Ingeniería didáctica para desarrollar el sentido algebraico de maestros en formación

  1. Lilia Aké 1
  2. Juan D. Godino 1
  3. Teresa Fernández 2
  4. Margherita Gonzato 1
  1. 1 Universidad de Granada (España)
  2. 2 Universidad de Santiago de Compostela (España)
Journal:
Avances de investigación en educación matemática

ISSN: 2254-4313

Year of publication: 2014

Issue: 5

Pages: 25-48

Type: Article

DOI: 10.35763/AIEM.V1I5.70 DIALNET GOOGLE SCHOLAR lock_openDialnet editor

More publications in: Avances de investigación en educación matemática

Abstract

In this paper we analyze a formative experience directed to prospective primary school teachers, which was aimed at developing their competence to discriminate algebraic objects and the different algebraization levels of school mathematical activity. The experience was performed in a Teaching and Learning primary school mathematics course, where elementary algebraic reasoning was a transversal topic for the remaining mathematical themes. The methodology was based on didactic engineering, which was understood in a generalized sense and was based on the onto-semiotic approach to mathematical knowledge and instruction. The activities designed to develop elementary algebraic reasoning were carried out by 56 students. Our preliminary analysis suggest the relevance of this content for teacher education, although the recognition of algebraic object and the assignment of algebraization levels were difficult to achieve with the resources allocated in the implemented training process.

