A Proposal to Enhance Preservice Teacher’s Noticing

Walter F Castro; Luis Pino-Fan; Hilduara Velásquez-Echavarría

doi:10.29333/ejmste/92017

Full Text (PDF)

Walter F Castro ¹ ^* , Luis Pino-Fan ², Hilduara Velásquez-Echavarría ¹

More Detail

¹ Universidad de Antioquia, COLOMBIA
² Universidad de Los Lagos, CHILE
^* Corresponding Author

Abstract

This paper presents a proposal for the development of ‘Teacher noticing’ with the help of dimensions taken from the teacher’s didactic-mathematical knowledge model, that makes up a Guide for Didactical Reflection. The proposal is based on a study conducted during a time span of two years while the preservice teachers were in their teaching practicum. The methodology was qualitative and data were taken in video, audio, observing rubrics, and interviews formats. The results not only indicate that the Guide can help develop teachers’ noticing, in order to identify and to question several specific domains of teacher knowledge involved in mathematics teaching, but also suggest that prospective teachers are moved into action and translate their noticing in didactic action during class. We hypothesize that preservice effective noticing occurs at the intersection of practice and discussion over the practice, with the help of ‘noticing tools’ with respect to the mathematical activities of students.

Keywords

teacher noticing
didactic-mathematical knowledge
didactical analysis
professional development
teacher training

