Mathematical and didactic knowledge of preservice primary teachers about the area of 2d figures

Authors

DOI:

https://doi.org/10.35763/aiem24.4076

Keywords:

Specialised knowledge, Subdomains of knowledge, Pre-service teachers, Area of flat figuresInterpreting student responses

Abstract

This study aims to characterize elements of the specialised knowledge of a group of pre-service teachers (PST). Emphasis is placed on the following subdomains: Knowledge of Topics, Knowledge of the Structure of Mathematics, Knowledge of the Features of Learning Mathematics and Knowledge of Mathematics Teaching. The procedures and written justifications that PST use in task-solving and in interpreting student responses to area tasks are analyzed. The results show that the use of procedures of a different nature is related to the mobilization of different indicators of Knowledge of Topics, while promoting the establishment of connections with other mathematical content. The indicators defined for the Knowledge of the Features of learning mathematics, and Knowledge of Mathematics teaching, are related to a greater capacity of the PST to interpret students’ responses.

Downloads

Download data is not yet available.
Supporting Agencies
ANID PFCHA/DOCTORADO BECAS CHILE/2018-72190032, PID2019-104964GB-I00 (MINECO-España) y GIPEAM, SGR-2017-101, AGAUR. Estudio realizado en el Programa de Doctorado en Educación de la Universidad Autónoma de Barcelona, España.

References

Badillo, E., & Fernández, C. (2018). Oportunidades que emergen de la relación entre perspectivas: análisis del conocimiento y/o competencia docente. En L. Rodríguez-Muñiz, L. Muñiz-Rodríguez, A. Aguilar-González, P. Alonso, F. García & A. Bruno (Eds.), Investigación en Educación Matemática XXII (pp. 66-80). SEIEM.

Ball, D. L., Thames, M., & Phelps, G. (2008). Content Knowledge for Teaching: What Makes It Special? Journal of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554

Bassey, M. (1990). On the nature of research in education. Research Intelligence.

Baturo, A., & Nason, R. (1996). Student teachers’ subject matter knowledge within the domain of area measurement. Educational studies in mathematics, 31(3), 235-268. https://doi.org/10.1007/BF00376322

Browning, C., Edson, A., Kimani, P., & Aslan-Tutak, F. (2014). Mathematical content knowledge for teaching elementary mathematics: A focus on geometry and measurement. The Mathematics Enthusiast, 11(2), 333-383. https://doi.org/10.54870/1551-3440.1306

Carrillo-Yañez, J., Climent, N., Contreras, L., & Muñoz-Catalán, M. (2013). Determining specialised knowledge for mathematics teaching. En B. Ubuz, C. Hasery & M. Mariotti (Eds.), Proceedings of the CERME 8 (pp. 2985-2994). ERME.

Carrillo-Yañez, J., Climent, N., Montes, M., Contreras, L., Flores-Medrano, E., Escudero-Ávila, D., Vasco, D., Rojas, N., Flores, P., Agular-González, A., Ribeiro, M., & Muñoz-Catalán, M. (2018). The mathematics teacher’s specialised knowledge (MTSK) model. Research in Mathematics Education, 20(3), 236-253. https://doi.org/10.1080/14794802.2018.1479981

Caviedes, S., De Gamboa, G., & Badillo, E. (2019). Conexiones matemáticas que establecen maestros en formación al resolver tareas de medida y comparación de áreas. Praxis, 15(1), 69-87. https://doi.org/10.21676/23897856.2984

Caviedes, S., De Gamboa, G., y Badillo, E. (2021a). Mathematical objects that configure the partial area meanings mobilized in task-solving. International Journal of Mathematical Education in Science and Technology, 54(6), 1092-1111. https://doi.org/10.1080/0020739X.2021.1991019

Caviedes, S., De Gamboa, G., & Badillo, E. (2021b). Aproximación al conocimiento especializado sobre área en estudiantes para maestro. En Diago, P. D., Yáñez D. F., González-Astudillo, M. T. & Carrillo, D. (Eds.), Investigación en Educación Matemática XXIV (pp. 213-220). SEIEM.

Fernández, C., & Choy, B. H. (2020). Theoretical lenses to develop mathematics teacher noticing. En S. Llinares & O. Chapman (Eds.), International Handbook of Mathematics Teacher Education (Vol. 2, pp. 337-360). Brill Sense.

Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Reidel.

Hong, D., & Runnalls, C. (2020). Examining Preservice Teachers’ Responses to Area Conservation Tasks. School Science and Mathematics, 120(5), 198-208. https://doi.org/10.1111/ssm.12409

Jacobs., Lamb, L., & Philipp, R. (2010). Professional noticing of children’s mathematical thinking. Journal for research in mathematics education, 41(2), 169-202. https://doi.org/10.5951/jresematheduc.41.2.0169

Krippendorff, K. (2004) Content Analysis: An Introduction to its Methodology. Sage.

Liñan, M., Barrera, V., & Infante, J. (2014). Conocimiento especializado de los estudiantes para maestro: La resolución de un problema con división de fracciones. Escuela Abierta, 17(1), 41-63. https://doi.org/10.29257/EA17.2014.04

Livy, S., Muir, T., & Maher, N. (2012). How do they measure up? Primary pre-service teachers’ mathematical knowledge of area and perimeter. Mathematics Teacher Education and Development, 14(2), 91-112.

Llinares, S. (2012). Formación de profesores de matemáticas. Caracterización y desarrollo de competencias docentes. Cuadernos, 10, 53-62.

Mason, J. (2002). Researching your own practice. The discipline of noticing. Routledge Falmer.

Montes, M., Aguilar, A., Carrillo, J., & Muñoz-Catalán, M. (2013). MTSK: From Common and Horizon Knowledge to Knowledge of Topics and Structures. En B. Ubuz, C. Haser, & M. Mariotti (Eds.), Proceedings of the CERME 8 (pp. 3185-3194). ERME.

Policastro, M., Mellone, M., Ribeiro, M., & Fiorentini, D. (2019). Conceptualising tasks for teacher education: from a research methodology to teachers’ knowledge development. En U. Jankvist, M. van den Heuvel-Panhuizen & M. Veldhuis (Eds.), Proceedings of the CERME 11 (No. 24). ERME.

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

Runnalls, C., & Hong. D. (2020). “Well, they understand the concept of area”: pre-service teachers’ responses to student area misconceptions. Mathematics Education Research Journal, 32(4), 629-651. https://doi.org/10.1007/s13394-019-00274-1

Sarama, J. & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. Routledge.

Scheiner, T., Montes, M., Godino, J. D., Carrillo-Yañez, J. & Pino-Fan, L. R. (2019). What makes mathematics teacher knowledge specialized? Offering alternative views. International Journal of Science and Mathematics Education, 17(1), 153-172. https://doi.org/10.1007/s10763-017-9859-6

Sherin, M. G., & van Es, E. (2009). Effects of Video Club Participation on Teachers’ Professional Vision. Journal of Teacher Education, 60(1), 20-37.

Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational researcher, 15(2), 4-14. https://doi.org/10.3102/ 0013189X015002004

Simon, M. & Blume, G. (1994). Building and understanding multiplicative relationships: A study of prospective elementary teachers. Journal for Research in Mathematics Education, 25(5), 472-494. https://doi.org/10.5951/jresematheduc.25.5.0472

Tatto, M., Peck, R., Schwille, J., Bankov, K., Senk, S. L., Rodriguez, M., Ingvarson, L., Reckase, M. & Rowley, G. (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-MM). International Association for the Evaluation of Educational Achievement.

Thomas, J., Jong, C., Fisher, M., & Schack, E. (2017). Noticing and Knowledge: Exploring Theoretical Connections between Professional Noticing and Mathematical Knowledge for Teaching. The Mathematics Educator, 26(2), 3-25.

Tierney, C., Boyd, C. & Davis, G. (1990). Prospective primary teachers’ conceptions of area. En G. Booker, P. P. Cobb & T. N. Mendicuti (Eds.), Proceedings of the IGPME 14 (Vol. 2, pp. 307-314). PME.

Published

2023-11-03

How to Cite

Caviedes, S., De Gamboa, G. ., & Badillo, E. (2023). Mathematical and didactic knowledge of preservice primary teachers about the area of 2d figures. Advances of Research in Mathematics Education, (24), 1–20. https://doi.org/10.35763/aiem24.4076

Issue

Section

Artículos