Observing Mathematics Teaching Practices to Promote Professional Development: An Analysis of Approaches to Probability

Claudia Vásquez; Ángel Alsina

doi:10.29333/iejme/5866

Full Text (PDF)

Claudia Vásquez ¹ ^* , Ángel Alsina ²

More Detail

¹ Pontificia Universidad Católica de Chile, CHILE² Universidad de Girona, SPAIN^* Corresponding Author

Abstract

This study aims to analyse the approaches to probability that were carried out by the participants of the teaching practice of Primary Education teachers and, more specifically, their teaching trajectories. To do this we analysed 23 video-recorded classes of all levels, using a previously validated instrument. Results show trajectories characterised by a strong presence of intuitive approach at initial levels, in conjunction with a much lower presence of frequency approach and an absence of other approaches. As the level increases, the presence of intuitive approach decreases, being replaced by subjective, frequency and classical ones, with the latter two having the greatest presence in the upper levels. We conclude that results will be useful for strengthening the professional development of Primary Education teachers in relation to the teaching of probability.

Keywords

teaching probability
approaches to probability
teaching trajectories
professional development
primary education

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

INT ELECT J MATH ED, Volume 14, Issue 3, October 2019, 719-733

https://doi.org/10.29333/iejme/5866

Publication date: 31 Jul 2019

Article Views: 3234

Article Downloads: 1959

Open Access References How to cite this article

References

Alsubaie, M. A. (2015). Hidden curriculum as one of current issue of curriculum. Journal of Education and Practice, 6(33), 125-128.
Batanero, C. (2005). Significados de la probabilidad en la educación secundaria. RELIME, 8(3), 247-264.
Batanero, C., & Díaz, C. (2007). Meaning and understanding of mathematics. The case of probability. In J. P. Van Bendegen and K. François (Eds.), Philosophical dimensions in mathematics education (pp. 107-127). New York: Springer. https://doi.org/10.1007/978-0-387-71575-9_6
Batanero, C., Henry, M., & Parzysz, B. (2005). The nature of chance and probability. In G. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 15-37). New York: Springer. https://doi.org/10.1007/0-387-24530-8_2
Bernoulli, J. (1987). Ars conjectandi- 4ème partie (N. Meunier, Trans.) Rouen: IREM.
Bisquerra, R. (2009). Metodología de la investigación educativa. Madrid: La Muralla.
Common Core State Standards Initiative. (2010). Common Core State Standards for Mathematics. Retrieved from http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf
de Finetti, B. (1937). La prevision: ses lois logiques, ses sources subjectives. Annales de l’Institut Henri Poincaré, 7, 1-68.
de Moivre A. (1967). The doctrine of chances. New York: Chelsea Publishing.
Everitt, B. S. (2008). Chance rules: An informal guide to probability, risk, and statistics. New York: Copernicus, Springer-Verlag. https://doi.org/10.1007/978-0-387-77415-2
Fischbein. (1975). The intuitive sources of probabilistic thinking in children. Dordrecht: Reidel. https://doi.org/10.1007/978-94-010-1858-6
Gal, I. (2005). Towards “probability literacy” for all citizens: building blocks and instructional dilemas. In G. Jones (Ed.), Exploring Probability in Schools: Challenges for Teaching and Learning (pp. 39-63). New York: Springer. https://doi.org/10.1007/0-387-24530-8_3
Godino, J. D., Batanero, C., & Cañizares, M. J. (1987). Azar y Probabilidad. Fundamentos didácticos y propuestas curriculares. Madrid: Síntesis.
Hacking, I. (1995). El surgimiento de la probabilidad: un estudio filosófico de las ideas tempranas acerca de la probabilidad, la inducción y la inferencia estadística. Barcelona: Gedisa.
Laplace, P. S. (1985). Ensayo filosófico sobre las probabilidades. Madrid: Alianza Editorial.
Lecoutre, M. P. (1992). Cognitive Models and Problem spaces in “Purely Random” Situations. Educational Studies in Mathematics, 23, 557-568. https://doi.org/10.1007/BF00540060
Ministerio de Educación de Chile [MINEDUC]. (2012). Bases Curriculares 2012: Educación Básica Matemática. Santiago de Chile: Unidad de Curriculum y Evaluación.
Ministerio de Educación y Ciencia [MEC]. (2007). Boletín oficial del Estado. ORDEN ECI/2211/2007, del 20 de julio, por la que se establece el currículo y regula la ordenación de la Educación Primaria. Madrid, Spain.
Ministry of Education Singapore. (2007). Curriculum Planning and Development Division. Ministry of Education, Singapore. Retrieved from http://www.moe.gov.sg
National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, Va.: The National Council of Teachers of Mathematics.
National Curriculum. (1999). The National Curriculum for England, Mathematics. Retrieved from www.nc.uk.net
Orón J. V., & Blasco, M. (2018). Revealing the hidden curriculum in Higher education. Studies in Philosophy and Education, 37(5), 481-498. https://doi.org./10.1007/s11217-018-9608-5
Praetorius, A.-K., Pauli, C., Reusser, K., Rakoczy, K., & Klieme, E. (2014). One lesson is all you need? Stability of instructional quality across lessons. Learning and Instruction, 31(1), 2-12. https://doi.org/10.1016/j.learninstruc.2013.12.002
Rojas, N., Carrillo, J., & Flores, P. (2012). Características para identificar a profesores de matemáticas expertos. In A. Estepa, A. Contreras, J. Deulofeu, M. C. Penalva, F. J. García and L. Ordoñez (Eds.), Investigación en Educación Matemática XVI (pp. 479-485). Jaén: SEIEM.
Schlesinger, L., & Jentsch, A. (2016). Theoretical and methodological challenges in measuring instructional quality in mathematics education using classroom observations. ZDM: The International Journal on Mathematics Education, 48(1-2), 29-40. https://doi.org/10.1007/s11858-016-0765-0
Shaughnessy, J. M. (1992). Research in probability and statistics: Reflections and directions. In D. A. Grows (Ed.), Handbook of research on mathematics teachingand learning (pp. 465-494). New York: MacMillan.
Steinbring, H. (1990). The nature of stochastical knowledge and the traditional mathematics curriculum. Some experiences with in-service training and developing materials. En A. Hawkins (Ed.), Training teachers to teach statistics (pp. 2-19). Voorburg: ISI.
Tinsley, H. E. A., & Brown, S. D. (2000). Handbook of Applied Multivariate Statistics and Mathematical Modeling. Gainesville, USA: Academic Press. https://doi.org/10.1016/B978-012691360-6/50002-1
Vásquez, C., & Alsina, A. (2014). Enseñanza de la probabilidad en Educación Primaria. Un desafío para la formación inicial y continua del professorado. Números, 85, 5-23.
Vásquez, C., & Alsina, Á. (2015). Un modelo para el análisis de objetos matemáticos en libros de texto chilenos: situaciones problemáticas, lenguaje y conceptos sobre probabilidad. Profesorado, Revista de currículum y formación del profesorado, 19(2), 441-462.
Vásquez, C., & Alsina, Á. (2017). Aproximación al conocimiento común del contenido para enseñar probabilidad desde el modelo del Conocimiento Didáctico-matemático. Educación Matemática, 29(3), 79-108.
Vásquez, C., & Alsina, Á. (in press). Diseño, construcción y validación de una pauta de observación de los significados de la probabilidad en el aula de Educación Primaria. REVEMAT.
von Mises, R. (1952). Probabilidad, estadística y verdad. Madrid: Espasa Calpe.

