Interpretación de diagramas de comparación multiplicativa por estudiantes de secundaria
DOI:
https://doi.org/10.30827/pna.v10i4.6084Palabras clave:
Comparación multiplicativa, Diagramas, Representación simbólica, Representación verbal, Resolución de problemasResumen
Este trabajo se centra en procesos de traducción de problemas gráficos de comparación multiplicativa a representación verbal y simbólica. Pedimos a 89 estudiantes del primer curso de educación secundaria que inventaran un problema que se ajustara a un diagrama y que escribieran una ecuación que integrara las relaciones del diagrama. Los dos procesos de traducción se han mostrado difíciles para los estudiantes, provocando diversidad de respuestas. El análisis conjunto de las respuestas reveló que la competencia de los estudiantes en el proceso de invención no es independiente de la traducción algebraica.
Interpretation of multiplicative comparison diagrams by secondary school students
Descargas
Citas
Aguilar, M., Navarro, J. I. y Alcalde, C. (2003). El uso de esquemas figurativos para ayudar a resolver problemas aritméticos. Cultura y Educación, 15(4), 385-397.
Ainsworth, S. y Th Loizou, A. (2003). The effects of self-explaining when learning with text or diagrams. Cognitive Science, 27(4), 669-681.
Beckmann, S. (2004). Solving algebra and other story problems with simple diagrams: A method demonstrated in grade 4-6 texts used in Singapore. The Mathematics Educator, 14(1), 42-46.
Castro, E. (1995). Niveles de comprensión en problemas verbales de comparación multiplicativa. Granada, España: Comares.
Castro, E. y Castro, E. (1997). Representaciones y modelización. En L. Rico (Coord.), La Educación Matemática en la enseñanza secundaria. Barcelona, España: ICE/Horsori.
Castro, E., Rico, L. y Castro, E. (1992). Choice of structure and interpretation of relation in multiplicative compare problems. En W. Geeslin y K. Graham (Eds.), Proceedings of the sixteenth Conference of International Group for the Psychology of Mathematics Education (Vol. 1, pp. 113-120). Durham, NH: University of New Hampshire.
Cheng, P. C-H. (2004). Why diagrams are (sometimes) six times easier than words: Benefit beyond locational indexing. En A. Blackwell, K. Marriott y A. Shimojima (Eds.), Diagrammatic representation and inference, third international conference, diagrams (pp. 242-254). Heidelberg, Alemania: Springer.
Clark, A. (2013). Singapore math: A visual approach to word problems. Boston, MA: Houghton Mifflin Harcourt.
Clark, H. H. (1969). Linguistic processes in deductive reasoning. Psychological Review, 76, 387-404.
Clement, J. (1982). Algebra word problem solutions: Thought processes underlying a common misconception. Journal for Research in Mathematics Education, 13(1), 16-30.
Cuoco, A. A. y Curcio, F. R. (2001). The role of representation in school mathematics. Reston, VA: NCTM.
Diezmann, C. M. y English, L. D. (2001). Promoting the use of diagrams as tools for thinking. En A. A. Cuoco y F. R. Curcio (Eds.), The roles of representation in school mathematics: 2001 Yearbook (pp. 77-89). Reston, VA: National Council of Teachers of Mathematics.
Fuson, K. C. y Willis, G. B. (1989). Second graders' use of schematic drawings in solving addition and subtraction word problems. Journal of Educational Psychology, 81(4), 514-520.
Goldin, G. (2002). Representation in mathematical learning and problem solving. En L. D. English (Ed.), Handbook of international research in mathematics education (pp. 197-218). Londres, Reino Unido: Lawrence Erlbaum Associates.
Greer, B. (1992). Multiplication and division as models of situations. En D. Grouws (Ed.), Handbook of research on learning and teaching mathematics (pp. 276-295). NuevaYork, NY: Macmillan.
Hembree, R. (1992). Experiments and relational studies in problem solving-a metaanalysis. Journal for Research in Mathematics Education, 23(3), 242-273.
Hiebert, J. y Carpenter, Th. P. (1992). Learning and teaching with understanding. En D. W. Grouws (Ed.), Handbook of research in teaching and learning of mathematics (pp. 65-97). Nueva York, NY: Macmillan.
Janvier, C. (1987). Problems of representation in the teaching and learning of mathematics. Hillsdale, NJ: Lawrence Erlbaum Associates.
Kelly, R. R., Lang H. G., Mousley, K. y Davis, S. M. (2003). Deaf college students' comprehension of relational language in arithmetic compare problems. Journal of Deaf Studies and Deaf Education, 8(2), 120-132.
Kieran, C. y Filloy, E. (1989). El aprendizaje del álgebra escolar desde una perspectiva psicológica. Enseñanza de las Ciencias, 7(3), 229-240.
