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Artículos

Vol. 18 No. 3 (2015): Noviembre

VISUAL CONTROL IN THE CONSTRUCTION OF THE AREA OF TWO- DIMENSIONAL PLANE FIGURES , IN TEXTBOOKS . AN ANALYSIS METHODOLOGY

DOI
https://doi.org/10.12802/relime.13.1831
Submitted
July 1, 2023
Published
2015-11-30

Abstract

To construct the concept of plane surfaces area, textbooks propose activities in which some information about how to see the figures is provided. The elements and strategies showed by the books, that favor some types of visualization above others, must be characterized and the types of visual control commanding must be analyzed. The model of analysis presented here includes an adaptation of the theoretical model exposed by Duval (1995, 2003, 2005), about the visualization associated with geometrical figures, and the notion of control structure from Balacheff and Gaudin (2010), about the existence of some elements that guide the ways students use to proceed when they are confronted with mathematical activities.

References

  1. Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52, 215-241. doi: 10.1023/A:1024312321077
  2. Balacheff, N. & Gaudin, N. (2010). Modeling Students’ Conceptions: The Case of Function. Research in Collegiate Mathematics Education, 16, 183-211.
  3. Brousseau, G. (1982). Les objets de la didactique des mathématiques- Ingénierie didactique. Actes de la deuxieme école d’été de didactique des mathematiques (pp. 10-60). Orléans, Francia: IREM d´Orléans.
  4. Burgermeister, P. et Coray, M. (2008). Processus de contrôle en résolution des problèmes dans le cadre de la proportionnalité des grandeurs: Une analyse descriptive. Recherches en Didactique des Mathématiques, 28(1), 63-105.
  5. Cantoral, R. y Montiel, G. (2003). Una representación visual del polinomio de Lagrange. Números, 55, 3-22.
  6. Cleary, T. J. & Zimmerman, B. J. (2004). Self-regulation empowerment program: A school-based program to enhance self-regulated and self-motivated cycles of student learning. Psychology in the Schools, 41(5), 537-550. doi: 10.1002/pits.10177
  7. Cobo, B. y Batanero, C. (2004). Significado de la medida en los libros de texto de secundaria. Enseñanza de las Ciencias, 22(1), 5-18.
  8. Dickson, L., Brown, M. y Gibson, O. (1991). El aprendizaje de las matemáticas. Barcelona, España: Editorial Labor S.A.
  9. Duval, R. (1995). Geometrical Pictures: kinds of representation and specific processing. In R. Suttherland & J. Mason (Eds.), Exploiting Mental Imagery with Computers in Mathematics Education (pp. 142-157). Berlin, Germany: Springer.
  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 (pp. 37-51). Dordrecht, Netherlands: Kluwer Academic Publishers.
  11. Duval, R. (1999). Semiosis y pensamiento humano. Registros semióticos y aprendizaje intelectuales (M. Vega Restrepo, Trad.), (1ª ed.). Cali, Colombia: Artes Gráficas Univalle.
  12. Duval, R. (2003). Voir en mathématiques. En E. Filloy (Ed.), Matemática educativa. Aspectos de la investigación actual (pp. 41–76). Distrito Federal, México: Centro de Investigación y Estudios Avanzados del IPN.
  13. Duval, R. (2005). Les conditions cognitives de l’apprentissage de la géométrie: développement de la visualisation, différenciation des raisonnements et coordination de leurs fonctionnements. Annales de didactique et sciences cognitives, 10, 5-53.
  14. Garofalo, J. & Lester, F. K. (1985). Metacognition, cognitive monitoring, and mathematical performance. Journal for Research in Mathematics Education, 16(3), 163–176. doi: 10.2307/748391
  15. Gettinger, M. & Seibert, J. K. (2002). Contributions of study skills to academic competence. School Psychology Review, 31(3), 350–365.
  16. Gutiérrez, A. (1996). Visualization in 3-dimensional geometry search of a framework. In L. Puig & A. Gutiérrez (Eds.), Proceedings of the 20th Conference of the International Group for the Psychology of Mathematics Education (Vol.1, pp. 3–19). Valencia, España: Universidad de Valencia.
  17. Kordaki, M. (2003). The effect of tools a computer microworld on student´s strategies regarding the concept of conservation of area. Educational Studies in Mathematics, 52(2), 177–209. doi: 10.1023/A:1024065107302.
  18. Kramarski, B., Weisse, I. & Kololshi-Minsker, I. (2010). How can self-regulated learning support the problem solving of third-grade students with mathematics anxiety? The International Journal on Mathematics Education, 42(2), 179–193. doi: 10.1007/s11858-009-0202-8.
  19. Lithner, J. (2004). Mathematical reasoning in calculus textbook exercises. Journal of Mathematical Behavior, 23(4), 405-427. doi:10.1016/j.jmathb.2004.09.003