License

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/92017

EURASIA J Math Sci and Tech Ed, 2018 - Volume 14 Issue 11, Article No: em1569

Publication date: 09 Jun 2018

Article Views: 606

Article Downloads: 125

Open Access References How to cite this article

References

Alsina, A., & Domingo, M. (2007). Cómo aumentar la motivación para aprender matemáticas. Suma, (56), 23-31.
Bisquerra, R. (1998). Educación emocional. Barcelona: Praxis.
Bisquerra, R. (2000). Educación emocional y bienestar. Barcelona: Praxis.
Bisquerra, R. (2005). La educación emocional en la formación del profesorado. Revista Interuniversitaria de formación del profesorado, 19(3), 95 -114.
Breda, A., Font, V., & Pino-Fan, L. (2018). Criterios valorativos y normativos en la Didáctica de las Matemáticas: el caso del constructo idoneidad didáctica [Evaluative and normative criteria in Didactics of Mathematics: the case of didactical suitability construct]. BOLEMA, 32(60), 255-278. https://doi.org/10.1590/1980-4415v32n60a13.
Breda, A., Pino-Fan, L., & Font, V. (2017). Meta didactic-mathematical knowledge of teachers: criteria for the reflection and assessment on teaching practice. Eurasia Journal of Mathematics, Science & Technology Education, 13(6), 1893-1918. https://doi.org/10.12973/eurasia.2017.01207a.
Bueno, C., Teruel, M. P., & Valero, A. (2005). La inteligencia emocional en alumnos de magisterio: La percepción y comprensión de los sentimientos y las emociones. Revista Interuniversitaria de formación del profesorado, 19(3), 169-194.
Campbell, P., & White, D. (1997). Project IMPACT: Influencing and supporting teacher change in predominantly minority schools. In E. Fennema & B. Nelson (Eds.), Mathematics teachers in transition (pp. 309-355). Mahwah, N.J.: Erlbaum.
Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C. P., & Loef, M. (1989). Using knowledge of children’s mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26, 499-531. https://doi.org/10.3102/00028312026004499.
Extremera, N. & Fernández, P. (2003). Inteligencia emocional en el contexto educativo: Hallazgos científicos de sus efectos en el aula. Revista de educación, (332), 97-116.
Fernández, M., Palomero, J., & Teruel, M. (2009). El desarrollo socioafectivo en la formación inicial de los profesores. Reifop, 12(1), 33-50.
Franke, M. L., Carpenter, T. P., Levi, L., & Fennema, E. (2001). Capturing teachers’ generative growth: A follow-up study of professional development in mathematics. American Educational Research Journal, 38, 653-689. https://doi.org/10.3102/00028312038003653.
Godino, J. (2011). Indicadores de la idoneidad didáctica de procesos de enseñanza y aprendizaje de las matemáticas. XIII Conferencia Interamericana de Educación Matemática. CIAEM. Recife, Brasil.
Godino, J., 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. https://doi.org/10.1007/s11858-006-0004-1.
Gómez-Chacón, I. (2002). Afecto y aprendizaje matemático: causas y consecuencias de la interacción emocional. En J. Carrillo (ed.) Reflexiones sobre el pasado, presente y futuro de las Matemáticas. Huelva.
Greene, M., & Campbell, C. (1993). Becoming a Teacher: the contribution of teacher education, ERIC Report ED369769 45, Alberta, Canada.
Hebert, E., & Worthy, T. (2001). Does the first year of teaching have to be a bad one? A case study of success. Teaching and teacher education, 17, 897-911. https://doi.org/10.1016/S0742-051X(01)00039-7.
Hill, H., Ball, D., & Schilling, S. (2008). Unpacking “pedagogical content knowledge”: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372-400.
Jacobs, V. R., Franke, M. L., Carpenter, T. P., Levi, L., & Battey, D. (2007). Professional development focused on children’s algebraic reasoning in elementary school. Journal for Research in Mathematics Education, 38, 258–288.
Kazemi, E., & Franke, M. L. (2004). Teacher learning in mathematics: Using student work to promote collective inquiry. Journal of Mathematics Teacher Education, 7, 203–235. https://doi.org/10.1023.
Lubinski, C., & Jaberg, P. (1997). Teacher change and mathematics K-4: Developing a theoretical perspective. In E. Fennema and B. Scott Nelson (Eds.). Mathematics teachers in transition (pp. 223-254). Mahwah, NJ. Lawrence Erlbaum Associates.
Miller, D. J., Glover, D., & Averis, D. (2008). Enabling enhanced mathematics teaching: Final Report for the National Centre for Excellence in the Teaching of Mathematics. Retrieved on June 15, 2011 from http://www.keele.ac.uk/media/keeleuniversity/fachumsocsci/sclpppp/education/interactivewhiteboard/ncetmreport-1.pdf.
Ministerio de Educación Nacional. (1998). Lineamientos Curriculares de Matemáticas. Bogotá.
Núñez, C. (1996). Lo que subyace tras el comportamiento de nuestro alumnado en una clase de matemáticas. Revista Uno, (7), 118-124.
Pino-Fan, L., & Godino, J. D. (2015). Perspectiva ampliada del conocimiento didáctico-matemático del profesor [An expanded view of teachers’ didactic–mathematical knowlodge]. PARADIGMA, 36(1), 87-109.
Pino-Fan, L., Assis, A., & Castro, W. F. (2015). Towards a methodology for the characterization of teachers' didactic-mathematical knowledge. Eurasia Journal of Mathematics, Science & Technology Education, 11(6), 1429-1456. https://doi.org/10.12973/eurasia.2015.1403a.
Pino-Fan, L., Assis, A., & Godino, J. D. (2015). Análisis del proceso de acoplamiento entre las facetas epistémica y cognitiva del conocimiento matemático en el contexto de una tarea exploratorio-investigativa sobre patrones. Educación Matemática, 27(1), 37-64.
Pino-Fan, L., Font, V., & Breda, A. (2017). Mathematics teachers' knowledge and competences model based on the onto-semiotic approach. In B. Kaur, W. K. Ho, T. L. Toh & B. H. Choy (Eds.), Proceedings of the 41st Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 33-40). Singapure: PME.
Pino-Fan, L., Godino, J. D., & Font, V. (2016). Assessing key epistemic features of didactic-mathematical knowledge of prospective teachers: the case of the derivative. Journal of Mathematics Teacher Education. http://dx.doi.org/10.1007/s10857-016-9349-8.
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(3), 255-281. https://doi.org/10.1007/s10857-005-0853-5.
Santagata, R., Zannoni, C., & Stigler, J. (2007). The role of lesson analysis in pre-service teacher education: An empirical investigation of teacher learning from a virtual video-based field experience. Journal of Mathematics Teacher Education, 10(2), 123-140. https://doi.org/10.1007/s10857-007-9029-9.
Schack, E. O., Fisher, M. H., & Wilhelm, J. (2017). Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks. New York: Springer.
Star, J. R., & Strickland, S. K. (2007). Learning to observe: using video to improve preservice mathematics teachers’ ability to notice. Journal of Mathematics Teacher Education, 11(2), 107-125. https://doi.org/10.1007/s10857-007-9063-7.
Star, J. R., Lynch, K., & Perova, N. (2011). Using video to improve preservice mathematics teachers’ abilities to attend to classroom features. In M. G. Sherin, V. R. Jacobs & R. A. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 117-133). New York: Routledge.
Steinberg, R. M., Empson, S. B., & Carpenter, T. P. (2004). Inquiry into children’s mathematical thinking as a means to teacher change. Journal of Mathematics Teacher Education, 7, 237–267. https://doi.org/10.1023/B:JMTE.0000033083.04005.d3.
Teruel, M. P. (2000). La inteligencia emocional en el currículo de la formación inicial de profesores. Revista Interuniversitaria de formación del profesorado, (38), 141-152.
Vacc, N., & Bright, G (1999). Elementary preservice teachers’ changing beliefs and instructional use of children’s mathematical thinking. Journal for Research in Mathematics Education, 30(1), 89-110.
Van Es, E. A., & Sherin, M. G. (2008). Mathematics Teachers´ “Learning to Notice” in the Context of a Video Club. Teaching and Teacher Education, 24, 244-276. https://doi.org/10.1016/j.tate.2006.11.005.
Veenman, S. (1984). Perceived problems of beginning teachers. Review of Educational Research, 54(2), 143-178. https://doi.org/10.3102/00346543054002143.
Vergnaud, G. (1981). L’enfant, la mathématique et la réalité. Berne, Peter Lang.
Vergnaud, G. (1983). Multiplicative structures. Acquisitions of mathematics concepts and processes. In R. Lesh y M. Landau (Eds.), 127-174.
Vergnaud, G. (1990). La teoría de los campos conceptuales. Recherches en Didactique des Mathématiques, 10(2-3), 133-170.