Küchemann, D. (1978). Children's understanding of numerical variables. Mathematics in School, 7(4), 23-26.
Küchemann, D. (1981). Algebra. En K. Hart (Ed.), Children's understanding of mathematics (pp. 11-16). Londres, Reino Unido: John Murray.
Lewis, A. B. (1989). Training students to represent arithmetic word problems. Journal of Educational Psychology, 81, 521-531.
Lewis, A. B. y Mayer, R. E. (1987). Students' miscomprehension of relational statements in arithmetic word problems. Journal of Educational Psychology, 79, 363-371.
Marshall, S. P. (1995). Schemas in problem solving. Nueva York, NY: Cambridge University Press.
Martínez, M. V., Fernández, F. y Flores, P. (2011). Clasificación de problemas verbales de álgebra elemental a partir de su resolución mediante un modelo geométrico-lineal. Unión, 25, 43-61.
Mayer, R. E. (2003). The promise of multimedia learning: Using the same instructional design methods across different media. Learning and Instruction, 13, 125-139.
National Governors Association Center for Best Practices y Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington, DC: Autores
Ng, S. F. y Lee, K. (2009). The model method: Singapore children's tool for representing and solving algebraic word problems. Journal for Research in Mathematics Education, 40(3), 282-313.
Novick, L. R., Hurley, S. M. y Francis, M. (1999). Evidence for abstract, schematic knowledge of three spatial diagram representations. Memory & Cognition, 27, 288-308.
Pantziara, M., Gagatsis, A. y Pitta-Pantazi, D. (2004). The use of diagrams in solving non routine problems. En M. Johnsen Hoines y A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 489-496). Bergen, Noruega: Bergen University College.
Pape, S. J. (2003). Compare word problems: Consistency hypothesis revisited. Contemporany Educational Psychology, 28, 396-142.
Philipp, R. A. (1992). The many uses of algebraic variables. The Mathematics Teacher, 85(7), 557-561.
Pólya, G. (1945). How to solve it: A new aspect of mathematical method. Princeton, NJ: Princeton University Press.
Rico, L. (2009). Sobre las nociones de representacio_n y comprensio_n en la investigacio_n en educacio_n matema_tica. PNA, 4(1), 1-14.
Rodri_guez-Domingo, S., Molina, M., Can_adas, M. C. y Castro, E. (2015). Errores en la traduccio_n de enunciados algebraicos entre los sistemas de representacio_n simbo_lico y verbal. PNA, 9(4), 273-293.
Schoenfeld, A. H. (1985). Mathematical problem solving. San Diego, CA: Academic Press.
Stern, E. (1993). What makes certain arithmetic word problems involving the comparison of sets so difficult for children? Journal of Educational Psychology, 85(1), 7-23.
Uesaka, Y., Manalo, E. e Ichikawa, S. (2007). What kinds of perceptions and daily learning behaviors promote students' use of diagrams in mathematics problem solving? Learning and Instruction, 17(3), 322-335.
Usiskin, Z. (1988). Conceptions of school algebra and uses of variables. En A. Coxford y A. P. Schulte (Eds.), Ideas of algebra, K-12, 1988 yearbook (pp. 8-19). Reston, VA: National Council of Teachers of Mathematics.
van der Schoot, M., Bakker-Arkema, A. H., Horsley, T. M. y van Lieshout, E. C. D. M. (2009). The consistency effect depends on markedness in less successful but not successful problem solvers: An eye fixation study in primary school children. Contemporary Educational Psychology, 34, 58-66.
van Garderen, D. (2007). Teaching students with LD to use diagrams to solve mathematical word problems. Journal of Learning Disabilities, 40(6), 540-553.
Verschaffel, L., De Corte, E. y Pauwels, A. (1992). Solving compare problems: An eye movement test of Lewis and Mayer's consistency hypothesis. Journal of Educational Psychology, 84, 85-94.
Verdi, M. P., Johnson, J. T., Stock, W. A., Kulhavy, R. W. y Whitman-Ahern, P. (1997). Organized spatial displays and texts. Effects of presentation order and display type on learning outcomes. Journal of Experimental Education, 4, 303-317.
Vergnaud, G. (1983). Multiplicative structures. En R. Lesh y M. Landau (Eds.), Acquisitions of mathematics concepts and processes (pp. 127-174). Londres, Reino Unido: Academy Press.
Vergnaud, G. (1988). Multiplicative structures. En J. Hiebert y M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 141-161). Reston, VA: National Council of Teachers of Mathematics.
Willis, G. B. y Fuson, K. C. (1988). Teaching children to use schematic drawings to solve addition and subtraction word problem. Journal of Educational Psychology, 80(2), 192-201.
Yancey, A. V., Thompson, C. S. y Yancey, J. S. (1989). Children must learn to draw diagrams. Arithmetic Teacher, 36(7), 15-23.