Explorando la percepción de futuros maestros de primaria sobre el pensamiento matemático de los alumnos en un problema de proporcionalidad
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Palabras clave

razonamiento proporcional
Formación de profesores
conocimiento didáctico-matemático
análisis cognitivo proportional reasoning
didactic-mathematical knowledge
cognitive analysis
teacher training

Cómo citar

Burgos, M., & Chaverri, J. (2023). Explorando la percepción de futuros maestros de primaria sobre el pensamiento matemático de los alumnos en un problema de proporcionalidad. Aula Abierta, 52(1), 43–52. https://doi.org/10.17811/rifie.52.1.2023.43-52

Resumen

Para garantizar un proceso de enseñanza y aprendizaje óptimo, el profesor de matemáticas debe ser capaz de analizar, interpretar y valorar la actividad matemática que desarrollan sus alumnos cuando resuelven las tareas que les propone. Esta competencia permite al profesor comprender los logros de aprendizaje y las dificultades que muestran los estudiantes de cara a tomar decisiones de acción pertinentes. El objetivo de este trabajo es describir y analizar la competencia de un grupo de 130 futuros maestros de educación primaria para interpretar las respuestas de estudiantes ante una situación de proporcionalidad (problema de comparación). Entre los resultados obtenidos destacamos un conocimiento didáctico-matemático del razonamiento proporcional insuficiente que impide a los futuros maestros interpretar de forma pertinente el grado de corrección en las soluciones o el pensamiento matemático aparente de los estudiantes.

https://doi.org/10.17811/rifie.52.1.2023.43-52
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Citas

Bartell, T. G., Webel, C., Bowen, B. y Dyson, N. (2013). Prospective teacher learning: recognizing evidence of conceptual understanding. Journal of Mathematics Teacher Education, 16(1), 57–79. https://doi.org/10.1007/s10857-012-9205-4

Ben-Chaim, D., Keret, Y. y Ilany, B. (2012) Ratio and proportion: Research and teaching in mathematics teachers’ education. Sense Publisher. https://doi.org/10.1007/978-94-6091-784-4

Buforn, A., Llinares, S. y Fernández, C. (2018) Características del conocimiento de los estudiantes para maestros españoles en relación con la fracción, razón y proporción. Revista Mexicana de Investigación Educativa, 23, 229–251. https://doi.org/10.1007/s10857-005-0853-5

Buforn, A., Llinares, S., Fernández, C., Coles, A. y Brown, L. (2020). Pre-service teachers’ knowledge of the unitizing process in recognizing students’ reasoning to propose teaching decisions. International Journal of Mathematics Education in Science and Technology, 1–9. https://doi.org/10.1080/0020739X.2020.1777333

Burgos, M. y Godino J. D. (2022a). Assessing the Epistemic Analysis Competence of Prospective Primary School Teachers on Proportionality Tasks. International Journal of Science and Mathematics Education, 20, 367–389. https://doi.org/10.1007/s10763-020-10143-0.

Burgos, M. y Godino, J. D. (2022b). Prospective Primary School Teachers’ Competence for the Cognitive Analysis of Students’ Solutions to Proportionality Tasks. Journal für Mathematik-Didaktik, 42 (2), 1-30. https://doi.org/10.1007/s13138-021-00193-4

Chapman, O. (2014). Overall commentary: understanding and changing mathematics teachers. En J. J. Lo; K. R. Leatham y L. R. Van Zoest (Eds.) Research Trends in Mathematics Teacher Education (pp. 295–309). Springer International Publishing. https://doi.org/10.1007/978-3-319-02562-9_16

Cohen, L., Manion, L., y Morrison, K. (2018). Research methods in education. Routledge.

