An approach to didactic-mathematical knowledge of future Basic Education teachers to teach elementary mathematics

Authors

DOI:

https://doi.org/10.15359/ru.35-2.8

Keywords:

didactic-mathematical knowledge, mathematics education, primary education, ontosemiotic approach, teacher training, elementary mathematics

Abstract

This paper presents a global analysis of the results obtained in an exploratory study about the didactic-mathematical knowledge (CDM) that future Basic Education teachers have in order to teach elementary mathematics. For this purpose, the math practices of 157 Chilean teachers under training were analyzed based on the CDM-Elementary Mathematics questionnaire, which includes six open ended questions to evaluate partial and initial aspects of such knowledge. The questions are based on the thematic areas proposed by the Chilean school curriculum and are closely related to the mathematical content of numbers and operations, patterns and algebra, measurement, geometry, data and probability. Results show that the level of performance obtained by future teachers is limited regarding didactic-mathematical knowledge for the different categories, when reaching an average of 24 points out of a total of 42. In addition, the thematic areas with the greatest difficulty are measurement, data, and probabilities. In conclusion, programs should be created to support teacher training in order to successfully address the teaching of elementary mathematics in the basic education classroom.

References

Alpízar-Vargas, M., & Alfaro-Arce, A. (2019). La formación universitaria de docentes de educación primaria: el caso de matemáticas. Uniciencia, 33(2), 110-154. doi: https://doi.org/10.15359/ru.33-2.8

Chapman, O. (2014). Overall Commentary: Understanding and Changing Mathematics Teachers. In: Lo, Jane-Jane; Leatham, Keith R.; Van Zoest, Laura R. (Ed.). Research Trends in Mathematics Teacher Education (pp. 295-309). Springer International Publishing. https://doi.org/10.1007/978-3-319-02562-9_16

Chapman, O., & An, S. (2017). A survey of university-based programs that support in-service and pre-service mathematics teachers’ change. ZDM Mathematics Education, Berlín, 49(2), 171-185. doi: http://doi.org/10.1007/s11858-017-0852-x

Clotfelter, C., Ladd, H., & Vigdor, J. (2007). Teacher credentials and student achievement: Longitudinal analysis with student fixed effects. Economics of Education Review, 26(6), 673-682. https://doi.org/10.1016/j.econedurev.2007.10.002

Darling-Hammond, L., & Bransford, J. (2005). Preparing Teachers for a Changing World: What Teachers Should Learn and Be Able to Do. San Francisco: Jossey-Bass.

Darling-Hammond, L., Wei, R., & Johnson, C. (2009). Teacher Preparation and Teacher Learning: A Changing Policy Landscape. In: Sykes, G.; Schneider, B.; Plank, D. (Ed.). Handbook of Education Policy Research (pp. 613-636). Nueva York: American Educational Research Association and Routledge.

Eurydice. (2013). Key Data on Teachers and School Leaders in Europe. 2013 Edition. Eurydice Report. Luxembourg: Publications Office of the European Union.

Even, R., & Ball, D. L. (2009). The professional education and development of teachers of mathematics. New York, NY: Springer. https://doi.org/10.1007/978-0-387-09601-8

Ghauri, P., & Gronhaug, K. (2010). Research methods in business studies. Prentice Hall, Harlow.

Godino, J. D. (2009). Categorías de análisis de los conocimientos del profesor de matemá-ticas. UNION, Revista Iberoamericana de Educación Matemática, 20, 13-31. https://union.fespm.es/index.php/UNION/issue/view/27

Godino, J. D., Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM Mathematics Education, 39(1), 127-135. doi: http://doi.org/10.1007/s11858-006-0004-1

Godino, J. D., Batanero, C., Font, V., & Giacomone, B. (2016). Articulando conocimientos y competencias del profesor de matemáticas: el modelo CCDM. In: Fernández, C. et ál. (Eds.), Investigación en Educación Matemática XX (pp. 288-297). Málaga: SEIEM. https://www.seiem.es/docs/actas/20/ActasXXSEIEM.pdf

Godino, J. D., Giacomone, B., Batanero, C., & Font, V. (2017). Enfoque ontosemiótico de los conocimientos y competencias del profesor de matemáticas. Bolema, 31(57), 90-113. doi: http://dx.doi.org/10.1590/1980-4415v31n57a05

Hanushek, E. A. (2004). Some simple analytics of school quality. Cambridge, MA: National Bureau of Economic Research. https://doi.org/10.3386/w10229

