Formas del discurso y razonamiento configural de estudiantes para maestros en la resolución de problemas de geometría
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Lista de autores
Clemente, Francisco y Llinares, Salvador
Resumen
Este trabajo tiene como objetivo estudiar la relación entre las formas del discurso generado por los estudiantes para maestro al resolver problemas de geometría de probar y el razonamiento configural. Analizamos las respuestas de 97 estudiantes para maestro a dos problemas de probar para determinar cómo identificaban y relacionaban propiedades geométricas para deducir nuevos hechos y propiedades de las figuras. Los resultados muestran tres formas del discurso generado por los estudiantes para maestro para comunicar su resolución: gráfico, texto y una mezcla de los dos; y que las formas del discurso generado no influyen en el truncamiento del razonamiento configural que desencadena los procesos deductivos.
Fecha
2015
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Referencias
Arzarello, F., Olivero, F., Paola, D. y Robutti, O. (2008). THe transition to formal proof in geometry. En P. Boero (ed.). Theorems in schools: from history, epistemology and cognition to classroom practices. Rotterdam, Netherland: Sense Publishers, pp. 307-424. Battista, M.T. (2007). The development of geometric and spatial thinking. En F. Lester (ed.). Second handbook of research on mathematics teaching and learning. Charlotte, NC: NCTM/Information Age Publishing, pp. 843-908. Battista, M.T. (2008). Representations and cognitive objects in modern school geometry. En M. Kathleen & G.W. Blume (eds.). Research on Technology and the Teaching and Learning of Mathematics. Charlotte: IAG, pp. 341-362. Brown, D.L. y Wheatley, G. (1997). Components of Imagery and Mathematical Understanding. Focus on Learning Problems in Mathematics, 19 (1), 45-70. Chen, Ch. y Herbst, P. (2013). The interplay among gestures, discourse, and diagrams in student’ geometrical reasoning. Educational Studies in Mathematics, 83(2), pp. 285-307. http://dx.doi.org/10.1007/s10649-012-9454-2 Chinnappan, M. y Lawson, M. (2005). A framework for analysis of teachers’ geometric content knowledge and geometric knowledge for teaching. Journal of Mathematics Teacher Education, 8, pp. 197-221. http://dx.doi.org/10.1007/s10857-005-0852-6 Clement, J. (2000). Analysis of clinical Interviews: Foundations and Model Viability. En A.E. Kelly y R.A. Lesh (eds.). Handbook of Research Design in Mathematics and Science Education. London: Lawrence Erlbaum Pubs, pp. 547-589. Clemente, F. y Llinares, S. (2013). Conocimiento de Geometría especializado para la enseñanza en Educación Primaria. En A. Berciano, G. Gutiérrez, A. Estepa y N. Climent (eds.). Investigación en Educación matemática XVII. Bilbao: SEIEM, pp. 229-236. Duval, R. (1995). Geometrical Pictures: Kinds of representation and specific processes. En R. Sutherland y J. Mason (eds.). Exploiting mental imagery with computers in mathematical education. Berlín: Springer, pp. 142-157. http://dx.doi.org/10.1007/978-3-642-57771-0_10 Duval, R. (1998). Geometry from a cognitive point of view. En C. Mammana y V. Villani (eds.). Perspectives on the teaching of geometry for the 21st century. An International Commission on Mathematical Instruction (ICMI) Study [Chapter 2.2]. The Netherlands: Dordrecht, Kluwer, pp. 37-52. Duval, R. (1999). Representation, Vision and Visualization: Cognitive functions in mathematical thinking. Basis Issues for learning. En F. Hitt y M. Santos (eds.). Proceedings of the 21st Annual Meeting North American Chapter of the International Group of PME. Cuernavaca, México. Columbus, Ohio, USA: ERIC/CSMEE Publications-The Ohio State University, pp. 3-26. Duval, R. (2007). Cognitive functioning and the understanding of mathematical processes of proof. En P. Boero (ed.). Theorems in School. From History, epistemology and Cognition to Classrroom Practice. Rotterdam: Sense Publishers, pp. 137-162. Fischbein, E. (1993). The Theory of Figural Concepts. Educational Studies in Mathematics, 24, pp. 139-162. http://dx.doi.org/10.1007/BF01273689 Hanna, G. (1998). Proof as Explanation in Geometry. Focus on learning Problems in Mathematics, 20 (2 y 3), pp. 4-13. Hanna, G. y Sidoli, N. (2007). Visualisation and proof: a brief survey of philosophical perspectives. ZDM. Mathematics Education, 39, pp. 73-78. http://dx.doi.org/10.1007/s11858-006-0005-0 Herbst, P. (2004). Interaction with diagrams and the making of reasoned conjectures in geometry. Zentralblatt für Didaktik der Mathematik, 36(5), pp. 129-139. http://dx.doi.org/10.1007/BF02655665 