A FUNCTIONAL GRAPHIC APPROACH TO INEQUATIONS

Vera H. G. de Souza; Rosana Nogueira; Tânia M. M. Campos

doi:10.12802/relime.13.1814

Artículos

Vol. 18 Núm. 1 (2015): Marzo

A FUNCTIONAL GRAPHIC APPROACH TO INEQUATIONS

Vera H. G. de Souza
Rosana Nogueira^▸^▾
Tânia M. M. Campos^▸^▾

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DOI: https://doi.org/10.12802/relime.13.1814
Enviado: julio 2, 2023
Publicado: 2015-03-31

Resumen

Presentamos algunos resultados de una encuesta aplicada a cinco maestros de matemáticas que trabajaran con un método gráfico para resolver desigualdades. Las actividades se desarrollaron utilizando registros algebraicos, gráficos y en lenguaje natural (Duval, 1995, 2000), lo cual llevó a un proceso de tratamientos y conversiones, que dejó ver las faltas cometidas por los maestros al utilizar los métodos algebraicos y al comparar estos últimos con los gráficos de resolución. Analizamos los protocolos de los maestros en busca de aspectos formales, intuitivos y algorítmicos (Fischbein, 1993). Los análisis mostraron que los maestros no explican por qué los métodos algebraicos y gráficos que utilizaron presentan diferentes soluciones. Esto último es evidencia de que ellos no dominan los aspectos formales de los métodos algebraicos de resolución que a menudo utilizan en sus clases.

Citas

Bachelard, G. (1996). A formação do espírito científico (1a ed.). (E. Abreu, Trad.). Rio de Janeiro, Brasil: Contraponto. (Reimpreso de La Formation de l’esprit scientifique: contribution à une psychanalyse de la connaissance, 1938, Paris, França: Libraine Philosophique J. Vrin)
Bazzini, L. & Tsamir, P. (2003). Connections between theory and research findings: the case of inequalities. In M. A. Mariotti (Ed.), Proceedings of the 3rd Conference of the European Society for Research in Mathematics Education (Vol. 10, pp. 1-3). Bellaria, Italia: ERME.
Borello, M. y Lezama, J. (2011). Hacia una resignificacion de las desigualdades e inequaciones a partir de las prácticas del profesor. En P. Lestón (Ed.), Acta Latinoamericana de Matemática Educativa (Vol. 24, pp. 921-929). México, DF: RELME.
De Souza, V. H. (2008). O uso de vários registros na resolução de inequações - uma abordagem funcional gráfica (Tese de Doutorado inédita). Pontifícia Universidade Católica de São Paulo, São Paulo, Brazil.
De Souza, V. H. & Campos, T. M. (2005). Sobre a resolução da inequacao x^2 < 25. IX Encontro Brasileiro de Estudantes de Pós-Graduação em Educação Matemática (Vol. 1, p. 40). São Paulo, Brazil: FEUSP.
Duval, R. (2000). Basic issues for research in Mathematics Education. In M. J. Hoines, & A. B. Fuglestad (Eds.), Proceedings of the 24th Conference fo the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 55-69). Hiroshima, Japan: PME.
Duval, R. (1995). Sémiosis et pensée humaine. Registres sémiotiques et apprentissages intellectuels. Neuchâtel, Suisse: Peter Lang.
Fischbein, E. (1993). The interaction between the formal, the algorithmic and the intuitive components in a mathematical activity. In R. Biehler, R. W. Scholz, R. Strässer, B. Winkelmann (Eds.), Didactics of Mathematics as a scientific discipline (pp. 231-240). Dordrecht, HO: Kluwer.
Kieran, C. (2004). The equation/inequality connection in constructing meaning for inequality situations. In M. J. Hoines & A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 143-147).
Bergen, Norway: PME.
Radford, L. (2004). Syntax and meaning. In M. J. Hoines, & A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 161-166). Bergen, Norway: PME.
Sackur, C. (2004). Problems related to the use of graphs in solving inequalities. In M. J. Hoines, & A. B. Fuglestad (Ed.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 148-152). Bergen, Norway: PME.
Tsamir, P. & Bazzini, L. (2001). Can x=3 be the solution of an inequality? A study of Italian and Israeli students. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 303-310).
Utrecht, Holland: PME.
Tsamir, P. & Bazzini, L. (2002). Student’s algorithmic, formal and intuitive knowledge: the case of inequalities. In I. Vakalis, D. H. Hallett, D. Quinney, C. Kourouniotis, & C. Tzanakis (Eds.), Proceedings of the Second International Conference on the Teaching of Mathematics. Crete,
Greece: ICTM. Recuperado de http://www.math.uoc.gr/~ictm2/Proceedings/pap511.pdf
Tsamir, P., Almog, N. & Tirosh, D. (1998). Students’ solution of inequalities. In A. Olivier and K. Newstead (Eds.), Proceedings of the 22nd Conference of the International Groupnd Conference of the International Groupnd for the Psychology of Mathematics Education (Vol. 4, pp. 129-136). Stellenbosch, South Africa: PME.