How to cite this article

Vancouver

Castro WF, Pino-Fan L, Velásquez-Echavarría H. A Proposal to Enhance Preservice Teacher’s Noticing. EURASIA J Math Sci and Tech Ed. 2018;14(11):em1569. https://doi.org/10.29333/ejmste/92017

APA

Castro, W. F., Pino-Fan, L., & Velásquez-Echavarría, H. (2018). A Proposal to Enhance Preservice Teacher’s Noticing. EURASIA Journal of Mathematics, Science and Technology Education, 14(11), em1569. https://doi.org/10.29333/ejmste/92017

AMA

Castro WF, Pino-Fan L, Velásquez-Echavarría H. A Proposal to Enhance Preservice Teacher’s Noticing. EURASIA J Math Sci and Tech Ed. 2018;14(11), em1569. https://doi.org/10.29333/ejmste/92017

Chicago

Castro, Walter F, Luis Pino-Fan, and Hilduara Velásquez-Echavarría. "A Proposal to Enhance Preservice Teacher’s Noticing". EURASIA Journal of Mathematics, Science and Technology Education 2018 14 no. 11 (2018): em1569. https://doi.org/10.29333/ejmste/92017

Harvard

Castro, W. F., Pino-Fan, L., and Velásquez-Echavarría, H. (2018). A Proposal to Enhance Preservice Teacher’s Noticing. EURASIA Journal of Mathematics, Science and Technology Education, 14(11), em1569. https://doi.org/10.29333/ejmste/92017

MLA

Castro, Walter F et al. "A Proposal to Enhance Preservice Teacher’s Noticing". EURASIA Journal of Mathematics, Science and Technology Education, vol. 14, no. 11, 2018, em1569. https://doi.org/10.29333/ejmste/92017