An Example of Connections between the Mathematics Teacher’s Conceptions and Specialised Knowledge

Álvaro Aguilar-González; María Cinta Muñoz-Catalán; José Carrillo

doi:10.29333/ejmste/101598

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Álvaro Aguilar-González ¹ ^* , María Cinta Muñoz-Catalán ², José Carrillo ³

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¹ Universidad de Oviedo, Oviedo, SPAIN
² Universidad de Sevilla, Sevilla, SPAIN
³ Universidad de Huelva, Huelva, SPAIN
^* Corresponding Author

Abstract

The motivation for this study is to understand the professional knowledge that a teacher displays in her classroom when she teaches mathematics classes. To this end, our goal is to describe the possible relationships of the subdomains of Mathematics Teacher’s Specialised Knowledge (MTSK) model and the Conceptions about Mathematics Teaching and Learning (CMTL) that are integrated in it. This article presents a position on professional knowledge, the methodological design used has been an interpretative approach with a case study design of a 5th grade teacher in Primary Education, and some results which exemplify how these relationships have been identified and analyzed, and how they have helped to explain and understand the knowledge that the teacher mobilizes in her classroom. Finally, we express how this study can be used for teacher training in mathematics.

Keywords

mathematics teacher’s specialised knowledged
conceptions about mathematics teaching and learning
teacher’s knowledged
professional knowledge