Hattie, J. (2008). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. London, UK: Routledge. https://doi.org/10.4324/9780203887332

Hattie, J. (2012). Visible Learning for Teachers. London, UK: Routledge. https://doi.org/10.4324/9780203181522

Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking Pedagogical Content Knowledge: Conceptualizing and Measuring Teachers’ Topic-specific Knowledge of Students. Journal for Research in Mathematics Education, 39(4), 372-400. www.jstor.org/stable/40539304

Hoover, M. (2014). Commentary on Section 1: Mounting Progress on Understanding Mathematics Teacher Content Knowledge. In: Lo, Jane-Jane; Leatham, K.; Van Zoest, L. R. (Ed.). Research Trends in Mathematics Teacher Education, (pp. 83-90). Springer International Publishing. https://doi.org/10.1007/978-3-319-02562-9_5

Krainer, K. (2011). Teachers as stakeholders in mathematics education research. In B. Ubuz (Ed.). Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education (PME35) (pp. 47-62). Ankara, Turkey: PME.

Ma, L. (2010). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Routledge. https://doi.org/10.4324/9780203856345

Ministerio de Educación. (2011). Estándares Orientadores para la Formación Inicial Docente. Unidad de Currículo y Evaluación: Santiago de Chile.

Ministerio de Educación. (2012a). Bases Curriculares 2012: Educación Básica Matemática. Unidad de Currículo y Evaluación: Santiago de Chile.

Ministerio de Educación. (2012b). Estándares Disciplinarios de Matemática con Ejemplos. Unidad de Currículo y Evaluación: Santiago de Chile.

Ministerio de Educación. (2018). Resultados Evaluación Diagnóstica Nacional 2017. Santiago, Chile.

Muñiz, J. (1994). Teoría Clásica de los Tests. Madrid: Pirámide.

Organisation for Economic Co‐Operation and Development (OECD). (2005). Teachers matter: Attracting, developing and retaining effective teachers. Paris, France: OCDE. https://www.oecd.org/education/school/34990905.pdf

Pincheira, N., & Vásquez, C. (2018). Conocimiento didáctico-matemático para la enseñanza de la matemática elemental en futuros profesores de educación básica: diseño, construcción y validación de un instrumento de evaluación. Revista Estudios Pedagógicos, 44(1), 25-48. doi: https://doi.org/10.4067/S0718-07052018000100025

Pino-Fan, L., & Godino, J. D. (2015). Perspectiva ampliada del conocimiento didáctico-matemático del profesor. Paradigma, 36(1), 87-109. http://ve.scielo.org/scielo.php?pid=S1011-22512015000100007&script=sci_abstract

Ponte, J. (2014). Práticas profissionais dos professores de Matemática. Portugal: Instituto de Educación de la Universidad de Lisboa.

Scheiner, T. (2015). Lessons we have (not) learned from past and current conceptualizations of mathematics teachers' knowledge. In: Krainer, K.; Vondrová, N. (Ed.). Proceedings of the CERME 9-Ninth Congress of the European Society for Research in Mathematics Education (pp. 3248-3253). Prague, Czech Republic. https://hal.archives-ouvertes.fr/hal-01289875

Segarra, J., & Julià, C. (2021). Conocimiento matemático de estudiantes para docentes de educación primaria: análisis de variables. Uniciencia, 35(1), 124-138. doi: http://doi.org/10.15359/ru.35-1.8

Tatto, M., et ál. (2012). Policy, Practice, and Readiness to Teach Primary and Secondary Mathematics in 17 countries: Findings from the IEA Teacher Education and Development Study in Mathematics (TEDS-M). International Association for the Evaluation of Educational Achievement. Herengracht 487, Amsterdam, 1017 BT, The Netherlands.

Vásquez, C., & Alsina, A. (2015). Conocimiento didáctico-matemático del profesorado de educación primaria sobre probabilidad: diseño, construcción y validación de un instrumento de evaluación. Bolema, 29(52), 681-703. http://dx.doi.org/10.1590/1980-4415v29n52a13

Vásquez, C., & Alsina, Á. (2017). Aproximación al conocimiento común del contenido para enseñar probabilidad desde el modelo de Conocimiento Didáctico-Matemático. Educación Matemática, 29(3), 79-108. doi: http://doi.org/10.24844/EM2903.03

Published

2021-07-31

Issue

Section

Original scientific papers (evaluated by academic peers)

Comentarios (ver términos de uso)