Examining the method of proofs and refutations in pre-service teachers education
Tipo de documento
Autores
Lista de autores
Karakus, Fatih y Bütün, Mesut
Resumen
There is some evidence in the mathematics education literature that Lakatos’ proofs and refutation methods can be useful to examining students’ conjecture production and proof construction process. The purpose of this study was to determine how the Lakatos method goes and which steps of the method works in the teacher education program. The population sample for this study consists of 24 senior pre-service teachers in elementary mathematics education in Turkey (16 women and 8 men). Pre-service teachers were given a problem in which they examined the relation between perimeter and area of a rectangle. Data was collected with a camera, field notes, and groups’ written solutions and analyzed on the basis of framework included in Larsen and Zandieh’s (2008) study. The finding revealed that Lakatos’ method was usable in the teacher education program. But some steps of the method described in Lakatos’ (1976) historical case study were not provided in the real classroom environment.
Fecha
2013
Tipo de fecha
Estado publicación
Términos clave
Formas geométricas | Inicial | Magnitudes | Otro (marcos) | Otro (procesos cognitivos)
Enfoque
Idioma
Revisado por pares
Formato del archivo
Volumen
27
Número
45
Rango páginas (artículo)
215-232
ISSN
19804415
Referencias
ATKINS, S. L. Lakatos’ Proofs and Refutations comes alive in an elementary classroom. School Science and Mathematics, Corvallis, v. 97, n. 3, p. 150-154, Mar. 1997. BOATS, J. J. et al. Geometric conjectures: The importance of counterexamples.Mathematics Teaching in the Middle School, Reston, v. 9, n. 4, p. 210-215, Dec. 2003. DAVIS, P. J.; HERSH, R. The Mathematical Experience. Harmondsworth: Penguin, 1980. ERNEST, P. The Philosophy of Mathematics Education. London: The Falmer Press, 1991. FREUDENTHAL, H. Mathematics as an Educational Task. Dordrecht: Reidel, 1973. FUJITA,T.et al. Proofs and refutations in lower secondary school geometry. 2011. Available at: Accessed at: Jan. 2012. GRAVEMEIJER, K.P.E. Developing Realistic Mathematics Education. Culenborg, Technipress, 1994. LAKATOS, I. Proofs and Refutations: The logic of Mathematics discovery. Cambridge: Cambridge University Press, 1976. LARSEN, S.; ZANDIEH, M. Proofs and refutations in the undergraduate mathematics classroom. Educational Studies in Mathematics, Dordrecht, v. 67, n. 3, p. 205-216, Mar. 2008. MA, L. Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah: Lawrence Erlbaum Associates Press, 1999. REICHEL, H. C. Lakatos and aspects of mathematics education. In: KAMPIS, G.; KVASZ, L.; STÖLTZNER, M. (Ed.). Appraising Lakatos: Mathematics, methodology and the man. Dordrecht: Kluwer Academic Publishers, 2002. p. 255-260. REID, D. Conjectures and refutations in grade 5 mathematics. Journal for Research in Mathematics Education, Reston, v. 33, n. 1, p. 5-29, Jan. 2002. SRIRAMAN, B. Can mathematical discovery fill the existential void? The use of Conjecture, Proof and Refutation in a high school classroom. Mathematics in School, Leicester, v. 32, n. 2, p. 2-6, Mar. 2003 SRIRAMAN, B. An Ode to Imre Lakatos: Quasi-thought experiments to bridge the Ideal and actual mathematics classrooms. Interchange, Dordrecht, v. 37, n. 1-2, p. 151- 178, Apr. 2006. STEINER, H. G. Philosophical and Epistemological Aspects of Mathematics and their Interaction with Theory and Practice in Mathematics Education. For the Learning of Mathematics, Kingston, v. 7, n. 1, p. 7-13, Feb. 1987. SWINYARD, C.; LARSEN, S. Proofs and refutations as a model for defining limit. In: ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICSEDUCATION, 13th, 2010, Raleigh, NC. Proceedings… Raleigh, North Carolina: RUME, 2010. p. 1-12. Available at: . Accessed at: Nov. 2011. THOM, R. Modern Mathematics: Does it Exist? In: HOWSON, A. G. (Ed.). Developments in Mathematics Education. Cambridge: Cambridge University Press, 1973. p. 194-209. TOUMASIS, C. The NCTM standards and the philosophy of mathematics. Studies in Philosophy and Education, Dordrecht, v. 16, n. 3, p. 317-330, July 1997. YIM, J. et al. The mathematically gifted elementary students’ revisiting of Euler’s polyhedron theorem. The Montana Mathematics Enthusiast, Montana, v. 5, n. 1, p. 125-142, Jan. 2008.