Building specialized knowledge in geometry: a teaching experiment in initial teacher training
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Keywords

Teaching Experiment
Videoanalysis
MTSK
Prospective Teacher Education
Polygon Experimento de Enseñanza
Vídeo Análisis
MTSK
Formación inicial de maestros
Polígono

How to Cite

Montes Navarro, M. Ángel, Climent, N., & Contreras, L. C. (2022). Building specialized knowledge in geometry: a teaching experiment in initial teacher training. Aula Abierta, 51(1), 27–36. https://doi.org/10.17811/rifie.51.1.2022.27-36

Abstract

We show a teaching experiment that uses video records as trigger for the construction of elements of professional knowledge, understood from the perspective of Mathematics Teachers’ Specialized Knowledge model. We will present the results of the implementation of a task with a whole group of prospective teachers, in particular, the session after the visualization of a video where a teacher of 5th year of Primary School builds a definition of polygon. The assessment of the achievements on the basis of specialized knowledge elements identified in a first implementation of the task conducted with three prospective primary teachers selected ad hoc, in the context of a one-to-one teaching experiment. These elements entail both mathematical a didactical content knowledge, in particular, knowledge about the definition of polygon, the mathematical practice of defining, tools and examples to teach polygons, difficulties in their learning, and the role of polygon in the syllabus. We will finish reflecting about how the task allows to build the specialized knowledge elements intended, and showing some future research possibilities.

https://doi.org/10.17811/rifie.51.1.2022.27-36
PDF (Español (España))

References

Alsawaie, O. N., y Alghazo, I. M. (2010). The effect of video-based approach on prospective teachers’ ability to analyze mathematics teaching. Journal of Mathematics Teacher Education, 13(3), 223-241. DOI: 10.1007/s10857-009-9138-8

Ball, D. L., Thames, M. H., y Phelps, G. (2008). Content knowledge for teaching: What makes its special? Journal of Teacher Education, 59(5), 389-407. DOI: 10.1177/0022487108324554

Barrantes, M., López, M. y Fernández, M. A. (2015). Análisis de las representaciones geométricas en los libros de texto. PNA, 9(2), 107-127. DOI: 10.30827/pna.v9i2.6105

Carrillo, J., y Climent, N. (2008). From professional tasks in collaborative environments to educational tasks in mathematics teacher education. En B. Clarke, B. Grevholm y R. Millman (eds.), Tasks in Primary Mathematics Teacher Education: Purpose, Use and Exemplars (Vol. 4, pp. 215-234). Springer. DOI: 10.1007/978-0-387-09669-8_15

Carrillo, J., Climent, N., Montes, M., Contreras, L. C., Flores-Medrano, E., Escudero-Ávila, D., Vasco, D., Rojas, N., Flores, P., Aguilar-González, A., Ribeiro, M., y Muñoz-Catalán, M. C. (2018). The Mathematics Teacher’s Specialised Knowledge (MTSK) model. Research in Mathematics Education, 20(3), 236-253. DOI: 10.1080/14794802.2018.1479981

Climent, N., Montes, M., Contreras, L. C., Carrillo, J., Liñán, M., Muñoz-Catalán, M. C, Barrera, V., y León, F. (2016). Construcción de conocimiento sobre características de aprendizaje de las Matemáticas a través del análisis de vídeos. Avances de Investigación En Educación Matemática, 9, 85-103. DOI: 10.35763/aiem.v0i9.108

Cobb, P., y Gravemeijer, K. (2008). Experimenting to support and understand learning processes. En A.E. Kelly, R. A. Lesh y J. Baek (eds.), Handbook of design research Methods in Education. Innovation in Science, technology, Engineering and Mathematics Learning and Teaching (pp. 68-95). Lawrence Erlbaum Associates. DOI:10.4324/9781315759593.

Codes, M., Climent, N., Oliveros, I. (2019). Prospective primary teachers’ knowledge about the mathematical practice of defining. En U. T. Jankvist, M. Van den Heuvel-Panhuizen y M. Veldhuis (eds.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME 11) (pp. 3871-3878). Freudenthal Group & Freudenthal Institute, Utrecht University y ERME.

De Villiers, M. (1998). To teach definitions in geometry or teach to define? En A. Oliver, y K. Newstead (ed.), Proceedings of the 22th Conference of the International Group for the Psychology of Mathematics Education. 2 (pp. 248-255). University of Stellenbosch.

De Villiers, M., Govender, R., y Patterson, N. (2009). Defining in Geometry. En T. Craine, y R. Rubinstein (eds.), Understanding Geometry for a Changing World (pp. 189-203). NCTM.

Escudero-Ávila, D., Gomes, J., Muñoz-Catalán, M.C., Flores-Medrano, E., Flores, P., Rojas, N., Aguilar, A. (2015). Aportaciones metodológicas de investigaciones con MTSK. En J. Carrillo, L.C. Contreras y M. Montes (Eds.), Reflexionando sobre el conocimiento del profesor. Actas de las II Jornadas del Seminario de Investigación de Didáctica de la Matemática de la Universidad de Huelva (pp. 60-68). SGSE.

Fernández, C., Sánchez-Matamoros, G., Valls, J., y Callejo, M. L. (2018). Noticing students’ mathematical thinking: characterization, development and contexts. Avances de Investigación en Educación Matemática, 13, 39-61.