  20. Love, E. & Pimm, D. (1996). “This is so”: a text on texts. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International Handbook of Mathematics Education (pp. 371-409). Dordrecht, Netherlands: Kluwer Academic Publishers.
  21. Malmivuori, M. L. (2006). Affect and Self-Regulation. Educational Studies in Mathematics, 63(2), 149-164. doi: 10.1007/s10649-006-9022-8.
  22. Marmolejo, G. A. (2007). Algunos Tópicos a tener en cuenta en el aprendizaje del registro semiótico de las figuras. Procesos de visualización y factores de visibilidad (Tesis de maestría no publicada). Universidad del Valle, Cali, Colombia.
  23. Marmolejo, G. A. (2010). La visualización en los primeros ciclos de la educación básica. Posibilidades y complejidad. Sigma, 10(2), 10-26.
  24. Marmolejo, G. A. y González, M. T. (2013a). Función de la visualización en la construcción del área de figuras bidimensionales. Una metodología de análisis y su aplicación a un libro de texto. Revista Integración, 31(1), 87-106.
  25. Marmolejo, G. A. y González, M. T. (2013b). Visualización en el área de regiones poligonales. Una metodología de análisis de textos escolares. Educación Matemática, 25(3), 61-102.
  26. Marmolejo, G. A. y Vega, M. (2012). La visualización en las f iguras geométricas. Importancia y complejidad de su aprendizaje. Educación Matemática, 24(3), 7-32.
  27. Mesa, V. (2004). Characterizing practices associated with functions in middle school textbooks: An empirical approach. Educational Studies in Mathematics, 56 (2), 255–286. doi: 10.1023/B: EDUC.0000040409.63571.56.
  28. Mesa, V. (2010). Strategies for Controlling the Work in Mathematics Textbooks for Introductory Calculus. Research in Collegiate Mathematics Education, 16, 235-260.
  29. Padilla, V. (1992). L´influence d´une acquisition de traitements purement figuraux pour l’apprentissage des Mathématiques (Thèse de doctorat non publié). Université de Strasbourg, Strasbourg, France.
  30. Pape, S. J., Bell, C. V. & Yetkin, I. E. (2003). Developing Mathematical Thinking and Self-Regulated Learning: A Teaching Experiment in a Seventh-Grade Mathematics Classroom. Educational Studies in Mathematics, 53(3), 179-202. doi: 10.1023/A:1026062121857.
  31. Pepin, B., Haggarty, L. & Keynes, M. (2001). Mathematics textbooks and their use in English, French and German classrooms: a way to understand teaching and learning culture. Zentralblatt für Didaktik der Mathematik, 33(5), 158-175.
  32. Presmeg, N. (2006). Research on visualization in learning and teaching mathematics. In A. Gutiérrez & P. Boero (Eds.), Handbook on the Psychology of Mathematics Education: Past, Present and Future (pp. 205-235). Rotterdam, Netherland: Sense Publishers.
  33. Rock, I. (1985). La percepción. Barcelona, España: Prensa Científica.
  34. Schmidt, W. H., Jorde, D., Cogan, L. S., Barrier, E., Gonzalo, I., Moser, U., … Wolfe, R. G. (1996). Characterizing pedagogical flow. An investigation of Mathematics and Science Teaching in Six Countries. Dordrecht, Netherlands: Kluwers Academic Publishers.
  35. Schneider, W. & Artelt, C. (2010). Metacognition and mathematics education. The International Journal on Mathematics Education, 42(2), 149–161. doi: 10.1007/s11858-010-0240-2.
  36. Schoenfeld, A. H. (1987). What’s the fuss about metacognition? In A. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 189–215). Hillsdale, NJ: Erlbaum
  37. Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334-370). New York, United States of America: Macmillan.
  38. Schunk, D.H. (1996). Goal and self-evaluative influences during children’s cognitive skill learning. American Educational Research Journal, 33(2), 359–382.
  39. Villani, V. (1998). Perspectives on the teaching of geometry for the 21st Century (Discussion Document for an ICMI Study). In C. Mammana & V. Villani (Eds.), Perspectives on the Teaching of Geometry for the 21st Century (pp. 337-346). Dordrecht, Netherlands: Kluwer Academic Publishers.
  40. Whitebread, D. & Coltman, P. (2010). Aspects of pedagogy supporting metacognition and mathematical learning in young children; evidence from an observational study. The International Journal on Mathematics Education, 42(2), 163-178.
  41. doi: 10.1007/s11858-009-0233-1.
  42. Zimmerman, B. J. (2002). Achieving self-regulation: The trial and triumph of adolescence. In F. Pajares & T. Urdan (Eds.), Academic motivation of adolescents (Vol. 2, pp. 1–27). Greenwich, CT: Information Age.
  43. Zimmermann, W. & Cunnigham, S. (1991). Editor´s introduction: What is Mathematical Visualization? In W. Zimmermann & S. Cunnigham (Eds.), Visualization in teaching and Learning Mathematics (pp. 1-8). Washington, DC: Mathematical Association of America.

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