Depaepe, F., Verschaffel, L. y Star, J. (2020). Expertise in developing students’ expertise in mathematics: Bridging teachers’ professional knowledge and instructional quality. ZDM. The International Journal on Mathematics Education, 52(2), 179–192. https://doi.org/10.1007/s11858-020-01148-8

Fernández, C., Llinares, C. y Valls, J. (2012). Learning to notice students' mathematical thinking through online discussions. ZDM. Mathematics Education, 44, 747–759. https://doi.org/10.1007/s11858-012-0425-y

Fernández, C., Llinares, S. y Valls, J. (2013). Primary school teacher’s noticing of students’ mathematical thinking in problem solving. The Mathematics Enthusiast, 10(1), 441–468. https://doi.org/10.54870/1551-3440.1274

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. https://doi.org/10.35763/aiem.v0i13.229

Godino, J. D., Batanero, C. y Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM. The International Journal on Mathematics Education, 39(1-2), 127-135. https://doi.org/10.1007/s11858-006-0004-1

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

Gómez, B. y García, A. (2014). Componentes críticas en tareas de comparación de razones desiguales. En M. T. González, M. Codes, D. Arnau y T. Ortega (Eds.), Investigación en Educación Matemática, XVIII (pp. 375-384). SEIEM.

Hilton, A. y Hilton, G. (2019). Primary school teachers implementing structured mathematics interventions to promote their mathematics knowledge for teaching proportional reasoning. Journal of Mathematics Teacher Education, 22, 545–574. https://doi.org/10.1007/s10857-018-9405-7

Izsák, A. y Jacobson, E. (2017). Preservice teachers’ reasoning about relationships that are and are not proportional: A knowledge-in-pieces account. Journal for Research in Mathematics Education, 48(3), 300–339. https://doi.org/10.5951/jresematheduc.48.3.0300

Ivars, P., Fernández, C., Llinares, S. y Choy, B. H. (2018). Enhancing noticing: Using a hypothetical learning trajectory to improve pre-service primary teachers’ professional discourse. Eurasia Journal of Mathematics, Science and Technology Education, 14(11), em1599. https://doi.org/10.29333/ejmste/93421

Jacobs, V. R., Lamb, L. C. y 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

Jakobsen, A., Ribeiro, C. M. y Mellone, M. (2014). Norwegian prospective teachers’ MKT when interpreting pupils’ productions on a fraction task. Nordic Studies in Mathematics Education, 19(3-4), 135–150.

Lamon, S. (2007). Rational number and proportional reasoning: toward a theoretical framework for research. En F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629–667). NC: Information Age Publishing.

Mason, J. (2016). Perception, interpretation and decision making: understanding gaps between competence and performance-a commentary. ZDM, 48(1-2), 219–226. https://doi.org/10.1007/s11858-016-0764-1

Nagar, G. G., Weiland, T., Brown, R. E., Orrill, C. H. y Burke, J. (2016). Appropriateness of proportional reasoning: Teachers’ knowledge used to identify proportional situations. En M. B. Wood, E. E. Turner, M. Civil, y J. A. Eli (Eds.), Proceedings of the 38th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 474–481). University of Arizona.

Ponte, J. P. y Chapman, O. (2016). Prospective mathematics teachers’ learning and knowledge for teaching. En L. D. English y D. Kirshner (Eds.), Handbook of international research in mathematics education (3rd ed., pp. 275–296). NY: Routledge.

Riley, K. J. (2010). Teachers’ understanding of proportional reasoning. En P. Brosnan, D. B. Erchick y L. Flevares (Eds.), Proceedings of the 32nd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (vol. 6, pp. 1055-1061). Ohio State University.

Scheiner, T., Montes, M. A., Godino, J. D., Carrillo, J. y 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

Simpson, A. y Haltiwanger, L. (2017). This is the first time I’ve done this: Exploring secondary prospective mathematics teachers’ noticing of students’ mathematical thinking. Journal of Mathematics Teacher Education, 20(4), 335–355. https://doi.org/10.1007/s10857-016-9352-0

Son, J. (2013). How preservice teachers interpret and respond to student errors: Ratio and proportion in similar rectangles. Educational Studies in Mathematics, 84, 49–70. https://doi.org/10.1007/s10649-013-9475-5

Weiland, T., Orrill, C., Brown, R. y Nagar, G. G. (2019). Mathematics teachers’ ability to identify situations appropriate for proportional reasoning. Research in Mathematics Education, 21(3), 233–250. https://doi.org/10.1080/14794802.2019.1579668

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