1, Rio de Janeiro: SBM.

Schwerdtfeger, H. (1979). Geometry of Complex Numbers. Montreal: McGill University.

Laborde, C. (1997). Affronter la complexité des situations didátiques d´apprentissage des mathématiques en classe: défis et tentatives. DIDASKALIA, 10(1), 97 – 112.

Krantz, S. G. (1990). Complex Analysis: the geometric view. New York: American Mathematical Society.

Margolinas, C. (1992). Éléments pour l´analyse du rôle du maître: les phases de conclusion. Recherche en Didactiques des Mathématiques. 12(1), 113 – 158.

Margolinas, C. (1995). D´evolution et institutionnalisation: deux aspects antagonistes du rôle du maître. Didactique des disciplines scientifiques et formation des enseignants, Paris: Maison Édition, 342-347

Margolinas, C. (2004). Points de vues de l´élève et du professeur : essai de développement de la théorie des situations didactiques (Habilitation de recherche). Provence: Université de Provence. 160f.

Needham, T. (2000). Visual Complex Analysis. Oxford: Oxford University Press.

Lins Neto, A. (1993). Funções de uma variável complexa. Rio de Janeiro: SBM.

Medvedev, F. (1991). Scenes from the History of Real Functions. Boston: Birkäuser-Verlag.

Pap, E. (1999). Complex Analysis: through examples and exercises. London: Klumer Academic Publishers.

Robert, A. (1984). Ingénierie didactique sur les suites numériques après le baccalauréat. Les Cahiers Rouges des Didactiques de Mathématiques, 1 – 25.

Robinet, J. (1983). De L´ingenierie Didactiques. Les Cahiers Blancs. 1(1), 1 – 11.

Shokranian, S. (2011). Uma introdução à Variável Complexa, Sao Paulo: Editora Moderna.

Soares, M. G. (2014). Cálculo em uma Variável Complexa. Rio de Janeiro: SBM.

Spiegel, M. R. et all. (2009). Complex Variables: with a introduction to a Conformal Mapping and its applications, New York: Schaum´s Outlines Series.

Tall, David. (1991). Advanced Mathematical Thinking. London: Klumer Publishers.

Tall, David. (1997). From school to university: the effects of learning styles in the transition from elementary to advancedmathematical thinking. THOMAS, M. J. (eds.). Proceeding of the Seventh Annual Australian Bridging Network Mathematics Conference, Aucland: Aucland University, 9 – 26.

Tirosh, D. & Almog, N. (1989). Conceptual adjustments in Progressing from Real and Complex Numbers. 13 th. Proceedings of Psychology of Mathematics Education, 221 – 227.

Vergnaud, G. (1981). Quelques orientation théoriques eet methodoloiques des recherches française en Didactiques des Mathématiques. Recherche en Didactiques des Mathématiques. 2(2), 215 – 231.




DOI: https://doi.org/10.5902/2179460X20466

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