Desenho e aplicação de um instrumento para explorar a faceta epistêmica do conhecimento didático-matemático de futuros professores sobre a derivada
Tipo de documento
Autores
Lista de autores
Pino-Fan, Luis R., Godino, Juan D. y Font, Vicenç
Resumen
O presente artigo é o primeiro de dois artigos vinculados nos quais apresentamos os resultados de uma investigação durante a qual se desenhou e implementou um instrumento para explorar e caracterizar uma das facetas do conhecimento didático-matemático acerca da derivada de futuros professores do ensino secundário/bacharelado. Na primeira parte apresenta-se o processo de desenho do instrumento, abordando tanto os aspectos teóricos e metodológicos contemplados para seu desenho, como as características e conhecimentos que se pretendem com cada uma das tarefas que o conformam. O instrumento resultante pode significar uma contribuição para os formadores de professores que desejam explorar e potencializar a faceta do conhecimento sobre a derivada que aqui abordamos. A metodologia empregada se antevê como uma metodologia relevante para aqueles interessados no desenho de instrumentos orientados a explorar aspectos do conhecimento didático-matemático dos professores.
Fecha
2013
Tipo de fecha
Estado publicación
Términos clave
Enfoque
Idioma
Revisado por pares
Formato del archivo
Volumen
8
Número
2
Rango páginas (artículo)
1-49
ISSN
19811322
Referencias
ARTIGUE, M. La enseñanza de los principios del cálculo: Problemas epistemológicos, cognitivos y didácticos. In: ARTIGUE, M.; DOUADY, R.; GÓMEZ, P. (Eds.). Ingeniería didáctica en educación matemática (p. 97-140). México: Grupo Editorial Iberoamérica, 1995. ARTIGUE, M.; BATANERO, C.; KENT, P. Mathematics thinking and learning at post- secondary level. In: LESTER, F. K. (Ed.). Second Handbook of Research on Mathematics Teaching and Learning (p. 1011-1049). Charlotte, N.C: NCTM and IAP, 2007. BADILLO, E. La derivada como objeto matemático y como objeto de enseñanza y aprendizaje en profesores de matemáticas de Colombia. Tesis doctoral, Universitat Autònoma de Barcelona, España, 2003. BADILLO, E.; AZCÁRATE, C.; FONT, V. Análisis de los niveles de comprensión de los objetos f’(a) y f’(x) en profesores de matemáticas [Analysing the extent to which mathematics teachers understand the objects f’(a) and f’(x)]. Enseñanza de las Ciencias, v. 29, n. 2, p. 191-206, 2011. BALL, D. L. Bridging practices: Intertwining content and pedagogy in teaching and learning to teach. Journal of Teacher Education, v. 51, p. 241-247, 2000. BALL, D. L.; BASS, H. With an eye on the mathematical horizont: Knowing mathematics for teaching to learnes’ mathematical futures. Paper presented at the 43Rd Jahrestagung Für Didaktik Der Mathematik Held in Oldenburg, Germany, 2009. BALL, D. L.; HILL, H. C.; BASS, H. Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, v. 29, p. 14-22, 2005. BALL, D. L.; LUBIENSKI, S. T.; MEWBORN, D. S. Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In: RICHARDSON, V. (Ed.). Handbook of research on teaching (4th ed., p. 433-456). Washington, DC: American Educational Research Association, 2001. BALL, D. L.; THAMES, M. H.; PHELPS, G. Content knowledge for teaching. What makes it special? Journal of Teacher Education, v. 59, n. 5, p. 389-407, 2008. BINGOLBALI, E.; MONAGHAN, J. Concept image revisited. Educational Studies in Mathematics, v. 68, n. 1, p. 19-35, 2008. BISHOP, A.; CLEMENTS, K.; KEITEL, C.; KILPATRICK, J.; LEUNG, F. (Eds.). Second International handbook of mathematics education. Dordrecht: Kluwer A. P., 2003. ÇETIN, N. The ability of students to comprehend the function-derivative relationship with regard to problems from their real life. PRIMUS, v. 19, n. 3, p. 232-244, 2009. COHEN, L.; MANION, L.; MORRISON, K. Research methods in education. London and New York: Routledge, 2011. DELOS SANTOS, A. An investigation of students’ understanding and representation of derivative in a graphic calculator-mediated teaching and learning environment. Doctoral thesis: University of Auckland, New Zealand, 2006. ENGLISH, L. D.; BARTOLINI-BUSI, M.; JONES, G. A., LESH, R.; TIROSH, D. Handbook of International research in mathematics education. London: Lawrence Erlbaum Ass, 2002. FENNEMA, E.; FRANKE, M. L. Teachers’ knowledge and its impact. In: GROUWS, A. (Ed.). Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (p. 147-164). New York, NY, England: Macmillan, 1992. FONT, V. Procediments per obtenir expressions simbòliques a partir de gràfiques. Aplicacions a la derivada [Procedures for obtaining symbolic expressions from graphs: Applications in relation to the derivative]. Tesis doctoral no publicada, Universitat de Barcelona, España, 1999. FONT, V. Rappresentazioni attivate nel calcolo della derivata. Atti del Convegno di Didáctica della Matematica. Alta Scuola Pedagogica: Locarno, Suiza. p. 13-24, 2008. FRANKE, M. L.; KAZEMI, E.; BATTEY, D. Understanding teaching and classroom practice in mathematics. In: LESTER, F. K. (Ed.). Second Handbook of Research on Mathematics Teaching and Learning (p. 225-256). Charlotte, N.C: NCTM and IAP, 2007. GODINO, J. D. Un enfoque ontológico y semiótico de la cognición matemática. Recherches en Didactique des Mathématiques, v. 22, n. 2/3, p. 237-284, 2002. GODINO, J. D. Categorías de análisis de los conocimientos del profesor de matemáticas. Unión, Revista Iberoamericana de Educación Matemática, v. 20, p. 13- 31, 2009. GODINO, J. D.; BATANERO, C.; FONT, V. The onto-semiotic approach to research in mathematics education. ZDM. The International Journal on Mathematics Education, v. 39, n. 1, p. 127-135, 2007. GODINO, J. D.; FONT, V.; WILHELMI, M.; LURDUY, O. Why is the learning of elementary arithmetic concepts difficult? Semiotic tools for understanding the nature of mathematical objects. Educational Studies in Mathematics, v. 77, n. 2, p. 247-265, 2011. GODINO, J. D.; PINO-FAN, L. The mathematical knowledge for teaching: a view from the onto-semiotic approach to mathematical knowledge and instruction. Eighth Congress of European Research in Mathematics Education (CERME 8). Antalya, Turkey, 2013. Acceso el: 14 de febrero de 2013 de HABRE, S.; ABBOUD, M. Students’ conceptual understanding of a function and its derivative in an experimental calculus course. Journal of Mathematical Behavior, v. 25, p. 52-72, 2006. HÄHKIÖNIEMI, M. Perceptual and symbolic representations as a starting point of the acquisition of the derivative. In: HOINES, M. J.; FUGLESTAD, A. B. (Eds.). Procceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (v. 3, p. 73-80). Bergen, Norway: PME, 2004. HÄHKIÖNIEMI, M. The role of representations in learning the derivative. Tesis doctoral, University of Jyväskylä, Finland, 2006. HILL, H. C.; BALL, D. L.; SCHLLING, S. G. Unpacking pedagogical content knowledge of students. Journal for Research in Mathematics Education, v. 39, p. 372- 400, 2008. HILL, H. C.; SLEEP, L.; LEWIS, J. M.; BALL, D. L. Assessing teachers’ mathematical knowledge: What knowledge matters. In: LESTER, F. K. (Ed.). Second Handbook of Research on Mathematics Teaching and Learning. (p. 111-156). Charlotte, N.C: NCTM and IAP, 2007. HILL, H. C.; SCHILLING, S.; BALL, D. L. Developing measueres of teachers’ mathematics knowledge for teaching. The Elementary School Journal, v. 105, n. 1, p. 11-30, 2004. LLINARES, S.; KRAINER, K. Mathematics (student) teachers and teacher educators as learners. In: GUTIÉRREZ, A.; BOERO, P. (Eds.). Handbook of Research on the Psychology of Mathematics Education: Past, Present and Future (p. 429-459). Rotterdam: Sense Publishers, 2006. MALASPINA, U.; FONT, V. The role of intuition in the solving of optimization problems. Educational Studies in Mathematics, v. 75, p. 1, p. 107-130, 2010. PHILIPP, R. Mathematics teachers’ beliefs and affect. In: LESTER, F. K. (Ed.). Second handbook of research on mathematics teaching and learning (p. 257-315). Charlotte, NC: Information Age Pub, 2007. PINO-FAN, L.; GODINO, J. D.; FONT, V. Faceta epistémica del conocimiento didáctico-matemático sobre la derivada [The epistemic facet of mathematical and didactic knowledge about the derivative]. Educação Matemática Pesquisa, v. 13, n. 1, p. 141-178, 2011. PONTE, J. P.; CHAPMAN, O. Mathematics teachers’ knowledge and practices. In: GUTIÉRREZ, A.; BOERO, P. (Eds.). Handbook of Research on the Psychology of Mathematics Education: Past, Present and Future (p. 461-494). Rotterdam: Sense Publishers, 2006. ROWLAND, T.; RUTHVEN, K. (Eds.). Mathematical Knowledge in Teaching, Mathematics Education Library 50. London: Springer, 2011. SÁNCHEZ, G.; GARCÍA, M.; LLINARES, S. La comprensión de la derivada como objeto de investigación en didáctica de la matemática. Revista Latinoamericana de Investigación en Matemática Educativa, v. 11, n. 2, p. 267-296, 2008. SANTI, G. Objectification and semiotic function. Educational Studies in Mathematics, v. 77, n. 2-3, p. 285-311, 2011. SHULMAN, L. S. Those who understand: Knowledge growth in teaching. Educational Researcher, v. 15, n. 2, p. 4-14, 1986. SHULMAN, L. S. Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, v. 57, n. 1, p. 1-22, 1987. SOWDER, J. T. The mathematical education and development of teachers. In: LESTER, F. K. (Ed.). Second Handbook of Research on Mathematics Teaching and Learning. (p. 157-223). Charlotte, N.C: NCTM and IAP, 2007. SULLIVAN, P.; WOOD, T. (Eds.). The international handbook of mathematics teacher education. Volume 1: Knowledge and beliefs in mathematics teaching and teaching development. Rotterdam: Sense Publishers, 2008. TSAMIR, P.; RASSLAN, S.; DREYFUS, T. Prospective teachers’ reactions to Right- or-Wrong tasks: The case of derivatives of absolute value functions. Journal of Mathematical Behavior, v. 25, n. 240-251, 2006. VIHOLAINEN, A. Finnish mathematics teacher student’s informal and formal arguing skills in the case of derivative. Nordic Studies in Mathematics Education, v. 13, n. 2, p. 71-92, 2008.