Conocimiento especializado del profesor de matemáticas sobre la división de fracciones en el contexto de la formulación de problemas
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Formulación del Problema, Conocimientos Docentes Especializados, División de FraccionesResumen
Este trabajo tiene como objetivo presentar los conocimientos especializados revelados por profesores de matemáticas a través de una tarea formativa relativa a la formulación de problemas de división de fracciones. El estudio trata de una investigación cualitativa combinada con un estudio de caso. Los análisis se basaron en las producciones de los profesores y en discusiones plenarias durante la formación. Los resultados muestran que los docentes tienen conocimientos respecto al significado de compartir, resolución de problemas mediante el algoritmo inversión-multiplicación y representación continua en forma rectangular. Sin embargo, los docentes presentan dificultades en cuanto al sentido de la medición de la división, la representación continua y discreta y la formulación de problemas, especialmente cuando el divisor y el dividendo son fracciones. Está claro que formular problemas contribuye al aprendizaje de la división de fracciones, ya que ayuda a comprender conceptos matemáticos y resolver problemas.
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Abu-Elwan, R. (2002). Effectiveness of problem posing strategies on prospective mathematics teachers’ problem-solving performance. Journal of Science and Mathematics Education in Southeast Asia, 25(1), 56-69.
Ball, D. (1988) The subject matter preparation of prospective mathematics teachers: Challenging the myths. The National Center for Research on Teacher Education.
Ball, D. L. (1990). Prospective elementary and secondary teachers’ understanding of division. Journal for Research in Mathematics Education, 21(2), 132-144.
Ball, D.L. & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.), Multiple Perspectives on Teaching and Learning (pp. 83-104). Springer.
Ball, D.L., Lubienski, S. & Mewborn, D. S. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In V. Richardson (Ed.), Handbook of Research on Teaching (pp. 433-456). American Educational Research Association.
Behr, M. J., Harel, G., Post, T. R. & Lesh, R. (1992). Rational number, ratio, and proportion. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 296-333). Macmillan.
Borko, H., Eisenhart, M., Brown, C. A., Underhill, R. G., Jones, D., & Agard, P. C. (1992). Learning to teach hard mathematics: Do novice teachers and their instructors give up too easily? Journal for Research in Mathematics Education, 23, 194-222.
Carrillo, J., Climent, N., Montes, M., Contreras, L. C., Flores-Medrano, E., Escudero-Àvila, D.; ... & Muñoz-Catalán, M. C. (2018) The mathematics teacher’s Specialized knowledge (MTSK) model. Research in Mathematics Education, 20(3), 236-253.
Climent, N. (2002). El desarrollo profesional del maestro de primaria respecto de la enseñanza de la matemática. [Tese de Doutorado]. Universidad de Huelva.
Dehaene, S. (1997). The number sense. Oxford University Press.
DeWolf, M., Grounds, M. A., Bassok, M., & Holyoak, K. J. (2014). Magnitude comparison with different types of rational numbers. Journal of Experimental Psychology: Human Perception and Performance, 40, 71-82.
Ervin, H.K. (2017). Fraction multiplication and division models: A practitioner reference paper. International Journal of Research in Education and Science, 3(1), 258-279.
Greer, B. (1992). Multiplication and division as models of situations. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 276-295). Macmillan.
Fazio, L., & Siegler, R. (2011). Educational practices series 22: teaching fractions. Unesco. http://www.iaoed.org/downloads/EdPractices_22.pdf.
Fischbein, E.; Deri, M., Nello, M. S., & Marino, M. S.(1985). The role of implicit models in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 16(1), 3-17.
Isik, C., & Kar, T. (2012). An error analysis in division problems in fractions posed by preservice elementary mathematics teachers. Educational Sciences: Theory & Practice, 12(3), 2289-2309.
Iskenderoglu, A. T. (2018). Fraction multiplication and division word problems posed by different years of pre-service elementary Mathematics teachers. European Journal of Educational Research, 7(2), 373-385.
Izsák, A. (2003). “We want a statement that is always true”. Criteria for good algebraic representations in the development of modeling knowledge. Journal for Reaserch in Mathematics Education, 34(3), 191-227.