Hershkowitz, R. (1990). Pshycological aspects of learning Geometry. En P. Nesher y J. Kilpatrick (eds.). Mathematics and Cognition. A Research Synthesis by the International Group for the Psychology of Mathematics Education. Cambridge University Press, pp. 70-95. Hilbert, T., Renkl, A., Kessler, S. y Reiss, K. (2008). Learning to prove in geometry: learning from heuristic examples and how it can be supported. Learning and Instruction, 18, pp. 54-65. http://dx.doi.org/10.1016/j.learninstruc.2006.10.008 Krutetskii, V.A. (1976). The psychology of mathematical abilities in schoolchildren. Chicago, USA: University of Chicago Press. Lin, F. y Yang, K. (2007). The reading comprehension of Geometric proofs: The contribution of knowledge and reasoning. International Journal of Science and Mathematics Education, 5(4), pp. 729-754. http://dx.doi.org/10.1007/s10763-007-9095-6 Llinares, S. y Clemente, F. (2014). Characteristics of Preservice Primary School Teachers’ configural Reasoning. Mathematical Thinking and Learning, 16(3), pp. 234-250. http://dx.doi.org/10.1080/10986065.2014.921133 Mayer, R.E. y Massa, L. (2003). Three Facets of Visual and Verbal Learners: Cognitive Ability, Cognitive style, and Learning Preference. Journal of Educational Psychology, 95(4), pp. 833-846. http://dx.doi.org/10.1037/0022-0663.95.4.833 Mesquita, A.L. (1998). On conceptual Obstacles Linked with External Representation in Geometry. Journal of Mathematical Behavior, 17(2), pp. 183-195. http://dx.doi.org/10.1016/S0364-0213(99)80058-5 Nason, R., Chalmers, CH. y Yeh, A. (2012). Facilitating growth in prospective teachers’ knowledge: teaching geometry in primary schools. Journal of Mathematics Teacher Education, 15, pp. 227-249. http://dx.doi.org/10.1007/s10857-012-9209-0 Parzysz, B. (1988). «Knowing» vs «Seeing». Problems of the plane representation of space geometry figures. Educational Studies in Mathematics, 19, pp. 79-92. http://dx.doi.org/10.1007/BF00428386 Pitta-Pantazi, D. y Christou, C. (2009). Cognitive styles, tasks presentation mode and mathematical performance. Research in Mathematics Education, 11(2), pp. 131-148. http://dx.doi.org/10.1080/14794800903063331 Presmeg, N. (2006). Research on Visualization in Learning and Teaching Mathematics. En A. Gutierrez, y P. Boero (eds.). Handbook of Research on the Psychology of mathematics Education. Past, Present and Future. Rotterdam/Taipei: Sense Publishers, pp. 205-236. Prior, J. y Torregrosa, G. (2013). Razonamiento configural y procedimientos de verificación en contexto geométrico. RELIME. Revista Latinoamericana de Investigación en Matemática Educativa, 16(3), pp. 339-368. http://dx.doi.org/10.12802/relime.13.1633 Prusak, N., Hershkowitz, R. y Schwarz, B. (2012). From visual reasoning to logical necessity through argumentative design. Educational Studies in Mathematics, 79, pp. 19-40. http://dx.doi.org/10.1007/s10649-011-9335-0 Robotti, E. (2012). Natural language as a tool for analyzing the proving process: the case of plane geometry proof. Educational Studies in Mathematics, 80(3), pp. 433-450. http://dx.doi.org/10.1007/s10649-012-9383-0 Steele, M.D. (2013). Exploring the mathematical knowledge for teaching geometry and measurement through the design and use of rich assessment tasks. Journal of Mathematics Teacher Education, 16(4), pp. 245-268. http://dx.doi.org/10.1007/s10857-012-9230-3 Stylianides, A.J. y Ball, D. (2008). Understanding and describing mathematical knowledge for teaching: knowledge about proof for engaging students in the activity of proving. Journal of Mathematics Teacher Education, 11, pp. 307-332. http://dx.doi.org/10.1007/s10857-008-9077-9 Stylianides, G., Stylianides, A. y Shilling-Traina, L.N. (2013). Prospective teachers’ Challenges in teaching reasoning-and-proving. International Journal of Science and Mathematics Education, 11(6), pp. 1463-1490. http://dx.doi.org/10.1007/s10763-013-9409-9 Torregrosa, G. y Quesada, H. (2007). Coordinación de procesos cognitivos en Geometría. RELIME. Revista Latinoamericana de Investigación en Matemática Educativa, 10(2), pp. 275-300. Torregrosa, G., Quesada, H. y Penalva, M.C. (2010). Razonamiento configural como coordinación de procesos de visualización. Enseñanza de las Ciencias, 28(3), pp. 327-340. Vinner, S.H. y Kopelman, E. (1998). Is Symmetry an Intuitive Basis for Proof in Euclidean Geometry? Focus on Learning Problems in Mathematics, 20 (2 y 3), pp. 14-26. Yang, K. y Lin, F. (2008). A model of reading comprehension of geometry proof. Educational Studies in Mathematics, 67(1), pp. 59-76. http://dx.doi.org/10.1007/s10649-007-9080-6