Errores cometidos por los candidatos a maestros al resolver problemas matemáticos
Tipo de documento
Autores
Lista de autores
Hernández, Omar y Villafañe, Wanda
Resumen
Se presentan los resultados de un estudio fenomenológico sobre la solución de problemas matemáticos. Participaron ocho estudiantes de educación, seis con especialidad en la enseñanza de las matemáticas a nivel elemental (grados 4 a 6) y dos cuya especialidad era educación secundaria en matemáticas (grados 7 a 12). Se realizaron entrevistas extensas con el objetivo de determinar sus creencias sobre los problemas matemáticos y la forma como los resuelven. También participaron en sesiones de solución de problemas con pensamiento en voz alta y entrevistas retrospectivas con el objetivo de determinar el tipo de representación que realizaban, las estrategias que utilizaban para resolverlos y los procesos de autorregulación que exhibían. El uso de estas técnicas permitió contrastar las creencias de las participantes con su ejecución. Se describen y analizan los errores más frecuentes cometidos por los estudiantes al resolver los problemas presentados.
Fecha
2009
Tipo de fecha
Estado publicación
Términos clave
Enfoque
Nivel educativo
Educación infantil, preescolar (0 a 6 años) | Educación primaria, escuela elemental (6 a 12 años) | Educación superior, formación de pregrado, formación de grado
Idioma
Revisado por pares
Formato del archivo
Referencias
Ball, D. L. (1988). Understanding to teach mathematics. For the learning of mathematics, 8(1), 40 – 48. Ball, D. L. (1990). The mathematical understandings that prospective teachers bring to teacher education. The Elementary School Journal, 90, 449 – 467. Cadenas, R. (2007). Carencias, dificultades y errores en los conocimientos matemáticos en alumnos del primer semestre de la escuela de educación de la Universidad de los Andes. ORBIS, Revista Científica Ciencias Humanas, 2 (6), 68 – 84. Chapman, O. (2005). Constructing pedagogical knowledge of problem solving: Preservice mathematics teacher. En H. L. Chick, y J. L. Vincent (Eds.), Proceedings of the 29th conference of the international group for the psychology of mathematics education: Vol. 2 (pp.225 – 232). Melbourne: PME. Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). categorization and representation of physics problems by experts and novices. Cognitive Science, 5, 121-152. Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers’ practices. educational Studies in Mathematics, 52, 243 – 270. D’Amore, B. (2006). Didáctica de la matemática. Bogotá: Cooperativa Editorial Magisterio. De Corte, E., Greer, B., & Verschaffel, L. (1996). Mathematics teaching and learning. In D. C. Berliner, & R. C. Calfee (Eds.), Handbook of educational psychology (pp. 491-549). New York: Macmillan. Departamento de Educación (1996). Marco curricular del programa de matemáticas. San Juan, P. R.: Autor. Departamento de Educación de Puerto Rico (2000). Estándares: Programa de matemáticas. San Juan, PR: Autor. Departamento de Educación (2003). Marco curricular del programa de matemáticas. San Juan, P. R.: Autor. Departamento de Educación (2007). Estándares de contenido y expectativas de grado. San Juan, P. R.: Autor English, L. D., & Halford, G. S. (1995). Mathematics education: Models and processes. Mahwah, N.J.: Lawrence Erlbaum Associates. Feiman-Memser, S., McDiarmid, W., Melnick, S., and Parker, M. (1987). Changing beginning teachers’conceptions: a description of an introductory teacher education course. Paper presented at the annual meeting of the American Education Research Association. Washington: DC. Fisher, L. C. (1988). Strategies used by secondary mathematics teachers to solve proportion problems. Journal for Research in Mathematics Education, 19 (2), 157-168. Flavell, J. H. (1976). Metacognitive aspects of problem solving. In L. Resnick (Ed.), The nature of intelligence (pp. 231-236). Hillsdale, NJ: Erlbaum. Garofalo, J., & Lester, F. K. (1985). Metacognition, cognitive monitoring, and mathematical performance. Journal for Research in Mathematics Education, 16 (3), 163-176. Ghatala, E. S. (1986). Strategy-monitoring training enables young learners to select effective strategies. Educational Psychologist, 21 (1&2), 43-54. Gholson, B., Morgan, D., Dattel, A. R., & Pierce, K. A. (1990). The development of analogical problem solving: Strategic processes in schema acquisition and transfer. In D. F.Bjorklund (Ed.), Children’s strategies: Contemporary views of cognitive development (p. 269-308). Hillsdale, NJ: Lawrence Erlbaum Associates. Gick, M. L. (1986). Problem-solving strategies. Educational Psychologist, 21 (1&2), 99-120. Greeno, J. G., Collins, A. M.,, & Resnick, L. B. (1996). Cognition and learning. In D. C. Berliner, & R. C. Calfee (Eds.), Handbook of educational psychology (pp. 15-46). New York: Macmillan Library Reference. Goos, M., & Galbraith, P. (1996). Do it this way! ,etacognitive strategies in collaborative mathematical problem solving. Educational Studies in Mathematics, 30, 229-260. Green, T. F. (1971). The activities of teaching. New York, NY: McGraw-Hill Book, Co. Grows, D., & Good, T. L. (2002). Issues in problem-solving instruction. In D. L. Chambers (Ed.), Putting research into practice in the elementary grades: Readings from journals of the National Council of Teachers of Mathematics (pp. 60-62). Reston, VA: NCTM. Hernández Rodríguez, O. (2002). Procesos cognoscitivos y metacognoscitivos en estudiantes universitarios puertorriqueños en la solución de problema matemáticos no típicos. Disertación doctoral. Janvier, C., Girandon, C., & Morand, J. C. (1993). Mathematical symbols and representation. In P. S. Wilson (Ed.), Research ideas for the classroom. New York: Macmillan Publishing Company. Krulik, S. (Ed.). (1980). Problem solving in school mathematics. Reston, VA: NCTM. Lampert, M. (1990). When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 25 (1), 29-63. Leikin, R. (2003). Problem-solving preferences of mathematics teachers: Focusing on symmetry. Journal of Mathematics Teacher Education, 6, 297–329. Leonard, J., y Joergensen, P. (2002). Empowering all elementary preservice teachers to teach children mathematics. (ERIC Document Reproduction Service No. ED469957). Lester, F. K. Jr. (1994). Musings about mathematical problem-solving research: 1970-1994. Journal for Research in Mathematics Education, 25 (6), 660-675. Liljedahl, P. (2005). Aha!: The effect and affect of mathematics discovery on undergraduate mathematics students. International Journal of Mathematics Education Science and Technology, 36(2/3), 219-236. Liljedahl, P., Rolka, K., and Rösken, B. (2007). Affecting affect: The reeducation of preservice tearchers’ beliefs about mathematics and mathematics learning and teaching. In G. W. Martin, M. E. Strutchens, and P. C. Elliott (Eds.), The learning of mathematics, (pp. 319-330). Reston, VA:NCTM. Maqsud, M. (1997). Effects of metacognitive skills and nonverbal ability on academic achievement of high school pupils. Educational Psychology, 17 (4), 387-398. Mewborn, D. S., & Cross, D. I. (2007). Mathematics teachers’ beliefs about mathematics and links to students’ learning. In W. G. Martin, M. E. Strutchens, & P. C. Elliot (Eds.), The learning of mathematics (pp. 259-269). Reston, VA: NCTM. National Council of Teachers of Mathematics. (1980). An agenda for action: Recommendations for school mathematics of the 1980's. Reston, VA: Author. National Council of Teachers of Mathematics. (1989). Curriculum and evaluation: Standards for school mathematics. Reston, VA: Author. National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author. Novick, L. R. (1988). Analogical transfer, problem similarity, and expertise. Journal of Experimental Psychology: Learning, Memory and Cognition, 14, 510-520. Novick, L. R. (1992). The role of expertise in solving arithmetic and algebra word problems by analogy. In J. I. D. Campbell (Ed.), The nature and origins of mathematical skills (pp. 155-188).Amsterdam: Elsevier. Santos Trigo, M. L. (1995). ¿Qué significa el aprender matemáticas? Una experiencia con estudiantes de cálculo. Educación Matemática, 7 (1), 46-61. Schoenfeld, A. H. (1985). Mathematical problem solving. New York: Academic Press. Schoenfeld, A. H. (1987). What’s all the fuss about metacognition? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 189-215). New Jersey, Erlbaum. Schoenfeld, A. H. (1989). Explorations of students’ mathematical belief and behavior. Journal for Research in Mathematics Education, 20 (4), 338-355. 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). NY:Macmillan. Schoenfeld, A. H., & Herrmann, D. J. (1982). Problem perception and knowledge structure in expert and novice mathematical problem solvers. Journal of Experimental Psychology: Learning, Memory and Cognition, 8, 484-494. Silver, E. A. (1981). Recall of mathematical problem Formulation: Solving related problems. Journal of Research in Mathematics Education, 12(1), 54-64. Swanson, H. L. (1990). Influence of metacognitive knowledge and aptitude on problem solving. Journal of Educational Psychology, 82 (2), 306-314. Swanson, H. L. (1992). The relationship between metacognition and problem solving in gifted children. Roeper Review, 15 (1), 43-49. Törner, G., & Grigutsch, S. (1994). Mathematics Weltbilder bei studienanfanger eine erhebung. Journal fur Mathematikdidaktik, 15(3/4), 211-252. Van Dooren, W., Verschaffel, L., & Onghena, P. (2003). Preservice teachers' preferred strategies for solving Arithmetic and Algebra word problems. Journal of Mathematics Teachers Education, 6 (1), 27 - 52.