Conocimiento sobre fracciones de docentes de primaria en formación

Autores/as

DOI:

https://doi.org/10.15359/ru.35-2.10

Palabras clave:

Análisis didáctico, contenidos didácticos, conocimiento en contenidos didácticos, formación de profesorado, fracciones, conocimiento matemático, educación matemática

Resumen

En este trabajo profundizamos en el conocimiento sobre contenidos didácticos que futuro profesorado de primaria pone en juego al responder preguntas relativas a la enseñanza y el aprendizaje del concepto de fracción. Llevamos a cabo una metodología cualitativa, específicamente un estudio de casos. Realizamos entrevistas estructuradas a 9 estudiantes para docentes de primaria que estaban finalizando sus estudios universitarios. Para ello, introdujimos a los sujetos en el tema a través de una narración que ellos mismos habían realizado anteriormente sobre cómo iniciar a escolares en el concepto de fracción. Tras su lectura, planteamos preguntas relativas al diseño de tareas, objetivos de aprendizaje, y errores y dificultades. En los resultados identificamos dos tendencias en el conocimiento manifestado por los sujetos participantes. La primera de ellas es una tendencia procedimental o técnica en la que el conocimiento manifestado hace hincapié en llevar a cabo procedimientos, procesos o modos de actuación. En la segunda de las tendencias, conceptual o cognitiva, el conocimiento manifestado pone el énfasis en la comprensión funcional de las fracciones y sus relaciones. Concluimos que es fundamental que la formación inicial de profesorado haga hincapié tanto en contenidos matemáticos como en contenidos didácticos.

Referencias

Adu-Gyamfi, K., Schwartz, C. S., Sinicrope, R. and Bossé, M. (2019). Making sense of fraction division: domain and representation knowledge of preservice elementary teachers on a fraction division task. Mathematics Education Research Journal, 31, 507-528. https://doi.org/10.1007/s13394-019-00265-2

Behr, M. J., Lesh, R. Post, T. R. and Silver, E. A. (1983). Rational number concept. In R. Lesh and M. Landau (Editors), Acquisitions of Mathematics Concepts and Processes (p. 91-126). Academy Press.

Behr, M. J., Wachsmuth, I., Post, T. R. and Lesh, R. (1984). Order and equivalence of rational numbers: A clinical teaching experiment. Journal for Research in Mathematics Education, 15(5), 323–341. https://doi.org/10.2307/748423

Castro-Rodríguez, E., Pitta-Pantazi, D., Rico, L. and Gómez, P. (2016). Prospective teachers’ understanding of the multiplicative part-whole relationship of fraction. Educational Studies in Mathematics, 92(1), 129-146. https://doi.org/10.1007/s10649-015-9673-4

Charalambous, C. Y. (2016). Investigating the Knowledge Needed for Teaching Mathematics: An Exploratory Validation Study Focusing on Teaching Practices. Journal of Teacher Education, 67(3) 220-237. https://doi.org/10.1177/0022487116634168

Charalambous, C. Y., Hill, H. C. and Ball, D. L. (2011). Prospective teachers’ learning to provide instructional explanations: How does it look and what might it take? Journal of Mathematics Teacher Education, 14(6), 441-463. https://doi.org/10.1007/s10857-011-9182-z

Cramer, K. A., Post, T. R., and del Mas, R. C. (2002). Initial fraction learning by fourth- and fifth-grade students: a comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum. Journal for Research in Mathematics Education, 33(2), 111-144. https://doi.org/10.2307/749646

D’Ambrosio, B. S. and Mendonça-Campos, T. N. (1992). Pre-service teachers’ representations of children’s understanding of mathematical concepts: Conflicts and conflict resolution. Educational Studies in Mathematics, 23(3), 213-230. https://doi.org/10.1007/BF02309530

Depaepe, F., Torbeyns, J., Vermeersch, N., Janssens, D., Janssen, R., Kelchtermans, G., and Van Dooren, W. (2015). Teachers’ content and pedagogical content knowledge on rational numbers: A comparison of prospective elementary and lower secondary school teachers. Teaching and teacher education, 47, 82-92. https://doi.org/10.1016/j.tate.2014.12.009

Domoney, B. (2001). Student teachers’ understanding of rational numbers. In J. Winter (Ed.), Proceedings of the British Society for Research into Learning Mathematics, (Vol. 21, num. 3, pp. 13-18). BSRLM.

