What mathematical knowledge for teaching in the early years? Challenges for training
DOI:
https://doi.org/10.18593/r.v46i.23839Keywords:
Mathematical knowledge for teaching, Teacher training, Early yearsAbstract
Today there are many and varied challenges for the training of mathematics teachers. When you think of teachers in the early years, the challenges are even greater. On the one hand, these teachers are generalists, and are not exclusively mathematics teachers. On the other hand, the mathematical knowledge of these teachers is often devalued because it is believed that the mathematics that is taught in the early years is simple and consequently easy to teach. It is a wrong belief because, despite being elementary, this Mathematics is the foundation of future mathematical constructions and contains the rudiments of many important concepts of advanced branches of the discipline. Assuming that teacher's knowledge is central to the teaching and learning process, it is important to determine what mathematical knowledge(s) is necessary to teach. In this article we will focus our attention on the mathematical knowledge for teaching and present some research results that illustrate critical points and difficulties in the knowledge of (future) teachers and that point out clues to conceptualize teacher training.
Downloads
References
ASKEW, M. Effective teachers of numeracy. London: King's College London, 1997.
BALL, D. L.; THAMES, M. H.; PHELPS, G. Content knowledge for teaching: what makes it special? Journal of Teacher Education, v. 59, n. 5, p. 389-407, 2008. DOI: https://doi.org/10.1177/0022487108324554
BALL, D. L. The mathematical understanding that prospective teachers bring to teacher education. Elementary School Journal, ano 90, p. 449-466, 1990. DOI: https://doi.org/10.1086/461626
BALL, D. L. What mathematical knowledge is needed for teaching mathematics. [S. l.]: Secretary’s Summit on Mathematics, US Department of Education, 2003.
BAUMERT, J. et al. Teachers' mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, v. 47, n. 1, p. 133-180, 2010. DOI: https://doi.org/10.3102/0002831209345157
CONFERENCE BOARD OF THE MATHEMATICAL SCIENCES. The mathematical education of teachers II. Providence RI and Washington DC: American Mathematical Society and Mathematical Association of America, 2012.
CHARALAMBOUS, C. Y. Investigating the knowledge need¬ed for teaching mathematics: an exploratory valida¬tion study focusing on teaching practices. Journal of Teacher Education, v. 67, n. 3, p. 220-237, 2016. DOI: https://doi.org/10.1177/0022487116634168
DAVIS, B.; SIMMT, E. Mathematics-for-teaching: an ongoing investigation of the mathematics that teachers (need to) know. Educational Studies in Mathematics, v. 61, n. 3, p. 293-319, 2006. DOI: https://doi.org/10.1007/s10649-006-2372-4
DE VILLIERS, M. The role and function of a hierarchical classification of the quadrilaterals. For the Learning of Mathematics, v. 14, n. 1, p. 11-18, 1994.
ELMORE, R. F. Bridging the gap between standards and achievement. Washington, DC: Albert Shanker Institute, 2002.
EUROPEAN COMMISSION. Boosting teacher quality: pathways to effective policies.
Luxembourg: Publications Office of the European Union, 2018.
EUROPEAN COMMISSION. Shaping career-long perspectives on teaching. A guide on policies to improve initial teacher education. Luxembourg: Publications Office of the European Union, 2015.
FENNEMA, E.; FRANKE, M. L. Teachers knowledge and its impact. In: GROWS, D. A. (ed.). Handbook of research on mathematics teaching and learning. New York: MacMillan, 1992. p. 147-164.
FONSECA, L. Geometria no Plano. In: PALHARES, P. (ed.). Elementos de Matemática para professores do Ensino Básico. Lisboa: Lidel, 2004. p. 251-302.
GOMES, A. et al. Tarefas em geometria: da sala de aula para a formação de professores. Descrição de um projeto. In: PINTO, H. et al. (ed.). Atas do Seminário de Investigação em Educação Matemática (SIEM). Lisboa: APM, 2012. p. 761-763.
GOMES, A.; RALHA, E. Conceitos Elementares em Matemática: o papel da definição. In: CONGRESSO IBERO-AMERICANO DE EDUCAÇÃO MATEMÁTICA, 5., 2005, Porto. Anais [...] Porto, 2005.
GOMES, A. Um estudo sobre o conhecimento matemático de (futuros) professores de 1.º ciclo. O problema dos conceitos fundamentais em Geometria. 2003. Tese (Doutorado) – Instituto da Criança, Universidade do Minho, Braga, 2004.
