Razonamiento algebraico en educación primariaUn reto para la formación inicial de profesores

  1. Castro Gordillo, Walter Fernando
  2. Diaz Godino, Juan
  3. Rivas Olivo, Mauro A.
Revista:
Unión: revista iberoamericana de educación matemática

ISSN: 1815-0640

Año de publicación: 2011

Número: 25

Páginas: 73-88

Tipo: Artículo

Otras publicaciones en: Unión: revista iberoamericana de educación matemática

Resumen

En este trabajo se realiza un estudio exploratorio sobre las competencias de análisis didáctico de dos grupos de futuros maestros. Se comenta su desempeño en el análisis de dos tareas, en el contexto del diseño de una Unidad Didáctica sobre el razonamiento algebraico elemental. La diversidad exhibida por los dos grupos de futuros maestros, al hacer los análisis epistémicos, se vincula con la necesidad de reforzar el estudio de este tipo de tareas en la formación inicial de maestros.

Referencias bibliográficas

  • Amit M., Neria D. (2008): Rising to the challenge: using generalization in pattern problems to unearth the algebraic skills of talented pre-algebra students. ZDM. The International Journal on Mathematics Education, 40(1), 11-119.
  • Asquith P., Stephens A., Knuth E., Alibali M. (2007):Middle school mathematics teachers’ knowledge of students’ understanding of core algebraic concepts: equal sign and variable. Mathematical Thinking and Learning, 9(3), 249-272.
  • Ball D. L., Thames M. H., Phelps G. (2008): Content Knowledge for Teaching: What Makes It Special?. Journal of Teacher Education,59(5), 389-407.
  • Beker J. R., Rivera F. D. (2008):Generalization in algebra: the foundation of algebraic thinking and reasoning across the grades. ZDM. The International Journal on Mathematics Education, 40(1), 1.
  • Blanton M. L., Kaput J.J. (2005): Characterizing a classroom practice that promotes algebraic reasoning. Journal for Research in Mathematics Education, 36(5), 412-446.
  • Britt M., Irwin K. (2008): Algebraic thinking with and without algebraic representation: a three-year longitudinal study. ZDM. The International Journal on Mathematics Education, 40(1), 39-53.
  • Burkhardt H. (2001): Algebra for all: What does it mean? How are we doing? En: H. Chick, K. Stacey, J. Vincent, J. Vincent (eds.) The future of the teaching and learning of algebra, Vol. 1, pp. 140-146. University of Melbourne, Australia.
  • Carpenter T., Levi L., Franke M.L., Zeringue J.K. (2005):Algebra in elementary school: Developing relational thinking. ZDM. The International Journal on Mathematics Education, 37, 53-59.
  • Carraher D. W., Schlieman A. (2007):Early algebra and algebraic reasoning. En: F. Lester (ed.) Second Handbook of Research on Mathematics Teaching and Learning, Vol. 2, 669-705. Information Age Publishing, Inc. y NCTM, Greenwich.
  • Castro W., Godino J.D. (2009): Cognitive configurations of pre-service teachers when solving an arithmetic-algebraic problem. Proceedings of the Sixth Conference of European Research in Mathematics Education. Université Claude Bernard, Lyon, France. Disponible en Internet: http://www.ugr.es/local/jgodino/indice_eos.htm.
  • Davis R. B. (1989): Theoretical considerations: Research studies in how humans think about algebra. En: S. Wagner, C. Kieran (eds.) Research Issues in the Learning and Teaching of Algebra Vol. 4, 266-274. NCTM y Laurence Erlbaum Associates, Reston, VA.
  • Derry S. J., Wilsman M. J., Hackbarth A. J. (2007):Using contrasting case activities to deepen teacher understanding of algebraic thinking and teaching. Mathematical Thinking and Learning, 9(3), 305-329.
  • Filloy E.; Rojano T., Puig L..(2008). Educational Algebra: A theoretical and Empirical Approach (Vol. 43): Springer.
  • Fong N. S. (2004):Developing algebraic thinking in early grades: A case study of the Singapore primary mathematics curriculum. The Mathematics Educator, 8(1), 39-59.
  • Fujii T., Stephens M. (2001):Fostering an understanding of algebraic generalisation through numerical expressions: The role of quasi-variables. En: H. L. Chick, K. Stacey, J. Vincent, J. Vincent (eds.) Proceedings of the 12th ICMI Study Conference. The Future of the Teaching and Learning of Algebra, Vol. 1, 258-264. University of Melbourne, Melbourne.