Isiksal, M. and Cakiroglu, E. (2011). The nature of prospective mathematics teachers’ pedagogical content knowledge: The case of multiplication of fractions. Journal of Mathematics Teacher Education, 14(3), 213-230. https://doi.org/10.1007/s10857-010-9160-x

Jacobson, E. and Izsák, A. (2015). Knowledge and motivation as mediators in mathematics teaching practice: The case of drawn models for fraction arithmetic. Journal of Mathematics Teacher Education, 18(5), 467-488. https://doi.org/10.1007/s10857-015-9320-0

Jacobson, E., Lobato, J. and Orrill, C. H. (2018). Middle school teachers’ use of mathematics to make sense of student solutions to proportional reasoning problems. International Journal of Science and Mathematics Education, 16, 1541-1559. https://doi.org/10.1007/s10763-017-9845-z

Kang, R. and Liu, D. (2018). The importance of multiple representations of mathematical problems: Evidence from Chinese preservice elementary teachers’ analysis of a learning goal. International Journal of Science and Mathematics Education, 16, 125-143. https://doi.org/10.1007/s10763-016-9760-8

Kieren, T. E. (1993). The Learning of Fractions: Maturing in a Fraction. Paper presented at the Conference Fraction Learning and Instruction, GA, Athens.

Klemer, A., Rapoport, S. and Lev-Zamir, H. (2019). The missing link in teachers’ knowledge about common fractions division. International Journal of mathematical education in science and technology, 50(8), 1256-1272. https://doi.org/10.1080/0020739X.2018.1522677

Krippendorff, K. (1990). Metodología de análisis de contenido. Teoría y práctica. Paidós. In Spanish.

Lamon, S. J. (2005). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers (2nd ed.). Lawrence Erlbaum Associates. https://doi.org/10.4324/9781410617132

Lee, M. Y. and Lee, J. E. (2019). Pre-service Teachers’ Perceptions of the Use of Representations and Suggestions for Students’ Incorrect Use. Eurasia Journal of Mathematics, Science and Technology Education, 15(9), em1745. https://doi.org/10.29333/ejmste/103055

Lee, S. J., Brown, R. E. and Orrill, C. H. (2011). Mathematics teachers’ reasoning about fractions and decimals using drawn representations. Mathematical Thinking and Learning, 13(3), 198-220. https://doi.org/10.1080/10986065.2011.564993

Li, Y. and Kulm, G. (2008). Knowledge and confidence of pre-service mathematics teachers: the case of fraction division. ZDM, 40, 833-843. https://doi.org/10.1007/s11858-008-0148-2

Lo, J. and Grant, T. (2012). Preservice elementary teachers’ conceptions of fractional units. In T. Y. Tso (Ed.), Proceedings of the 36th PME (Vol. 3, p. 169-176). PME.

Lupiáñez, J. L. (2009). Expectativas de aprendizaje y planificación curricular en un programa de formación inicial de profesores de matemáticas de secundaria [Doctoral Dissertation]. Universidad de Granada, España. https://fqm193.ugr.es/produccion-cientifica/tesis/ver_detalles/5489/. In Spanish.

Lupiáñez, J. L. (2013). Análisis didáctico: La planificación del aprendizaje desde una perspectiva curricular. In L. Rico, J. L. Lupiáñez and M. Molina (Editors), Análisis didáctico en educación matemática (p. 81-102). Comares. In Spanish.

Mack, N. K. (1990). Learning fractions with understanding: building on informal knowledge. Journal for Research in Mathematics Education, 21(1), 16-32. https://doi.org/10.5951/jresematheduc.21.1.0016

Marks, R. (1990). Pedagogical Content Knowledge: From a Mathematical Case to a Modified Conception. Journal of Teacher Education, 41(3), 3-11. https://doi.org/10.1177/002248719004100302

Morris, A. K., Hiebert, J. and Spitzer, S. M. (2009). Mathematical knowledge for teaching in planning and evaluating instruction: What can preservice teacher learn? Journal for Research in Mathematics Education, 40(5), 491-529. https://doi.org/10.5951/jresematheduc.40.5.0491

Movshovitz-Hadar N., Zaslavsky O. and Inbar S. (1987). An empirical classification model for errors in high school mathematics. Journal for Research in Mathematics Education, 18, 3-14. https://doi.org/10.2307/749532

Newton, K. J. (2008). An Extensive Analysis of Preservice Elementary Teachers’ Knowledge of Fractions. American Educational Research Journal, 45(4), 1080-1110. https://doi.org/10.3102/0002831208320851

Rico, L. (2016). Matemática y análisis didáctico. In L. Rico and A. Moreno (Editors), Elementos de didáctica de la matemática para el profesor de secundaria (p. 85-100). Pirámide. In Spanish.

