Keywords
Formación de profesores
conocimiento didáctico-matemático
análisis cognitivo proportional reasoning
didactic-mathematical knowledge
cognitive analysis
teacher training
How to Cite
Abstract
In order to ensure an optimal teaching and learning process, the mathematics teacher must be able to analyse, interpret and assess the mathematical activity of his/her students when they solve the tasks he/she sets them. This competence enables the teacher to understand the learning achievements and difficulties that students show to make relevant decisions for action. The aim of this paper is to describe and analyse the competence of a group of 130 prospective primary school teachers to interpret students' responses to a situation of proportionality (comparison problem). Among the results obtained, we highlight an insufficient didactic-mathematical knowledge of proportional reasoning, which prevents future teachers from interpreting in a relevant way the degree of correctness in the solutions or the apparent mathematical thinking of the students.
References
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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