  • Godino J. D. (2009):Categorías de análisis de los conocimientos del profesor de matemáticas. UNIÓN Revista Iberoamericana de Educación Matemática, 20, 13-31.
  • Godino J. D., Batanero C., Font V. (2007):The onto-semiotic approach to research in mathematics education. ZDMThe International Journal on Mathematics Education, 39(1-2), 127-135. [Versión ampliada en español: Un enfoque ontosemiótico del conocimiento y la instrucción matemática. Disponible en Internet: http://www.ugr.es/local/jgodino/indice_eos.htm]
  • Godino J. D., Rivas M., Castro W. F., Konic P. (2008):Desarrollo de competencias para el análisis didáctico del profesor de matemáticas. Actas de las VI Jornadas de Educación Matemática Región de Murcia. Centro de Profesores y Recursos. Murcia. Disponible en Internet: http://www.ugr.es/local/jgodino/indice_eos.htm .
  • Hill H. C., Ball D.L., Schilling S.G. (2008):Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers' topic-specific knowledge of students. Journal for Research in Mathematics Education,39, 372-400.
  • Jaworski B. (2005):Tools and tasks for learning and meta-learning. Journal of Mathematics Teacher Education, 8, 359-361.
  • Kaput J. J. (2000):Transforming algebra from an engine of inequity to an engine of mathematical power by "algebrafying" the K–12 curriculum. En: National Research Council (ed.) The nature and role of algebra in the K–14 curriculum: Proceedings of a National Symposium. National Academy Press, Washington, DC. Disponible en http://eric.ed.gov/ (Eric # ED441664).
  • Kieran C. (1996):The changing face of school algebra. En B. Hodgson, C. Alsina, J. Alvarez, C. Laborde, A. Pérez (eds.) 8vo Congreso Internacional de Educación Matemática: Selección de conferencias, 271-290. Sociedad Andaluza de Educación Matemática “Thales”, Sevilla, España.
  • MacGregor M., Price E. (1999):An exploration of aspects of language proficiency and algebra learning. Journal for Research in Mathematics Education, 30(4), 449-467.
  • National Council of Teachers of Mathematics (2000): Principles and standards for school mathematics. NCTM, Reston, VA.
  • Radford L. (2006):The anthropology of meaning. Educational Studies in Mathematics, 61(1-2), 39-65.
  • Schoenfeld A. H., Kilpatrick J. (2008):Towards a theory of proficiency in teaching mathematics. En: D. Tirosh, T. Wood (eds.) Tools and Processes in Mathematics Teacher Education, 321-354. Sense Publishers, Rotterdam.
  • Shulman L. S. (1986):Those who understand: Knowledge growth in teaching.Educational Researcher,15(2), 4-14.
  • Stephens A. C. (2006):Equivalence and relational thinking: Preservice elementary teachers’ awareness of opportunities and misconceptions. Journal of Mathematics Teacher Education, 9, 249-278.
  • Stump S. L., Bishop J. (2002): Preservice elementary and middle school teachers’ conceptions of algebra revealed through the use of exemplary curriculum materials. En: D. S. Mewborn, P. Sztajn, D. Y. White, H. G. Wiegel, R. L. Bryant, K. Nooney (eds.) Proceedings of the Twenty-Fourth annual meeting of the International Group for the Psychology of Mathematics Education, 1903-1914, PME, Columbus, OH.
  • Van Dooren W., Verschaffel L., Onghema P. (2003): Pre-service teachers’ preferred strategies for solving arithmetic and algebra word problems. Journal of Mathematics Teacher Education, 6, 27-52.
  • Vergnaud G. (1988): Long terme et court terme dans l’apprentissage de l'algèbre. En: C. Laborde, N. Balacheff (eds.) Actes du Premier Colloque Franco-Allemand de Didactique des Mathématiques et de l’informatique, 189-199, La Pensée Sauvage, Grenoble, Paris.
  • Watanabe T. (2008): Algebra in elementary school: A Japanese perspective. En: C. E. Greenes, R. Rubenstein (eds.) Algebra and Algebraic Thinking in School Mathematics, 183-193. National Council of Teachers of Mathematics, Reston, VA.
  • Wubbels T., Korthagen F., Broekman H. (1997):Preparing teachers for realistic mathematics education. Educational Studies in Mathematics, 32, 1-28.