Rojas, N., Flores, P. and Carrillo, J. (2015). Conocimiento especializado de un profesor de matemáticas de Educación Primaria al enseñar los números racionales. Boletim de Educação Matemática, 29(51), 143-166. https://doi.org/10.1590/1980-4415v29n51a08. In Spanish.

Rosli, R., Goldsby, D., Onwuegbuzie, A. J., Capraro, M. M., Capraro, R. M. and González, E. G. Y. (2020). Elementary preservice teachers’ knowledge, perceptions, and attitudes towards fractions: A mixed-analysis. Journal on Mathematics Education, 11(1), 59-76. http://doi.org/10.22342/jme.11.1.9482.59-76.

Şahin, O., Gökkurt, B. and Soylu, Y. (2016). Examining prospective mathematics teachers’ pedagogical content knowledge on fractions in terms of students’ mistakes. International Journal of Mathematical Education in Science and Technology, 47(4), 531-551. https://doi.org/10.1080/0020739X.2015.1092178

Sánchez, M. (2011). A review of research trends in mathematics teacher education. PNA, 5(4), 129-145.

Socas, M. M. (1997). Dificultades, obstáculos y errores en el aprendizaje de las matemáticas en la educación secundaria. In L. Rico (Coord.), E. Castro, E. Castro, M. Coriat, A. Marín, L. Puig, et al., La educación matemática en la enseñanza secundaria (p. 125-154). Horsori. In Spanish.

Stake, R. E. (2010). Investigación cualitativa: El estudio de cómo funcionan las cosas. The Guilford Press. In Spanish.

Steffe, L. P. and Olive, J. (1990). Constructing fractions in computer microworlds. In G. Booker, P. Cobb and T. N. de Mendicuti (Editors), Proceedings of the 14th PME (p. 59-66). CONACYT.

Streefland, L. (1991). Fractions in Realistic Mathematics Education: A Paradigm of Developmental Research. Kluwer Academic Publishers. https://doi.org/10.1007/978-94-011-3168-1

Tirosh, D. (1999). Forms of mathematical knowledge: learning and teaching with understanding. In D. Tirosh (Ed.), Forms of mathematical knowledge (p. 1-9). Springer. https://doi.org/10.1007/978-94-017-1584-3_1

Tröbst, S., Kleickmann, T., Depaepe, F., Heinze, A. and Kunter, M. (2019). Effects of instruction on pedagogical content knowledge about fractions in sixth-grade mathematics on content knowledge and pedagogical knowledge. Unterrichtswissenschaft, 47(1), 79-97. https://doi.org/10.1007/s42010-019-00041-y

Tröbst, S., Kleickmann, T., Heinze, A., Bernholt, A., Rink, R. and Kunter, M. (2018). Teacher knowledge experiment: Testing mechanisms underlying the formation of preservice elementary school teachers’ pedagogical content knowledge concerning fractions and fractional arithmetic. Journal of Educational Psychology, 110(8), 1049-1065. https://doi.org/10.1037/edu0000260

Whitacre, I., Atabaş, Ş. and Findley, K. (2019). Exploring unfamiliar paths through familiar mathematical territory: Constraints and affordances in a preservice teacher’s reasoning about fraction comparisons. The Journal of Mathematical Behavior, 53, 148-163. https://doi.org/10.1016/j.jmathb.2018.06.006

Wu, H. H. (2018) The content knowledge mathematics teachers need. In Y. Li, W. Lewis, J. Madden (Editors), Mathematics matters in education. Advances in STEM education (p. 43-91). Springer. https://doi.org/10.1007/978-3-319-61434-2_4

Publicado

2021-07-31

Número

Sección

Artículos científicos originales (arbitrados por pares académicos)

Comentarios (ver términos de uso)

Artículos más leídos del mismo autor/a

1 2 3 4 5 6 7 8 9 10 > >>