Formas del discurso y razonamiento configural de estudiantes para maestros en la resolución de problemas de geometría

  1. Francisco Clemente 1
  2. Salvador Llinares 1
  1. 1 Universitat d'Alacant
    info

    Universitat d'Alacant

    Alicante, España

    ROR https://ror.org/05t8bcz72

Revista:
Enseñanza de las ciencias: revista de investigación y experiencias didácticas

ISSN: 0212-4521,  2174-6486

Año de publicación: 2015

Volumen: 33

Número: 1

Páginas: 9-27

Tipo: Artículo

DOI: 10.5565/REV/ENSCIENCIAS.1332 DIALNET GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Enseñanza de las ciencias: revista de investigación y experiencias didácticas

Objetivos de desarrollo sostenible

Resumen

Aquest treball té com a objectiu estudiar la relació entre les formes del discurs generat pels estudiants per a mestre en resoldre problemes de geometria de provar i el raonament *configural. Analitzem les respostes de 97 estudiants per a mestre a dos problemes de provar per determinar com identificaven i relacionaven propietats geomètriques en la deducció de nous fets i propietats de les figures. Els resultats mostren tres formes del discurs generat pels estudiants per a mestre per comunicar la seva resolució: gràfic, text i una mescla dels dos; i que les formes del discurs generat no influeixen en el truncament del raonament *configural que desencadena els processos deductius.

Referencias bibliográficas

  • 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 represen tation and specific processes. En R. Sutherland y J. Mason (eds.). Exploiting mental imagery with computers in mathe matical 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
Fuente de los datos: Dialnet