El conocimiento matemático y la mirada profesional de estudiantes para maestro en el contexto de la generalización de patrones. Caracterización de perfiles

  1. Zapatera Llinares, Alberto 1
  2. Callejo de la Vega, María Luz 2
  1. 1 Universidad CEU Cardenal Herrera (Elche)
  2. 2 Universitat d'Alacant
    info

    Universitat d'Alacant

    Alicante, España

    ROR https://ror.org/05t8bcz72

Journal:
Revista complutense de educación

ISSN: 1130-2496 1988-2793

Year of publication: 2018

Volume: 29

Issue: 4

Pages: 1217-1235

Type: Article

DOI: 10.5209/RCED.55070 DIALNET GOOGLE SCHOLAR lock_openOpen access editor

More publications in: Revista complutense de educación

Abstract

The aim of this research is to study the relationship between mathematical knowledge and teacher competence of professional noticing of children’s mathematical thinking in the context of generalization of patterns. For this purpose, 40 prospective teachers (PPT) were asked to solve a problema of generalization of patterns and to describe and interpret the answers of three elementary students to the same problem. The resolution of the problem allowed to determinate the degree of knowledge of the PPT and the ability to interpret the students’ comprehension from the identification of the significant mathematical elements in the students’ answers allowed to determine the degree of competence. From the analysis of the skills to identify and interpret were generated descriptors to characterize four profiles in the development of the competence, which were later refined by incorporating knowledge descriptors. The research evidenced that the PPT with low level of knowledge, and some with a sufficient level of knowledge, were not able to interpret the comprehension of the elementary students, therefore, although the mathematical knowledge of the content is necessary to have a professional noticing, this knowledge does not guarantee the teaching competence. The materials used and the inferred trajectory can be used as a reference to compose teaching modules about the competence of professional noticing of children’s mathematical thinking in the context of generalization of patterns.

Funding information

Esta investigación ha recibido el apoyo en parte del Proyecto I+D+i, EDU2014-54526— R y de EDU2017-87411— R, financiados por el Ministerio de Economía y Competitividad (MINECO), Gobierno de España.

Funders

  • MINECO Spain
    • EDU2014-54526— R
    • EDU2017-87411— R

Bibliographic References

  • Ball, D.L., Thames, M.H. y Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407.
  • Bartell, T.G., Webel, C., Bowen, B. y Dyson, N. (2013). Prospective teacher learning: recognizing evidence of conceptual understanding. Journal of Mathematics Teacher Education, 16, 57-79.
  • Callejo, M.L. y Zapatera, A. (2016). Prospective primary teachers ’noticing of students’ understanding of pattern generalization Journal of Mathematics Teacher Education. DOI 10.1007/s10857-016-9343-1
  • Carpenter, T.P., Franke, M. L., y Levi, L. (2003).Thinking mathematically: integrating arithmetic and algebra in elementary school. Portsmouth: Heinemann.
  • Carraher, D.W., Martinez, M.V. y Schliemann, A.D. (2008). Early algebra and mathematical generalization. ZDM. Mathematics Education, 40, 3-22.
  • Dreyfus, T (1991). Advanced mathematical thinking process. Mathematics Education Library, 11, 25-41.
  • Fernández, C., Valls, J. y Llinares, S. (2011). El desarrollo de un esquema para caracterizar la competencia docente mirar con sentido el pensamiento matemático de los estudiantes. En M. Marín, G. Fernández, L. Blanco y M. Palarea (Eds), Investigación en Educación Matemática XV (pp. 351-360). Ciudad Real: SEIEM.
  • Jacobs, V.R., Lamb. L.C., y Philipp, R.A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169-202.
  • Mason, J. (2002). Researching your own practice: The discipline of noticing. London: Routledge Falmer.
  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
  • Pólya, G. (1954). Patterns of Plausible Inference. Princeton: Princeton University Press.
  • Radford, L. (2008). Iconicity and contraction: a semiotic investigation of forms of algebraic generalizations of patterns in different contexts. The International Journal on Mathematics Education (ZDM), 40(1), 83-96.
  • Radford, L. (2014). The progressive development of early embodied algebraic thinking. Mathematics Education Research Journal, 26, 257-277.
  • Rivera, F.D. (2010). Second grade students’ preinstructional competence in patterning activity. En Pinto, M.F. y Kawasaki, T.F. (Eds.). Proceedings of the 34th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, pp. 81-88. Belo Horizonte, Brazil: PME.
  • Sánchez-Matamoros, G., Fernández, C., Llinares, S. y Valls, J. (2013). El desarrollo de la competencia de estudiantes para profesor de matemáticas de educación secundaria en identificar la comprensión de la derivada en estudiantes de bachillerato. En A. Berciano, G. Gutiérrez, A. Estepa y N. Climent (Eds.), Investigación en Educación Matemática XVII, 501 — 509. Bilbao: SEIEM.
  • Sánchez-Matamoros, G., Fernández, C. y Llinares, S. (2014). Developing pre-service teachers’ noticing of students’ understanding of the derívate concept. International Journal of Science and Mathematics Education, DOI 10.1007/s10763-014-9544-y.
  • Schack E.O., Fisher M.H., Thomas J.N, Eisenhardt S., Tassell J. y Yoder M. (2013). Prospective elementary school teachers’ professional noticing of children’s esarly numeracy. Journal of Mathematics Teacher Education, 16, 379-397.
  • Sherin, M.G., Jacobs, V.R. y Philipp, R.A. (Eds.). (2011). Mathematics teacher noticing:Seeing through teachers’ eyes. New York: Routledge.
  • Shulman, L.S. (1986). Those who understand.Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
  • Star, J.R. y Strickland, S.K. (2007). Learning to observe: Using video to improve preservice teachers’ ability to notice. Journal of Mathematics Teacher Education, 11, 107-125.
  • van Es, E.A. y Sherin, M.G. (2002). Learning to Notice: Scaffolding new teachers’ interpretations of classroom interactions. Journal of Technology and Teacher Education, 10(4), 571-596.
  • Warren, E. (2005). Young children’s ability to generalise the pattern rule for growing patterns. En Chick, H.L. y Vincent, J.L. (Eds.).Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, pp. 305-312. Melbourne: PME.
  • Wilson, P.H., Mojica, G.F. y Confrey, J. (2013). Learning trajectories in teacher education: Supporting teachers’ understandings of students’ mathematical thinking. Journal of Mathematical Behaviour, 32, 103-121.
  • Zapatera, A. y Callejo, M. L. (2013). Preservice primary teacher’s noticing of students’ generalization process En Lindmeier, A. M. y Heinze, A. (Eds.). Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, pp. 425-432. Kiel, Germany: PME.
  • Zapatera, A. (2015). La competencia mirar con sentido de estudiantes para maestro (EPM) analizando el proceso de generalización en alumnos de Educación Primaria. Tesis doctoral. Universidad de Alicante.