Janvier, C. (1987). Representation and understanding: The notion of function as an example. In JANVIER, C. (Ed.). Problems of representation in the teaching and learning of mathematics. (pp. 67-71) Lawrence Erlbaum Associates Inc.
Kilic, C. (2015). Analyzing pre-service primary teachers’ fraction knowledge structures through problem posing. Eurasia Journal of Mathematics, Science & Technology Education, 11(6), 1603-1619.
Lamon, S. (2007). Rational numbers and proportional reasoning: Towards a theoretical framework for research. In F. K. Lester Jr (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629-667). National Council of Teachers of Mathematics.
Lesser, L. M., & Tchoshanov, M. A. (2005, 2, October). The effect of representation and representational sequence on students’ understanding.27º Annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Roanoke.
Lee, S. J., Brown, R. E., & Orrill, C. H. (2011). Mathematics teachers’ reasoning about fractions and decimals using drawn representations. Mathematical Thinking and Learning, 13(3), 198-220.
Lo, J. J., & Luo, F. (2012). Prospective elementary teachers’ knowledge of fraction division. Journal of Mathematics Teacher Education, 15(6), 481-500.
Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Earlbaum.
National Council of Teachers of Mathematics. (2000). Principles and standards of school mathematics.
Ribeiro, M., Almeida, A. & Mellone, M. (2021). Conceitualizando Tarefas Formativas para Desenvolver as Especificidades do Conhecimento Interpretativo e Especializado do Professor. Perspectivas da Educação Matemática,14(35), 1-32.
Rizvi, N. F., & Lawson, M. J. (2007). Prospective teachers’ knowledge: Concept of division. International Education Journal, 8(2), 377-392.
Rojas, N., & Moriel-Junior, J. G. (2016). Fracciones y decimales. En J. Carrillo, L. C. Contreras, N. Climent, M. Montes, D. I. Escudero, E. Flores, y M. C. Muñoz-Catalán (Eds.), Didáctica de las Matemáticas para maestros de Educación Primária (pp. 75-98). Ediciones Paraninfo, S.A.
Stake, R. E. (1995). The art of case study research. Sage Publications, Inc.
Silva, F. A. F. ., Vidal, F. A., & Carvalho Filho, E. A. de . (2023). Análise da compreensão de professores de Matemática sobre as características visuais de figuras geométricas para o estabelecimento da relação parte-todo dos números racionais. Revista Internacional De Pesquisa Em Educação Matemática, 13(2), 1-16. https://doi.org/10.37001/ripem.v13i2.3728
Silver, E. A. (1994). On mathematical problem posing. For the Learning of mathematics, 14, 19-28.
Simon, M. A. (1993). Prospective Elementary Teachers’ Knowledge of Division. Journal for Research in Mathematics Education, 24(3), 233-254.
Tirosh, D., & Graeber, A. (1990a). Evoking cognitive conflict to explore preservice teachers’ thinking about division. Journal for Research in Mathematics Education, 21, 98-108.
Tirosh, D., & Graeber, A. (1990b). Inconsistencies in preserving elementary teachers’ beliefs about multiplication and division. Focus on Learning Problems in Mathematics, 20, 95-102.
Tirosh, D. (2000). Enhancing prospective teachers’ knowledge of children’s conceptions: The case of division of fractions. Journal for Research of Mathematics Education, 31(1), p. 5-25.
Toluk-Ucar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25(1), 166-175.
Utley, J., & Redmond, A. (2008, March). Prospective Elementary Teachers’ Attitudes Towards and Knowledge of the Division of Fractions. [Paper presentation]. Annual meeting of the Research Council on Mathematics Learning, Oklahoma City.
Xie, J., & Masingila, J. O. (2017). Examining interactions between problem posing and problem solving with prospective primary teachers: A case of using fractions. Educational Studies in Mathematics, 96:101–118
Zembat, I. O. (2004). Conceptual development of prospective elementary teachers: The case of division of fractions. [Ph.D. dissertation]. The Pennsylvania State University.
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