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Palabras clave

Funciones
Gráficos
Desigualdades
Fischbein
Aspectos

Cómo citar

Souza, V. H. G. de, Nogueira, R., & Campos, T. M. M. (2015). A FUNCTIONAL GRAPHIC APPROACH TO INEQUATIONS. Revista Latinoamericana De Investigación En Matemática Educativa, 18(1), 109–125. https://doi.org/10.12802/relime.13.1814

Derechos de autor 2015 Revista Latinoamericana de Investigación en Matemática Educativa

Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial 4.0.

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[1] Bachelard, G. (1996). A formação do espírito científico (1a ed.). (E. Abreu, Trad.). Rio de Janeiro, Brasil: Contraponto. (Reimpreso de La Formation de l’esprit scientifique: contribution à une psychanalyse de la connaissance, 1938, Paris, França: Libraine Philosophique J. Vrin)

[2] Bazzini, L. & Tsamir, P. (2003). Connections between theory and research findings: the case of inequalities. In M. A. Mariotti (Ed.), Proceedings of the 3rd Conference of the European Society for Research in Mathematics Education (Vol. 10, pp. 1-3). Bellaria, Italia: ERME.

[3] Borello, M. y Lezama, J. (2011). Hacia una resignificacion de las desigualdades e inequaciones a partir de las prácticas del profesor. En P. Lestón (Ed.), Acta Latinoamericana de Matemática Educativa (Vol. 24, pp. 921-929). México, DF: RELME.

[4] De Souza, V. H. (2008). O uso de vários registros na resolução de inequações - uma abordagem funcional gráfica (Tese de Doutorado inédita). Pontifícia Universidade Católica de São Paulo, São Paulo, Brazil.

[5] De Souza, V. H. & Campos, T. M. (2005). Sobre a resolução da inequacao x^2 < 25. IX Encontro Brasileiro de Estudantes de Pós-Graduação em Educação Matemática (Vol. 1, p. 40). São Paulo, Brazil: FEUSP.

[6] Duval, R. (2000). Basic issues for research in Mathematics Education. In M. J. Hoines, & A. B. Fuglestad (Eds.), Proceedings of the 24th Conference fo the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 55-69). Hiroshima, Japan: PME.

[7] Duval, R. (1995). Sémiosis et pensée humaine. Registres sémiotiques et apprentissages intellectuels. Neuchâtel, Suisse: Peter Lang.

[8] Fischbein, E. (1993). The interaction between the formal, the algorithmic and the intuitive components in a mathematical activity. In R. Biehler, R. W. Scholz, R. Strässer, B. Winkelmann (Eds.), Didactics of Mathematics as a scientific discipline (pp. 231-240). Dordrecht, HO: Kluwer.

[9] Kieran, C. (2004). The equation/inequality connection in constructing meaning for inequality situations. In M. J. Hoines & A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 143-147).

[10] Bergen, Norway: PME.

[11] Radford, L. (2004). Syntax and meaning. In M. J. Hoines, & A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 161-166). Bergen, Norway: PME.

[12] Sackur, C. (2004). Problems related to the use of graphs in solving inequalities. In M. J. Hoines, & A. B. Fuglestad (Ed.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 148-152). Bergen, Norway: PME.

[13] Tsamir, P. & Bazzini, L. (2001). Can x=3 be the solution of an inequality? A study of Italian and Israeli students. In M. van den Heuvel-Panhuizen (Ed.), Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 303-310).

[14] Utrecht, Holland: PME.

[15] Tsamir, P. & Bazzini, L. (2002). Student’s algorithmic, formal and intuitive knowledge: the case of inequalities. In I. Vakalis, D. H. Hallett, D. Quinney, C. Kourouniotis, & C. Tzanakis (Eds.), Proceedings of the Second International Conference on the Teaching of Mathematics. Crete,

[16] Greece: ICTM. Recuperado de http://www.math.uoc.gr/~ictm2/Proceedings/pap511.pdf

[17] Tsamir, P., Almog, N. & Tirosh, D. (1998). Students’ solution of inequalities. In A. Olivier and K. Newstead (Eds.), Proceedings of the 22nd Conference of the International Groupnd Conference of the International Groupnd for the Psychology of Mathematics Education (Vol. 4, pp. 129-136). Stellenbosch, South Africa: PME.