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

https://doi.org/10.29333/ejmste/101598

EURASIA J Math Sci Tech Ed, 2019 - Volume 15 Issue 2, Article No: em1664

Publication date: 14 Dec 2018

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References

Ball, D. L. (1990). Prospective elementary and secondary teachers’ understanding of division. Journal for Research in Mathematics Education, 21, 132-144. https://doi.org/10.2307/749140.
Ball, D. L., Lubienske, S. T., & Mewborn, D. S. (2001). Research on teaching mathematics: The unsolved problem of teachers’ mathematical knowledge. In V. Richardson (Ed.), Handbook of research on teaching (4th ed.) (pp.433-456). New York: Macmillan.
Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59, 389-407. https://doi.org/10.1177/0022487108324554.
Bassey, M. (1999). Case study research in educational settings. Buckingham: Open University Press.
Blumer, H. (1969). Symbolic Interactionism. Perspective and Method. Englewood Cliffs: N. J. Prentice Hall.
Carrillo, J. (1998). Modos de resolver problemas y concepciones sobre la matemática y su enseñanza. Huelva: University of Huelva Publicaciones.
Carrillo-Yañez, J., Climent, N., Montes, M., Contreras, L. C., Flores-Medrano, E., Escudero-Ávila, E., Vasco, D., Rojas, N., Flores, P., Aguilar-González, Á., Ribeiro M. & Muñoz-Catalán, M. C. (2018): The mathematics teacher’s specialised knowledge (MTSK) model. Research in Mathematics Education, https://doi.org/10.1080/14794802.2018.1479981.
Chinnappan, M., & Lawson, M.J. (2005). A framework for analysis of teachers’ geometric content knowledge and geometric knowledge for teaching. Journal of Mathematics Teacher Education, 8, 197-221. https://doi.org/10.1007/s10857-005-0852-6.
Climent, N. (2005). The professional development of the Primary teacher regarding the teaching of mathematics. A case study (Doctoral dissertation). Michigan: Proquest Michigan University. www.proquest.co.uk.
Conner, A., Edenfield, K. W., Gleason, B. W., & Ersoz, F. (2011). Impact of a content and methods course sequence on prospective secondary mathematics teachers’ beliefs. Journal of Mathematics Teacher Education, 14(6), 483-504. https://doi.org/10.1007/s10857-011-9186-8.
Contreras, L. C. (1999). Concepciones de los profesores sobre la resolución de problema. Huelva: Universidad de Huelva Publicaciones. [Vol. I: 30].
Cooney, T. J., & Shealy, B. E. (1994). Conceptualizing teacher education as field of inquiry: theoretical and practical implications. In J. P. Ponte & J. F. Matos (Eds.) Proceedings of the eighteenth International Conference for PME, Vol II, pp. 225-232. Lisboan.
Davis, B., & Simmt, E. (2006). Mathematics-for-teaching: An ongoing investigation of the mathematics that teachers (need to) know. Educational Studies in Mathematics, 61, 293-319. https://doi.org/10.1007/s10649-006-2372-4.
Ernest, P. (1988). The Epistemological Basis of Qualitative Research in mathematics education: A Postmodern Perspective. In A.R. Teppo (Ed.), Qualitative Research Methods in Mathematics Education, (pp. 22-39). Reston, Va: National Council of teachers of Mathematics.
Even, R., & Tirosh, D. (2008). Teacher knowledge and understanding of students’ mathematical learning and thinking. In L. D. English, M. B. Bussi, G. A. Jones, R. A. Lesh, B. Sriraman, & D. Tirosh (Eds.), Handbook of international research in mathematics education (pp. 202-222). New York: Routledge.
Fennema, E., & Franke, M. L. (1992). Teachers’ knowledge and Its Impact. In D.A. Grouws (Eds.), Handbook of Research on Mathematics Teaching and Learning, (pp. 147-164). Reston, Virginia: NCTM.
Flores, E., Escudero, D.I., & Aguilar, A. (2013). Opportunities offered by some scenarios to show evidence of MTSK. In A. Berciano, G. Gutiérrez, A. Estepa, y N. Climent (Eds.), Investigación en Educación Matemática XVII (pp. 275-282). Bilbao: SEIEM.
Flores-Medrano, E., Escudero-Ávila, D., & Carrillo, J. (2013). A theoretical review of Specialized Content Knowledge. In B. Ubuz, C. Haser, & M.A. Mariotti (Eds.), Proceedings of the CERME 8 (pp. 3055–3064). Antalya, Turkey: METU and ERME.
Gess-Newsome, J. (1999). Secondary teachers’ knowledge and beliefs about subject matter and their impact on instruction. In J. Gess-Newsom & N. G. Lederman (Eds.), Examining pedagogical content knowledge (pp.51-94). The Netherlands: Kluwer Academic Publisher.
Kvale, S. (1996). Interviews: An introduction to qualitative research interviewing. Thousand Oaks: Sage.
Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic Inquiry. Beverly Hills, Ca: Sage.
Maasepp, B., & Bobis, J. (2015). Prospective Primary Teachers’ Beliefs about Mathematics. Mathematics Teacher Education and Development, 16(2), 89-107.
Merriam, S. B. (1988). Case Study Research in Education: A qualitative approach. San Francisco, CA: Jossey-Bass Publishers.
Montes, M.A., Aguilar, A., Carrillo, J., & Muñoz-Catalán, M.C. (2013). MTSK: From Common and Horizon Knowledge to Knowledge of Topics and Structures. In B. Ubuz, C. Haser, & M.A. Mariotti (Eds.), Proceedings of the CERME 8 (pp. 3185-3194). Antalya, Turkey: ERME.
Mora, D. V., Climent, N., Escudero-Ávila, D., Montes, M. A., & Ribeiro, M. (2016). Conocimiento Especializado de un Profesor de Álgebra Lineal y Espacios de Trabajo Matemático. Bolema: Boletim de Educação Matemática, 30(54), 222-239. https://doi.org/10.1590/1980-4415v30n54a11.
Pajares, F. (1992). Teachers’ beliefs and educational research: Cleaning up a messy construct. Review of Educational Research, 62(39), 307-332. https://doi.org/10.3102/00346543062003307.
Philipp, R. A. (2007). Mathematics teachers’ beliefs and affect. Second handbook of research on mathematics teaching and learning, 1, 257-315.
Ponte, J. P. (1992). Concepçoes dos professores de matemática e processos de formaçao. Educaçao Matemática. Lisboan: Instituto de Inovaçao Educacional.
Ponte, J. P. (2012). Estudiando el conocimiento y el desarrollo profesional del profesorado de matemáticas. In N. Planas (Ed.). Teoría, crítica y práctica de la educación matemática (pp. 83-96). Barcelona, Spain: Graó, de IRIF, S.L.
Rowland, T., Huckstep, P., & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: the knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8, 255-281. https://doi.org/10.1007/s10857-005-0853-5.
Santos, L. (2002). A investigação e os seus implícitos: contributos para uma discussão. Actas del VI Simposio de la SEIEM: Logroño, pp. 157-170.
Schoenfeld, A. (2000). Models of the Teaching Process. Journal of Mathematical Behavior, 18(3), 243-261. https://doi.org/10.1016/S0732-3123(99)00031-0.
Schoenfeld, A. H. (1998a). Toward a theory of teaching-in-context. Issues in Education, 4(1), 1-94. https://doi.org/10.1016/S1080-9724(99)80076-7.
Schoenfeld, A. H. (1998b). On modelling teaching. Issues in Education, 4(1), 149-162. https://doi.org/10.1016/S1080-9724(99)80084-6.
Shulman, L. S. (1986). Those who understand: Knowledge growth in Teaching. American Educational Research Association, 15(2), 4-14. https://doi.org/10.3102/0013189X015002004.
Stake, R. E. (2000). Case Studies. In Denzin, N.K. y Lincoln, Y. (Eds.), Handbook of qualitative research (435-454). Thousand Oaks: Sage Publications.
Stake, R. E. (2005). Qualitative Case Studies. In N.K. Denzin y Y.S. Lincoln (Eds.), The Sage handbook of qualitative research. Third edition (443-166). Thousand Oaks: Sage Publications.
Strauss, A., & Corbin, J. (1994). Grounded Theory Methodology: An overview. In N.K. Denzin, & Y. Lincoln, (Eds) Handbook of qualitative research (pp. 273- 285). Thousand Oaks, C.A: Sage.
Stylianides A. J., & Delaney S. (2018). Pre-service Mathematics Teachers’ Knowledge and Beliefs. In Stylianides G., Hino K. (eds) Research Advances in the Mathematical Education of Pre-service Elementary Teachers. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-68342-3_15.
Thompson, A. G. (1984). The relationship of teachers’ conceptions of mathematics and mathematics teaching to instructional practice. Educational Studies in Mathematics, 15, 105-127. https://doi.org/10.1007/BF00305892.
Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research in mathematics teaching and learning (pp. 127-146). New York, NY: Macmillan.
Tsamir, P., Tirosh, D., Levenson, E., et al. (2015). Early-years teachers’ concept images and concept definitions: triangles, circles, and cylinders. ZDM Mathematics Education, 47, 497. https://doi.org/10.1007/s11858-014-0641-8.
Vasco, D. (2015). Specialized knowledge of the Linear Algebra teacher. A case study at the university level (Doctoral dissertation). Huelva, España: University of Huelva. http://hdl.handle.net/10272/11901.
Wilkins, J. L. M., & Brand, B. R. (2004). Change in preservice teachers’ beliefs: An evaluation of a mathematics methods course. School Science and Mathematics, 104(5), 226-232. https://doi.org/10.1111/j.1949-8594.2004.tb18245.x.
Zoitsakos, S., Zachariades, T., & Sakonidis. C. (2015). Secondary mathematics teachers’ content knowledge for teaching in two contexts: Interpreting versus managing didactically students’ understandings. In Konrad Krainer; Naďa Vondrová. CERME 9 - Ninth Congress of the European Society for Research in Mathematics Education. pp. 3296-3302, Prague, Czech Republic.