DOI: 10.35763/aiem.v0i13.229

Fortuny, J. M., y Rodríguez, R. (2012). Aprender a mirar con sentido: facilitar la interpretación de las interacciones en el aula. Avances de Investigación en Educación Matemática, 1, 23-37.

García, F. J., Maas, K., y Wake, G. (2010). Theory meets practice: Working pragmatically within diferent cultures and traditions. En R. Lesh, P. Galbraith, C. Haines y A. Hurford (eds.), Modeling Students’ Mathematical Modeling Competencies (pp. 445-457). Springer. https://doi.org/10.1007/978-1-4419-0561-1

Grevholm, B., Millman, R., y Clarke, B. (2009). Function, Form, and Focus: The role of Tasks in Elementary Mathematics Teacher Education. En B. Clarke, B. Grevholm y R. Millman (eds.), Tasks in Primary Mathematics Education: Purpose, Use and Exemplars (pp. 1-5). New York. DOI: 10.1007/978-0-387-09669-8_1

Lampert, M., y Ball, D.L. (1998). Teaching, Multimedia and Mathematics: Investigations of Real Practice. Teachers College Press, Columbia University.

Lin, F.L., y Rowland, T. (2016). Pre-Service and In-Service Mathematics Teachers’ Knowledge and Professional Development. En Á. Gutiérrez, G.C. Leder y P. Boero (eds.), The Second Handbook of Research on the Psychology of Mathematics Education (pp. 483-519). Sense Publishers. DOI:10.1007/978-94-6300-561-6_14

Mason, J. (2021). Learning about noticing, by, and through, noticing. ZDM Mathematics Education, 53, 231–243. DOI: 10.1007/s11858-020-01192-4

Millman, R., Svec, K., y Williams, D. (2009). Tasks using video clips of children in a content Mathematics course for future elementary school teachers. En B. Clarke, B. Grevholm y R. Millman (eds.), Tasks in Primary Mathematics Teacher Education: Purpose, Use, and Exemplars (pp. 105-112). Springer. DOI: 10.1007/978-0-387-09669-8_8

Molina, M., Castro, E., Molina, J.L., y Castro, E. (2011). Un acercamiento a la investigación de diseño a través de los experimentos de enseñanza. Enseñanza de las Ciencias, 29(1), 75-88. https://doi.org/10.5565/rev/ec/v29n1.435

Montes, M., Carrillo, J., Contreras, L. C., Liñán-García, M. M., y Barrera-Castarnado, V. J. (2019). Estructurando la formación inicial de Profesores de Matemáticas: una propuesta desde el modelo MTSK. En E. Badillo, N. Climent, C. Fernández y M. T. González (eds.), Investigación sobre el profesor de matemáticas: formación, práctica de aula, conocimiento y competencia profesional (pp. 157-176). Ediciones Universidad de Salamanca.

Rowland, T., Turner, F., Thwaites, A., y Huckstep, P. (2009). Developing primary mathematics teaching. Reflecting on practice with the Knowledge Quartet. SAGE. DOI: 10.4135/9781446279571

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

Star, J. R., y Strickland, S. K. (2008). Learning to observe: Using video to improve preservice mathematics teachers’ ability to notice. Journal of Mathematics Teacher Education, 11(2), 107-125. DOI: 10.1007/s10857-007-9063-7

Ulusoy, F. (2020). Prospective Early Childhood and Elementary School Mathematics Teachers’ Concept Images and Concept Definitions of Triangles. International Journal of Science and Mathematics Education, 1-22. https://doi.org/10.1007/s10763-020-10105-6

van Es, E. A., y Sherin, M. G. (2010). The influence of video clubs on teachers’ thinking and practice. Journal of Mathematics Teacher Education, 13(2), 155–176. DOI: 10.1007/s10857-009-9130-3

Vinner, S. (1991). The role of definitions in the teaching and learning of mathematics. En D. Tall (ed.), Advanced Mathematical Thinking (pp. 65-81). Kluwer Academic Publishers. DOI:10.1007/0-306-47203-1_5

Vinner, S., y Hershkowitz, R. (1983). On concept formation in geometry. ZDM, 83, 20-25. DOI: 10.1007/BF00452223

Ward, R. A. (2004). An Investigation of K-8 Preservice Teachers' Concept Images and Mathematical Definitions of Polygons. Issues in Teacher Education, 13(2), 39-56.

Watson, A., y Mason, J. (2005). Mathematics as a constructive activity: Learners generating examples. Erlbaum. DOI: 10.4324/9781410613714

Zakaryan, D., y Ribeiro, M. (2019). Mathematics teachers’ specialized knowledge: a secondary teacher's knowledge of rational numbers. Research in Mathematics Education, 21(1), 25-42. DOI:10.1080/14794802.2018.1525422

Zaslavsky, O., Harel, G., y Manaster, A. (2006). A teacher’s treatment of examples as reflection of her knowledge-base. En J. Novotná, H. Moraová, M. Krátká y N. Stehliková (Eds.), Proceedings of the 30th conference of the international group for the psychology of mathematics education (Vol. 5, pp. 457-464).

Zaslavsky, O., y Shir, K. (2005). Students’ Conception of a Mathematical Definition. Journal for Research in Mathematics Education, 36(4), 317-346. DOI:10.2307/30035043

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