HIEBERT, J.; GROUWS, D. The effects of classroom mathematics teaching on students’ learning. In: LESTER, F. (ed.). Handbook of Research on Mathematics Teaching and Learning. NCTM: Information Age Publishing, 2007. p. 371-404.
HILL, H. C.; BALL, D. L. Learning mathematics for teaching: results from California’s mathematics professional development institutes. Journal for Research in Mathematics Education, v. 35, n. 5, p. 330-351, 2004. DOI: https://doi.org/10.2307/30034819
HILL, H. C. et al. Assessing Teachers’ Mathematical Knowledge: What knowledge matters and what evidence counts? In: LESTER, F. (ed.). Second Handbook of Research on Mathematics Teaching and Learning. Charlotte NC: Information Age Publishing, 2007. p. 111-155.
HILL, H. C. et al. Mathematical knowledge for teaching and the mathematical quality of instruction: an exploratory study. Cognition and Instruction, v. 26, n. 4, p. 430-511, 2008. DOI: https://doi.org/10.1080/07370000802177235
HILL, H. C.; ROWAN, B.; BALL, D. L. Effects of teachers' mathematics knowledge for teaching on student achievement. American Education Research Journal, v. 42, n. 2, p. 371-406, 2005. DOI: https://doi.org/10.3102/00028312042002371
HOOVER, M. et al. Making pro¬gress on mathematical knowledge for teaching. The Mathematics Enthusiast, v. 13, n. 1, p. 3-34, 2016. DOI: https://doi.org/10.54870/1551-3440.1363
HOURIGAN, M.; LEAVY, A. M. Preservice primary teachers’ geometric thinking: Is pre-tertiary mathematics education building sufficiently strong foundations? The Teacher Educator, v. 52, n. 4, p. 346-364, 2017. DOI: https://doi.org/10.1080/08878730.2017.1349226
JONES, K.; TZEKAKI, M. Research on the teaching and learning of geometry. In: GUTIÉRREZ, A.; LEDER, G.; BOERO, P. (ed.). The second handbook of research on the psychology of mathematics education: the journey continues. Rotterdam: Sense, 2016. p. 109-149. DOI: https://doi.org/10.1007/978-94-6300-561-6_4
MA, L. Knowing and teaching elementary mathematics: teachers' understanding of fundamental mathematics in China and the US. Mahwash, NJ: Lawrence Erlbaum Associates, Publishers, 1999. DOI: https://doi.org/10.4324/9781410602589
NEWELL, R. The extent to which a primary maths teacher’s success in the classroom is
dependent on subject knowledge. In: SMITH, C. (ed.). Proceedings of the British Society for Research into Learning Mathematics, v. 31, n. 1, p. 103-108, Mar. 2011.
RIBEIRO, C. M. Future primary teachers MKT in Geometry: some examples concerning rectangles. In: GUNNARSDOTTIR, G. H. et al. (ed.). Nordic Conference on Mathematics Education, NORMA 11. Reykjavík: NORME, 2012. p. 533-541.
ROWLAND, T. The knowledge quartet: a framework for analysing and developing mathematics teaching. In: FERNANDES, J. A. et al. (ed.). Atas do XXIV Seminário de Investigação em Educação Matemática. Braga: Centro de Investigação em Educação da Universidade do Minho, 2013. p. 31-47.
SCHMIDT, W. H. et al. Teacher education matters: a study of middle school mathematics teacher preparation in six countries. New York: Teachers College Press. 2011
SHULMAN, L. Those who understand: knowledge growth in teaching. Educational Researcher, v. 15, n. 2, p. 4-14, 1986. DOI: https://doi.org/10.3102/0013189X015002004
SKEMP, R. Relational understanding and instrumental understanding. Mathematics Teaching, ano 77, p. 20-26, 1976.
STEIN, M. K. et al. Implementing standards-based mathematics instruction: a casebook for professional development. New York: Teachers College Press, 2000.
VINNER, S. The role of definitions in the teaching and learning of mathematics. In: TALL, D. (ed.). Advanced mathematical thinking. Dordrecht: Kluwer, 1991. p. 65-81. DOI: https://doi.org/10.1007/0-306-47203-1_5
WINICKI, G.; LEIKIN, R. On equivalent and non-equivalent definitions: part 1. For the Learning of Mathematics, v. 20, n. 1, p. 17-21, 2000.
Published
How to Cite
Issue
Section
License
Copyright (c) 2021 Alexandra Gomes

This work is licensed under a Creative Commons Attribution 4.0 International License.
Copyright Notice
The authors retain copyright and grant the Journal the right of first publication, with the work simultaneously licensed under a Creative Commons – Attribution – 4.0 International license.





