The width of a proof

Autores/as

  • Gila Hanna Ontario Institute for Studies in Education, University of Toronto, Canada

DOI:

https://doi.org/10.30827/pna.v9i1.6109

Palabras clave:

Argumentación, Demostración, Explicación, Memorable

Resumen

This paper’s aim is to discuss the concept of width of a proof put forward by Timothy Gowers. It explains what this concept means and attempts to show how it relates to other concepts discussed in the existing literature on proof and proving. It also explores how the concept of width of a proof might be used productively in the mathematics curriculum and how it might fit with the various perspectives on learning to prove.

La amplitud de una demostración

El objetivo de este artículo es discutir el concepto de amplitud de una demostración presentado por Timothy Gowers. Se explica el significado de este concepto y se trata de mostrar cómo se relaciona con otros conceptos discutidos en la literatura existente sobre prueba y demostraciones. También se explora cómo el concepto de amplitud de una demostración podría utilizarse productivamente en el currículo de matemáticas y cómo podría encajar con las diferentes perspectivas sobre el aprendizaje de la demostración.

Handle: http://hdl.handle.net/10481/33233

Nº de citas en SCOPUS (2017): 1 (Citas de 2º orden, 0)

Descargas

Los datos de descargas todavía no están disponibles.

Citas

Balacheff, N. (2010). Bridging knowing and proving in mathematics: A didactical perspective. In G. Hanna, H. N. Jahnke, & H. Pulte (Eds.), Explanation and proof in mathematics. Philosophical and educational perspectives (pp. 115-136). New York, NY: Springer.

De Villiers, M. (2010). Experimentation and proof in mathematics. In G. Hanna, H. N. Jahnke, & H. Pulte (Eds.), Explanation and proof in mathematics. Philosophical and educational perspectives (pp. 205-222). New York, NY: Springer.

Douek, N. (2007). Some remarks about argumentation and proof. In P. Boero (Ed.), Theorems in school (pp. 163-184). Rotterdam, The Netherlands: Sense Publishers.

Durand-Guerrier, V., Boero, P., Douek, N., Epp, S., & Tanguay, D. (2012). Argumentation and proof in the classroom. In G. Hanna & M. de Villiers (Eds.), Proof and proving in mathematics education: The 19th ICMI Study (pp. 349-368). New York, NY: Springer.

Gowers, W. T. (2007). Mathematics, memory and mental arithmetic. In M. Leng, A. Paseau & M. Potter (Eds.), Mathematical knowledge (pp. 33-58). Oxford, United Kingdom: Oxford University Press.

Hanna, G. (2000). Proof, explanation and exploration: An overview. Educational Studies in Mathematics, 44(1-2), 5-23.

Hanna, G. & Barbeau, E. (2009). Proofs as bearers of mathematical knowledge. In G. Hanna, H. N. Jahnke, & H. Pulte (Eds.), Explanation and proof in mathematics. Philosophical and educational perspectives (pp. 85-100). New York, NY: Springer.

Hemmi, K. (2008). Students' encounter with proof: The condition of transparency. ZDM, 40(3), 413-426.

Jahnke, H. N. (2009). Proof and the empirical sciences. In F. L. Lin, F. J. Hsieh, G. Hanna, & M. de Villiers (Eds.), ICMI Study 19: Proof and proving in mathematics education (Vol. 1, pp. 238-245). Taipei, Taiwan: The Department of Mathematics, National Taiwan Normal University.

Knipping, C. (2008). A method for revealing structures of argumentation in classroom proving processes. ZDM, 40(3), 427-441.

Leron, U. (1983). Structuring mathematical proofs. American Mathematical Monthly, 90(3), 174-185.

Leron, U. & Zaslavsky, O. (2009). Generic proving: Reflections on scope and method. In F. L. Lin, F. J. Hsieh, G. Hanna, & M. de Villiers (Eds.), ICMI Study 19: Proof and proving in mathematics education (Vol. 2, pp. 53-58). Taipei, Taiwan: The Department of Mathematics, National Taiwan Normal University.

Manin, Y. I. (1998). Truth, rigour, and common sense. In H. G. Dales & G. Oliveri (Eds.), Truth in mathematics (pp. 147-159). Oxford, United Kingdom: Clarendon Press.

Mariotti, A. (2006). Proof and proving in mathematics education. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 173-204). Rotterdam, The Netherlands: Sense Publishers.

Mejia-Ramos, J. P, Fuller, E., Weber, K., Rhoads, K., & Samkoff, A. (2012). An assessment model for proof comprehension in undergraduate mathematics. Educational Studies in Mathematics, 79(1), 3-18.

Pedemonte, B. (2007). How can the relationship between argumentation and proof be analysed? Educational Studies in Mathematics, 66(1), 23-41.

Raman, M. (2003). Key ideas: What are they and how can they help us understand how people view proof? Educational Studies in Mathematics, 52(3), 319-325.

Thurston, W. P. (1994). On proof and progress in mathematics. Bulletin of the American Mathematical Society, 30(2), 161-177.

Descargas

Publicado

2014-09-01

Número

Sección

Artículos