Banner Portal
Knowledge of mathematics teaching rational numbers
PDF (Português (Brasil))

Keywords

Mathemtics teachers specialized knowledge
Pedagogical content knowledge
Rational numbers

How to Cite

ZAKARYAN, Diana; RIBEIRO, Miguel. Knowledge of mathematics teaching rational numbers: an example of relationships. Zetetike, Campinas, SP, v. 24, n. 3, p. 301–321, 2017. DOI: 10.20396/zet.v24i3.8648095. Disponível em: https://periodicos.sbu.unicamp.br/ojs/index.php/zetetike/article/view/8648095. Acesso em: 7 jul. 2024.

Abstract

This paper aims at characterizing the relationships between different subdomains of mathematics teachers’
specialized knowledge. In particular, when searching for improving teachers’ practices, such relationships and
its role in practice have a crucial role in the mathematical critical situations, such as the teaching and learning of
rational numbers. Considering teachers’ knowledge in the perspective of the Mathematics Teachers Specialized
Knowledge, an identification and characterization of the relationships between one of its subdomains
(Knowledge of Mathematics Teaching) and the remaining is made. For doing so, the practice of a Chilean upper
secondary teacher is analysed, when she is teaching rational numbers. Using a map of connections, a set of
relationships between different subdomains is presented. Some future pathways for research are presented.

https://doi.org/10.20396/zet.v24i3.8648095
PDF (Português (Brasil))

References

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.

Behr, M.J., Lesh, R., Post, T.R., & Silver, E.A. (1983). Rational number concepts. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and process (pp. 91-126). New York: Academic Press, Inc.

Carrillo, J., Climent, N., Contreras, L. C. & Muñoz-Catalán, M. C. (2013). Determining Specialized Knowledge for Mathematics Teaching. In B. Ubuz, C. Haser, & M. A. Mariotti (Eds.), Proceedings VIII Congress of the European Society for Research in Mathematics Education (CERME 8) (pp. 2985-2994). Antalya: Middle East Technical University, Ankara.

Cohen L. & Manion L. (2002). Métodos de investigación educativa. Madrid: La Muralla.

Escudero-Avila, D. (2015). Una caracterización del conocimiento didáctico del contenido como parte del conocimiento especializado del profesor de matemáticas de secundaria. Tesis doctoral. Huelva: Universidad de Huelva.

Flores, A. (2002). Profound understanding of division of fraction. In B. Litwiller & G. Bright (Eds.), Making sense of fractions, ratios, and proportions: 2002 Yearbook (pp. 237-246). Reston: NCTM.

Flores-Medrano, E., Escudero-Avila, D., Montes, M., Aguilar, A. & Carrillo, J. (2014). ¿Cómo se relaciona el conocimiento que tiene el profesor acerca del aprendizaje de las matemáticas con su entendimiento sobre los Espacios de Trabajo Matemático? En I. Gómez-Chacón, J. Escribano, A. Kuzniak & P.R. Richard (Eds.), Proceedings Fourth ETM Symposium (pp. 473-485), Madrid, España.

Graeber, A., Tirosh, D., & Glover, R. (1989). Preservice teachers’ misconceptions in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 20(1), 95-102.

Harel, G., Behr, M., Post, T., & Lesh, R. (1994). The impact of number type on the solution of multiplication and division problems: Further considerations. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 365-388). Albany, NY: SUNY Press.

Jakobsen, A., Ribeiro, C. M. & Mellone, M. (2014). Norwegian prospective teachers’ MKT when interpreting pupils’ productions on a fraction task. Nordic Studies in Mathematics Education, 19(3-4), 135-150.

Kieren, T. (1976). On the mathematical, cognitive, and instructional foundations of rational numbers. In R. Lesh (Ed.), Number and measurement: papers from a research workshop (pp. 101-144). Columbus, OH: ERIC/SMEAC.

Kuzniak, A. (2011). L'espace de Travail Mathématique et ses genèses. Annales de didactique et de sciences cognitives. 16, 9-24.

Lamon, S. (2007). Rational numbers and proportional reasoning. In F. Lester (Ed.), Second handbook of mathematics teaching and learning (pp. 629-667). Greenwich, CT: Information Age Publishing.

Ma, L. (1999). Knowing and teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Erlbaum.

Ministerio de Educación de Chile (2009). Objetivos Fundamentales y Contenidos Mínimos Obligatorios de la Educación Básica y Media. Santiago de Chile: Autor.

Muñoz-Catalán, M.C., Contreras, Luis C., Carrillo, J., Rojas, N., Montes, M.Á. & Climent, N. (2015). Conocimiento especializado del profesor de matemáticas (MTSK): un modelo analítico para el estudio del conocimiento del profesor de matemáticas. La Gaceta de la Real Sociedad Matemática Española, 18(3), 589-605.

Nye, B., Konstantopoulos, S. & Hedges, L. V. (2004). How large are teacher effects? Educational Evaluation and Policy Analysis, 26(3), 237-257.

Pinto, H. & Ribeiro, C. M. (2013). Conhecimento e formação de futuros professores dos primeiros anos - o sentido de número racional. Da Investigação às Práticas, 3(1), 85-105.

Potari, D., Berg, C., Charalambous, C., Figueiras, L., Hošpesová, A., Ribeiro, C.M., Santos, L., Skott, J. & Zehetmeier, S. (2013). Group 17 - From a study of teaching practices to issues in teacher education: Introduction. In B. Ubuz, Ç. Haser & M. A. Mariotti (Eds.), Atas do CERME 8 (pp. 2896-2907). Antalia, Turquia: ERME.

Ribeiro, C.M. & Carrillo, J. (2011). The role of beliefs and knowledge in practice. In B. Roesken, & M. Casper (Eds.), Current state of research on mathematical beliefs XVII – MAVI 17 (pp. 192-201). Bochum: Professional School of Education, Ruhr-Universität Bochum.

Ribeiro, C.M., Carrillo, J. & Monteiro, R. (2012). Cognições e tipo de comunicação do professor de matemática. Exemplificação de um modelo de análise num episódio dividido. Revista Latinoamericana de Investigación en Matemática Educativa, 15(1), 277-310.

Rowland, T. (2008). The purpose, design and use of examples in the teaching of elementary mathematics. Educational Studies in Mathematics, 69, 149-163.

Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15 (2), 4-14.

Stake, R.E. (2007). Investigación con estudio de casos. Madrid: Morata.

Stein, M.K., Smith, M.S., Henningsen, M.A. & Silver, E.A. (2000). Implementing standards-based mathematics instruction: a Casebook for Professional Development. New York: Teachers College Press.

Vanhille, L.S., & Baroody, A.J. (2002). Fraction instruction that fosters multiplicative reasoning. In B. Litwiller (Ed.), Making sense of fractions, ratios, and proportions: NCTM 2002 Yearbook (pp. 224-236). Reston,VA: National Council of Teachers of Mathematics.

Vergnaud, G. (1983). Multiplicative structures. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 127-174). New York, NY: Academic Press.

Zakaryan, D., Ribeiro, C.M., & Carrillo, J. (sometido). Conocimiento del profesor de los números racionales como objeto de aprendizaje: Un estudio de caso. Perfiles Educativos.

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Copyright (c) 2017 Zetetike

Downloads

Download data is not yet available.