Bibliographic References

  • Aké, L. (2013). Evaluación y desarrollo del razonamiento algebraico elemental en maestros en formación. Tesis doctoral. Departamento de Didáctica de la Matemática. Universidad de Granada.
  • Aké, L., Castro, W. F., & Godino, J. D. (2011). Conocimiento didáctico-matemático sobre el razonamiento algebraico elemental: un estudio exploratorio. En M. Marín, G. Fernández, L. Blanco y M. Palarea (Eds), Investigación en Educación Matemática. XV Simposio de la SEIEM (pp. 227-236). Ciudad Real.
  • Aké, L., Godino, J. D., & Gonzato, M. (2013). Contenidos y actividades algebraicas en Educación Primaria. UNION, Revista Iberoamericana de Educación Matemática, 33, 39- 52.
  • Artigue, M. (1989). Ingénierie didactique. Recherches en Didactique des Mathématiques, 9(3), 281-308.
  • Artigue, M. (2011). L'ingénierie didactique comme thème d'étude. En C. Margolinas, M. Abboud-Blanchard, L. Bueno-Ravel, N. Douek, A. Fluckiger, P. Gibel, F. Vandebrouck & F. Wozniak (Eds.), En amont et en aval des ingénieries didactiques (pp. 15-25). Grenoble: La Pensée Sauvage.
  • Blanton, M. L., & Kaput, J. J. (2003). Developing elementary teachers’ “algebra eyes and ears: Understanding characteristics of professional development that promote generative and self-Sustaining change in teacher practice”. Teaching Children Mathematics, 10, 70- 77.
  • Bolea, P. (2003). El proceso de algebrización de organizaciones matemáticas escolares. Monografía del Seminario Matemático García de Galdeano, 29. Zaragoza: Departamento de Matemáticas de la Universidad de Zaragoza.
  • Cai, J., & Knuth, E. (2011). Early algebraization. A global dialogue from multiple perspectives. Berlin: Springer-Verlag.
  • 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.
  • Chevallard, Y., & Bosch, M. (2012). L’algèbre entre effacement et réaffirmation. Aspects critiques de l’offre scolaire d’algèbre. En L. Coulange, J.-P. Drouhard, J. L. Dorier, & A. Robert (Coord.), Enseignement de l’algèbre élémentaire. Bilan et perspectives. Recherches en Didactique des Mathématiques, special issue (pp. 13-33).
  • Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32, 1, 9–13.
  • Cobb, P., & Gravemeijer, K. (2008). Experimenting to support and understand learning processes. En A. E. Kelly, R.A. Lesh, y J. Y. Baek (Eds.), Handbook of design research methods in education. Innovations in science, technology, engineering and mathematics learning and teaching (pp. 68-95). Mahwah, NJ: Lawrence Erlbaum Associates.
  • Filloy, E., Puig, L., & Rojano, T. (2008). Educational algebra. A theoretical and empirical approach. New York: Springer.
  • Godino, J. D. (2002). Un enfoque ontológico y semiótico de la cognición matemática. Recherches en Didactiques des Mathematiques, 22 (2/3), 237-284.
  • 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. (2011). Indicadores de la idoneidad didáctica de procesos de enseñanza y aprendizaje de las matemáticas. XIII CIAEM-IACME, Recife, Brasil.
  • Godino, J. D., Aké, L., Gonzato, M., & Wilhelmi, M. R. (2014). Niveles de algebrización de la actividad matemática escolar. Implicaciones para la formación de maestros. Enseñanza de las Ciencias, 32.1, 199-219.
  • Godino, J. D. Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM. The International Journal on Mathematics Education, 39 (1-2), 127-135.
  • Godino, J. D., Batanero, C., Contreras, A., Estepa, A., Lacasta, E. y Wilhelmi, M. (2013). Didactic engineering as design-based research in mathematics education. En B. Ubuz, Ç. Haser, & M. A. Mariotti (Eds), Proceedings of the Eight Congress of the European Society for Research in Mathematics Education (pp. 2810 2819). Ankara, Turkey: Middle East Technical University.
  • Godino, J. D., Castro, W., Aké, L., & Wilhelmi, M. D. (2012). Naturaleza del razonamiento algebraico elemental. Boletim de Educação Matemática BOLEMA, 26 (42B), 483-511.
  • Godino, J. D., Contreras, A., & Font, V. (2006). Análisis de procesos de instrucción basado en el enfoque ontológico-semiótico de la cognición matemática. Recherches en Didactiques des Mathematiques, 26 (1), 39-88.
  • Godino, J. D., Font, V., Wilhelmi, M. R., & De Castro, C. de (2009). Aproximación a la dimensión normativa en Didáctica de la Matemática desde un enfoque ontosemiótico. Enseñanza de las Ciencias, 27(1), 59–76.
  • Kaput, J. (2000). Transforming algebra from an engine of inequity for an engine of mathematical power by "algebrafying" the K-12 curriculum. Dartmouth, MA: National Center of Improving Student Learning and Achievement in Mathematics and Science (NCISLA).
  • Kaput, J. (2008). What is algebra? What is algebraic reasoning? En J. Kaput, D. W. Carraher, & M. L. Blanton (Eds), Algebra in the early grades (pp. 5-17). New York: Routledge.
  • Kelly, A. E., Lesh, R. A., & Baek, J. Y. (Eds.) (2008). Handbook of design research in methods in education. Innovations in science, technology, engineering, and mathematics learning and teaching. New York, NY: Routledge.
  • Kieran, C. (1989) A perspective on algebraic thinking. En G. Vergnaud, J. Rogalski & M. Artigue (Eds), Proceedings of the 13th Annual Conference of the International Group for the Psychology of Mathematics Education (PME), Vol. 2, (pp. 163-171). Paris.
  • Kieran, K. (2007). Learning and teaching algebra at the middle school through college levels. Building meaning for symbols and their manipulation. En, F. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (Vol. 2, 707-762). Charlotte, N.C: Information Age Publishing, Inc. y NCTM
  • Molina, M. (2009). Una propuesta de cambio curricular: integración del pensamiento algebraico en educación primaria. PNA, 3(3), 135-156.
  • National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Autor.
  • Radford, L. (2010). Algebraic thinking from a cultural semiotic perspective. Research in Mathematics Education, Vancouver, 12 (1), 1 – 19.
  • Ruiz-Munzón, N., Bosch, M., & Gascón, J. (2011). Un modelo epistemológico de referencia del algebra como instrumento de modelización. En M. Bosch, J. Gascón, A. Ruiz, M. Artaud, A. Bronner, Y. Chevallard, G. Cirade, C. Ladage & M. Larguier (Eds.), Un panorama de la TAD (pp. 743-765). CRM Documents, vol. 10. Bellaterra (Barcelona): Centre de Recerca Matemàtica.
  • Schliemann, A. D., Carraher, D., & Brizuela, B. M. (2007). Bringing out the algebraic character of arithmetic: from children's ideas to classroom practice. Mahwah, NJ: Lawrence Erlbaum and Associates.
  • Stephens, A. C. (2006). Equivalence and relational thinking: Preservice elementary teachers’ awareness of opportunities and misconceptions. Journal of Mathematics Teacher Education, 9(3), 249-278.
  • Stephens, A. C. (2008). What “counts” as algebra in the eyes of preservice elementary teachers? The Journal of Mathematical Behavior, 27(1), 33-47.
  • Zazkis, R., & Liljedahl, P. (2002). Generalization of patterns: The tension between algebraic thinking and algebraic notation. Educational Studies in Mathematics, 49(3), 379-402.