Perfiles del profesorado sobre la enseñanza y uso de la demostración

  1. Caçilda dos Santos 1
  2. Tomás Ortega 2
  1. 1 Agrupamento de Escolas Fernão de Magalhães Chaves (Portugal)
  2. 2 Didáctica de la Matemática. Universidad de Valladolid (España)
Revista:
Avances de investigación en educación matemática: AIEM

ISSN: 2254-4313

Año de publicación: 2013

Número: 4

Páginas: 27-45

Tipo: Artículo

DOI: 10.35763/AIEM.V1I4.51 DIALNET GOOGLE SCHOLAR lock_openDialnet editor

Otras publicaciones en: Avances de investigación en educación matemática: AIEM

Objetivos de desarrollo sostenible

Resumen

In this article we describe problems and feelings, affinities, beliefs and attitudes of teachers regarding proof. This allows us to detect the existence of different categories of teachers according to their underlying attitudes in their teaching on mathematical proof. This categorization has emerged from the analysis of the responses to two questionnaires and from interviews with colleagues, attending to different items, such as how to present mathematics, their way of dealing with proof, the frequency

Referencias bibliográficas

  • Asch, A.G., Van (1993). To prove, why and how? International Journal of Mathematical Education in Science and Technology, 24 (2), 301-313.
  • Balacheff, N. (1988). Aspects of proof in pupils' practice of school mathematics. En D. Pimm (ed.) Mathematics, Teachers and Children, (pp. 316-230), London: Hodder and Stoughton.
  • Bell, A. (1976). A study of pupils’ proof-explanations. Mathematical Situations: Educational Studies in Mathematics, 7, 23-40.
  • Brown, A., & Dowling, P. (1998). Doing research/reading research: A mode of interrogation for education, London: Falmer Press.
  • Chazan, D. (1993). Reports interviews with high school students describing their views of proofs as evidence, versus their acceptance of examples as verification. Educational Studies in Mathematics.
  • Cobb, P., Confrey, J., diSessa, A., Leherer, R., & Schauble, L. (2003). Design experiments in education research. Educational Researcher, 32 (1), 9-13.
  • Collins, A., Joseph, D., & Bielaczyc, K. (2004). Design Research: Theoretical and Methodological Issues. The Journal of the Learning Sciences, 1(13), 15-42.
  • Confrey, J. (2006). The evolution of design studies as methodology. En R.K. Sawyer, The Cambridge Handbook of the Learning Sciences, Washington University, St Louis.
  • Davis, P.J. (1993). Visual Theorems. Educational Studies in Mathematics, 24, 333-344.
  • Dormolen, J. Van. (1977). Learning to understand what giving a proof really means. Educational Studies in Mathematics, 8(1), 17-34.
  • Fischbein, E. (1982). Intuition and proof. For the learning of Mathematics, 3(2), 8-24.
  • Galbraith, P.L. (1981). Aspects of proving: A clinical investigation of process. Educational Studies in Mathematics, 12, 1-28.
  • González, J.C. (2012). Estudio de Contraste sobre la preferencia y significación de pruebas formales y preformales. (Tesis doctoral no publicada). Universidad de Valladolid.
  • Hanna, G. (1983). Rigorous proof in mathematics education. The Ontario Institut for Studies in Education, Toronto.
  • Hanna, G. (1989). More than formal proof. For the learning of mathematics, 9(1), 20-25.
  • Harel, G., & Sowder, L. (1998). Students' proof schemes: Results from exploratory studies. Issues in Mathematics Education, 7, 234-283.
  • Hersh, R. (1993) Proving is convincing and explaining. Educational Studies in Mathematics, 24, 389-399.
  • Ibañes, M., & Ortega, T. (1998). La Demostración en Matemáticas. Clasificación y ejemplos en el marco de la educación secundaria. Educación Matemática, 9(1), 65-104.
  • Ibañes, M., & Ortega, T. (2001). Un estudio sobre los esquemas de prueba en alumnos de primer curso de bachillerato. UNO, 28, 39-60.
  • Ibañes, M., & Ortega, T. (2002). Reconocimiento de procesos matemáticos en alumnos de primer curso de bachillerato. Enseñanza de las Ciencias, 21, 49-63.
  • Lakatos, I. (1976). Proofs and Refutations, Cambridge: Cambridge University Press.
  • Leron, U. (1983). Structuring mathematical proofs. American Mathematical Monthly, 90, 174-185.
  • Martin, G., & Harel, G. (1989). Proof frame of pre-service elementary teachers. Journal for Research in Mathematics Education, 20, 41-51.
  • Molina, M. (2006). Desarrollo de pensamiento relacional y comprensión del signo igual por alumnos de tercero de educación primaria. (Tesis doctoral no publicada), Universidad de Granada, Granada, España.
  • Movshovitz-Hadar, N. (1988). Stimulating presentation of theorems followed by responsive proofs. For the Learning of Mathematics, 8(2), 12-19.
  • Movshovitz-Hadar, N., Zaslavsky, O., & Inbar, S. (1987). An empirical classification model for errors in high school mathematics. Journal for Research in Mathematics Education, 18(1), 3-14.
  • Pecharromán, C., & Ortega, T. (2009). Diseño de un marco de investigación. Aplicación al proceso de aprendizaje de las propiedades globales de las funciones. En M.J. González, M.T. González & J. Murillo (Eds.), Investigación en Educación Matemática XIII (pp. 367-378) Santander: SEIEM.
  • Radatz, H. (1979) Error Analysis in Mathematics Education. Journal for Research in Mathematics Education, 9, 163-172.
  • Radford, L. (1994). La Enseñanza de la Demostración: Aspectos teóricos y prácticos. Educación Matemática, 6(3), 21-35.
  • Semadeni, Z. (1984). Action Proofs in Primary Mathematics Teaching and in Teacher Training. For the Learning of Mathematics, 4, 32-34.
  • Villiers, M.D. de (1990). The Role and Function of Proof in Mathematics. Pythagoras, 24, 7- 24.