How to cite this article

APA

Vásquez, C., & Alsina, Á. (2019). Observing Mathematics Teaching Practices to Promote Professional Development: An Analysis of Approaches to Probability. International Electronic Journal of Mathematics Education, 14(3), 719-733. https://doi.org/10.29333/iejme/5866

Vancouver

Vásquez C, Alsina Á. Observing Mathematics Teaching Practices to Promote Professional Development: An Analysis of Approaches to Probability. INT ELECT J MATH ED. 2019;14(3):719-33. https://doi.org/10.29333/iejme/5866

AMA

Vásquez C, Alsina Á. Observing Mathematics Teaching Practices to Promote Professional Development: An Analysis of Approaches to Probability. INT ELECT J MATH ED. 2019;14(3), 719-733. https://doi.org/10.29333/iejme/5866

Chicago

Vásquez, Claudia, and Ángel Alsina. "Observing Mathematics Teaching Practices to Promote Professional Development: An Analysis of Approaches to Probability". International Electronic Journal of Mathematics Education 2019 14 no. 3 (2019): 719-733. https://doi.org/10.29333/iejme/5866

Harvard

Vásquez, C., and Alsina, Á. (2019). Observing Mathematics Teaching Practices to Promote Professional Development: An Analysis of Approaches to Probability. International Electronic Journal of Mathematics Education, 14(3), pp. 719-733. https://doi.org/10.29333/iejme/5866

MLA

Vásquez, Claudia et al. "Observing Mathematics Teaching Practices to Promote Professional Development: An Analysis of Approaches to Probability". International Electronic Journal of Mathematics Education, vol. 14, no. 3, 2019, pp. 719-733. https://doi.org/10.29333/iejme/5866