How to cite this article

APA

Aguilar-González, Á., Muñoz-Catalán, M. C., & Carrillo, J. (2019). An Example of Connections between the Mathematics Teacher’s Conceptions and Specialised Knowledge. Eurasia Journal of Mathematics, Science and Technology Education, 15(2), em1664. https://doi.org/10.29333/ejmste/101598

Vancouver

Aguilar-González Á, Muñoz-Catalán MC, Carrillo J. An Example of Connections between the Mathematics Teacher’s Conceptions and Specialised Knowledge. EURASIA J Math Sci Tech Ed. 2019;15(2):em1664. https://doi.org/10.29333/ejmste/101598

AMA

Aguilar-González Á, Muñoz-Catalán MC, Carrillo J. An Example of Connections between the Mathematics Teacher’s Conceptions and Specialised Knowledge. EURASIA J Math Sci Tech Ed. 2019;15(2), em1664. https://doi.org/10.29333/ejmste/101598

Chicago

Aguilar-González, Álvaro, María Cinta Muñoz-Catalán, and José Carrillo. "An Example of Connections between the Mathematics Teacher’s Conceptions and Specialised Knowledge". Eurasia Journal of Mathematics, Science and Technology Education 2019 15 no. 2 (2019): em1664. https://doi.org/10.29333/ejmste/101598

Harvard

Aguilar-González, Á., Muñoz-Catalán, M. C., and Carrillo, J. (2019). An Example of Connections between the Mathematics Teacher’s Conceptions and Specialised Knowledge. Eurasia Journal of Mathematics, Science and Technology Education, 15(2), em1664. https://doi.org/10.29333/ejmste/101598

MLA

Aguilar-González, Álvaro et al. "An Example of Connections between the Mathematics Teacher’s Conceptions and Specialised Knowledge". Eurasia Journal of Mathematics, Science and Technology Education, vol. 15, no. 2, 2019, em1664. https://doi.org/10.29333/ejmste/101598