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Componentes de conocimiento del profesor para la enseñanza de la resolución de problemas en educación primaria

    1. [1] Universidad de Granada

      Universidad de Granada

      Granada, España

  • Localización: PNA: Revista de investigación en didáctica de la matemática, ISSN-e 1887-3987, Vol. 13, Nº. 2, 2019, págs. 104-129
  • Idioma: español
  • DOI: 10.30827/pna.v13i2.7876
  • Títulos paralelos:
    • Teacher knowledge components for teaching problem solving in primary education
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  • Resumen
    • español

      La importancia que presenta la resolución de problemas en la enseñanza y aprendizaje de la matemática es una premisa aceptada en la comunidad de educadores matemáticos. No obstante, los marcos que describen o caracterizan el conocimiento de los profesores sobre las matemáticas escolares han dado poca relevancia a este proceso. Partiendo de revisiones curriculares y teóricas, presentamos una organización del conocimiento del profesor de educación primaria sobre la resolución de problemas de matemáticas. En ella diferenciamos un conocimiento sobre la resolución de problemas del que emergen los componentes relativos al concepto de problema, proceso de resolución y disposición para afrontar un problema; y un conocimiento pedagógico sobre la resolución de problemas en el que distinguimos un componente referido al aprendizaje y otro a la enseñanza. Nuestra reflexión ratifica la idea que la naturaleza distinta de un proceso como la resolución de problemas provoca un conocimiento que los modelos han omitido.Teacher knowledge components for teaching problem solving in primary educationProblem solving is central in teaching and learning of mathematics, an accepted premise in the community of mathematics educators. However, the frameworks that describe or characterize teachers' knowledge have given little relevance to this process. Starting from curricular and theoretical revisions, we present a proposal of organization for the knowledge of primary teacher about problem solving. We differentiate a knowledge of the process from which the components related to the concept of problem, resolution process and disposition to face a problem emerge; and a pedagogical knowledge where we distinguish a component referring to learning and another to the teaching of problem solving. Our reflection confirms the idea that the different nature of a process such as problem solving, causes a knowledge that the models have omitted.doi: 10.30827/pna.v13i2.7876

    • English

      Problem solving is central in teaching and learning of mathematics, an accepted premise in the community of mathematics educators. However, the frameworks that describe or characterize teachers' knowledge have given little relevance to this process. Starting from curricular and theoretical revisions, we present a proposal of organization for the knowledge of primary teacher about problem solving. We differentiate a knowledge of the process from which the components related to the concept of problem, resolution process and disposition to face a problem emerge; and a pedagogical knowledge where we distinguish a component referring to learning and another to the teaching of problem solving. Our reflection confirms the idea that the different nature of a process such as problem solving, causes a knowledge that the models have omitted.

