Análisis de la actividad matemática mediante dos herramientas teóricasRegistros de representación semiótica y configuración ontosemiótica
- Juan, Diaz, Godino 1
- Miguel, R. Wilhelmi 2
- Teresa, F. Blanco 3
- Ángel, Contreras 4
- Belén, Giacomone 1
-
1
Universidad de Granada
info
-
2
Universidad de Navarra
info
-
3
Universidade de Santiago de Compostela
info
-
4
Universidad de Jaén
info
ISSN: 2254-4313
Year of publication: 2016
Issue: 10
Pages: 91-110
Type: Article
More publications in: Avances de investigación en educación matemática: AIEM
Abstract
To understand the difficulties and conflicts of learning is necessary to analyse the mathematical tasks and the various ways of addressing them by students. This analysis provides information about the design of the tasks and the management of knowledge in the classroom, being necessary to apply specific theoretical tools for its realisation. In this paper, we analyse a task that requires the formulation of a conjecture and its proof using figural and algebraic representations, and applying two different theoretical tools: the notions of semiotic representation register and onto-semiotic configuration. The results reveal some complementarities that allowed us to show the potential utility of the epistemic and cognitive analysis carried out. The aim is to show the potential synergy between these tools and the possibility to progress in the articulation of the corresponding theoretical frameworks.
Funding information
Trabajo realizado en el marco de los proyectos de investigación EDU2012-31869 y EDU2013-41141-P, Ministerio de Economía y Competitividad (MINECO).Funders
-
Ministerio de Asuntos Económicos y Transformación Digital, Gobierno de España
Spain
- EDU2012-31869
- EDU2013-41141-P
Bibliographic References
- Bikner-Ahsbahs, A. & Prediger, S. (Eds.). (2014). Networking of theories as a research practice in Mathematics Education, Advances in Mathematics Education. Dordrecht, The Netherlands: Springer.
- Dickson, L., Brown, M. & Gibson, O. (1991). El aprendizaje de las matemáticas. Barcelona, España: Labor.
- Duval, R. (1995). Sémiosis et pensée: registres sémiotiques et apprentissages intellectuels. Berne, Switzerland: Peter Lang.
- Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1-2), 103-131.
- Eco, U. (1976). Tratado de semiótica general. Barcelona: Lumen.
- Font, V., Godino, J. D. & Contreras, A. (2008). From representation to onto-semiotic configurations in analysing mathematics teaching and learning processes. En, L. Radford, G. Schubring y F. Seeger (Eds.), Semiotics in mathematics education: epistemology, history, classroom, and culture (pp. 157–173). Rotterdam: Sense Publishers.
- Font, V., Godino, J. D. & Gallardo, J. (2013). The emergence of objects from mathematical practices. Educational Studies in Mathematics, 82, 97-124.
- Font, V. & Peraire, R. (2001). Objetos, prácticas y ostensivos asociados. El caso de la cisoide. Educación Matemática, 13(2), 55-67.
- Fontes, S., García, C., Quintanilla, L., Rodríguez, R., Rubio & P. Sarriá, E. (2010). Fundamentos de investigación en psicología. Madrid: UNED.
- Godino, J. D. (2012). Origen y aportaciones de la perspectiva ontosemiótica de investigación en Didáctica de la Matemática. En A. Estepa, A. Contreras, J. Deulofeu, M. C. Penalva, F. J. García & L. Ordóñez (Eds.), Investigación en Educación Matemática XVI (pp. 49 68). Jaén: SEIEM.
- Godino, J.D., Batanero, C. & Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM-The International Journal on Mathematics Education, 39(1), 127-135.
- Godino, J. D., Bencomo, D., Font, V. & Wilhelmi, M. R. (2006). Análisis y valoración de la idoneidad didáctica de procesos de estudio de matemáticas. Paradigma, 27(2), 221-252.
- Godino, J. D. & Font, V. (2010). The theory of representations as viewed from the ontosemiotic approach to mathematics education. Mediterranean Journal for Research in Mathematics Education, 9(1), 189-210.
- Godino, J. D., Font, V., Wilhelmi, M. & Lurduy, O. (2011). Why is the learning of elementary arithmetic concepts difficult? Semiotic tools for understanding the nature of mathematical objects. Educational Studies in Mathematics, 77(2), 247-265.
- Hjelmslev, L. (1943). Prolegomena to a theory of language. Madison, WI: University of Wisconsin Press.
- Montiel, M., Wilhelmi, M. R., Vidakovic, D. & Elstak, I. (2009). Using the onto-semiotic approach to identify and analyze mathematical meaning when transiting between different coordinate systems in a multivariate context. Educational Studies in Mathematics, 72, 139-160.
- Ortega, T. & Pecharomán, C. (2015). Aprendizaje de conceptos geométricos a través de visualizaciones. Avances de Investigación en Educación Matemática, 7, 95-117.
- Peirce, C. S. (1978). The collected papers of Charles Sanders Peirce. Cambridge, MA: The Belknap Press of Harvard University.
- Pino-Fan, L., Guzmán, I., Duval, R. & Font, V. (2015). The theory of registers of semiotic representation and the onto-semiotic approach to mathematical cognition and instruction: linking looks for the study of mathematical understanding. En Beswick, K., Muir, T. & Wells, J. (Eds.), Proceedings of the 39th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 33-40). Hobart, Australia: PME Group.
- Prediger, S., Bikner-Ahsbahs, A. & Arzarello, F. (2008). Networking strategies and methods for connection theoretical approaches: first steps towards a conceptual framework. ZDMThe International Journal on Mathematics Education, 40(2), 165-178.
- Rojas, P. (2015). Objetos matemáticos, representaciones semióticas y sentidos. Enseñanza de las Ciencias, 33(1), 151-165.