  • Referencias bibliográficas
    • Abrantes, P. (2001). Mathematical competence for all: Options, implications and obstacles. Educational Studies in Mathematics, 47(2), 125-143.
    • Agre, G. P. (1982). The concept of problem. Educational Studies, 13(2), 121-142.
    • Ball, D. L., Hill, H. C. y Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and...
    • Ball, D. L., Thames, M. H. y Phelps, G. (2008). Content knowledge for teaching. What makes it special? Journal of Teacher Education, 59(5),...
    • Borasi, R. (1986). On the nature of problems. Educational Studies in Mathematics, 17(2), 125-141.
    • Bromme, R. (1994). Beyond subject matter: A psychological topology of teachers’ professional knowledge. En R. Biehler, R. Scholz, R. Sträber...
    • Brown, S. I. y Walter, M. I. (2005). The art of problem posing. Mahwah, NJ: Lawrence Erlbaum.
    • Cai, J. (2010). Helping elementary school students become successful mathematical problem solvers. En D. V. Lambdin y F. K. Lester (Eds.),...
    • Carpenter, T. P., Fennema, E., Peterson, P. L. y Carey, D. A. (1988). Teachers’ pedagogical content knowledge of students’ problem solving...
    • Carrillo, J., Climent, N., Montes, M., Contreras, L. C., Flores-Medrano, E., Escudero-Ávila, D., … Muñoz-Catalán, M. C. (2018). The mathematics...
    • Chapman, O. (2015). Mathematics teachers’ knowledge for teaching problem solving. LUMAT, 3(1), 19-36.
    • Charles, R. I., Lester, F. K. y O’Daffer, P. G. (1987). How to evaluate progress in problem solving. Reston, VA: NCTM.
    • Fennema, E. y Franke, M. L. (1992). Teachers’ knowledge and its impact. En D. A. Grows (Ed.), Handbook of research on mathematics teaching...
    • Foong, P. Y. (2002). The role of problems to enhance pedagogical practices in the Singapore. The Mathematics Educator, 6(2), 15-31.
    • Foster, C., Wake, G. y Swan, M. (2014). Mathematical knowledge for teaching probem solving: Lessons from lesson study. En S. Oesterle, P....
    • Garofalo, J. y Lester, F. K. (1985). Metacognition, cognitive monitoring, and mathematical performance. Journal for Research in Mathematics...
    • Goldin, G. A. y McClintock, C. E. (1979). Task variables in mathematical problem solving. Columbus, OH: Information Reference Center (ERIC/IRC),...
    • Grønmo, L. S., Lindquist, M. y Arora, A. (2014). TIMSS advanced 2015 mathematics framework. En I. V. S. Mullis y M. O. Martin (Eds.), TIMSS...
    • Kaur, B. (1997). Difficulties with problem solving in mathematics. The Mathematics Educator, 2(1), 93-112.
    • Kelly, C. A. (2006). Using manipulatives in mathematical problem solving: A performance- based analysis. The Mathematics Enthusiast, 3(2),...
    • Kilpatrick, J. (2016). Reformulating: Approaching mathematical problem solving as inquiry. En P. Felmer, E. Pehkonen y J. Kilpatrick (Eds.),...
    • Kilpatrick, J., Swafford, J. y Findell, B. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
    • Lesh, R., English, L. D., Riggs, C. y Sevis, S. (2013). Problem solving in the primary school (K-2). The Mathematics Enthusiast, 10(1&2),...
    • Lester, F. K. (2013). Thoughts about research on mathematical problem- solving instruction. The Mathematics Enthusiast, 10(1&2), 245-278.
    • Lester, F. K. y Cai, J. (2016). Can mathematical problem solving be taught? Preliminary answers from 30 years of research. En P. Felmer, E....
    • Lester, F. K., Garofalo, J., & Kroll, D. L. (1989). Self-confidence, interest, beliefs, and metacognition: Key influences on problem-solving...
    • Liljedahl, P. (2016). Building thinking classrooms: Conditions for problem-solving. En P. Felmer, E. Pehkonen y J. Kilpatrick (Eds.), Posing...
    • Mason, J. (2016). When is a problem…? “When” is actually the problem! In P. Felmer, E. Pehkonen y J. Kilpatrick (Eds.), Posing and solving...
    • Mayer, R. E. y Wittrock, M. C. (2006). Problem solving. En P. A. Alexander y P. H. Winne (Eds.), Handbook of Educational Psychology (pp. 287-303)....
    • McLeod, D. B. y McLeod, S. H. (2002). Synthesis - Beliefs and mathematics education: Implications for learning, teaching, and research. En...
    • NCTM. (1980). An agenda for action: Recommendations for school mathematics of the l980’s. Reston, VA: Author.
    • NCTM. (2000). Principles and standards for school mathematics. Reston, VA: Author.
    • Nipper, K. y Sztajn, P. (2008). Expanding the instructional triangle: conceptualizing mathematics teacher development. Journal of Mathematics...
    • OECD. (2013). Draft PISA 2015 Mathematics Framework. París, Francia: OECD Publishing.
    • Piñeiro, J. L., Castro, E. y Castro-Rodríguez, E. (2016). Conocimiento profesional para la enseñanza de la resolución de problemas en primaria:...
    • Polya, G. (1981). Cómo plantear y resolver problemas. DF, México: Trillas.
    • Ponte, J. P. y Chapman, O. (2016). Prospective mathematics teacher’s learning and knowledge for teaching. En L. D. English y D. Kirshner (Eds.),...
    • Posamentier, A. S. y Krulik, S. (1998). Problem-solving strategies for efficient and elegant solutions: A resource for the mathematics teacher....
    • Rico, L. (2007). La competencia matemática en PISA. PNA, 1(2), 47-66.
    • Rico, L., Lupiáñez, J. L. y Molina, M. (2013). Análisis didáctico en educación matemática. Metodología de investigación, formación...
    • Rowland, T., Huckstep, P. y Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: The knowledge quartet and the case of...
    • Santos-Trigo, M. y Camacho, M. (2013). Framing the use of technology in problem solving approaches. The Mathematics Enthusiast, 10(1&2),...
    • Schmidt, W. H., McKnight, C. C., Valverde, G. A., Houang, R. T. y Wiley, D. E. (1997). Many visions, many aims. Volume 1. A cross-national...
    • Schoenfeld, A. H. (1985). Mathematical problem solving. Orlando, FL: Academic Press.
    • Schoenfeld, A. H. (1992). Learning to think mathematically: problem solving, metacognition and sense making in mathematics. En D. Grows (Ed.),...
    • Schoenfeld, A. H. (2012). Problematizing the didactic triangle. ZDM, 44(5), 587-599.
    • Schroeder, T. L. y Lester, F. K. (1989). Developing understanding in mathematics via problem solving. In P. R. Trafton y A. P. Shulte (Eds.),...
    • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
    • Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19-28.
    • Smith, R. P. (2003). Representation in school mathematics: Children’s representations of problems. En J. Kilpatrick (Ed.), A research companion...
    • Thames, M. H. y Ball, D. L. (2010). What math knowledge does teaching require? Teaching Children Mathematics, 17(4), 220-229.
    • Wilson, J. W., Fernández, M. L. y Hadaway, N. (1993). Mathematical problem solving. En P. S. Wilson (Ed.), Research ideas for the classroom:...
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