Uso de una trayectoria hipotética de aprendizaje para proponer actividades de instrucción

Pedro Ivars, Ceneida Fernández, Salvador Llinares

Resumen

Decidir cómo continuar la enseñanza se ha identificado como la destreza más difícil de entre las tres que configuran la competencia de mirar profesionalmente el pensamiento matemático del estudiante. En este estudio 95 estudiantes para maestro de Educación Primaria resolvieron una tarea en la que debían proponer un objetivo de aprendizaje y actividades para apoyar el desarrollo de la comprensión del significado de fracción como parte-todo usando como referencia una trayectoria hipotética de aprendizaje. Los resultados sugieren que la trayectoria hipotética de aprendizaje ayudó a los estudiantes para maestro a proponer actividades centradas en la comprensión de los estudiantes usando los elementos matemáticos que articulan la trayectoria hipotética de aprendizaje.

Palabras clave

Mirar profesionalmente; Fracciones; Trayectoria hipotética de aprendizaje; Formación de maestros; Actividades instruccionales

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Referencias

Barnhart, T. y van Es, E. (2015). Studying teacher noticing: Examining the relationship among pre-service science teachers’ ability to attend, analyze and respond to student thinking. Teaching and Teacher Education, 45, 83-93. https://doi.org/10.1016/j.tate.2014.09.005

Battista, M. T. (2012). Cognition-Based Assessment and teaching of fractions: Building on students’ reasoning. Portsmouth: Heinemann.

Chao, T., Murray, E. y Star, J. R. (2016). Helping mathematics teachers develop noticing skills: Utilizing smartphone technology for one-on-one teacher/student interviews. Contemporary Issues in Technology and Teacher Education, 16(1), 22-37.

Choy, B. H. (2013). Productive mathematical noticing: What it is and why it matters. En V. Steinle, L. Ball y C. Bardini (Eds.), Proceedings of the 36th Annual Conference of Mathematics Education Research Group of Australasia (pp. 186-193). Melbourne, Victoria: MERGA.

Clarke, D., Roche, A. y Mitchell, A. (2011). One-to-one student interviews provide powerful insights and clear focus for the teaching of fractions in the middle years. En J. Way y J. Bobis (Eds.), Fractions: Teaching for Understanding (pp. 23-41). Australia: A.A.M.T. Inc.

D’Ambrosio, B. S. y Mewborn, D. S. (1994). Children’s constructions of fractions and their implications for classroom instruction. Journal of Research in Childhood Education, 8(2), 150-161. https://doi.org/10.1080/02568549409594863

Daro, P., Mosher, F. y Corcoran, T. (2011). Learning trajectories in mathematics: A foundation for standards, curriculum, assessment, and instruction (CPRE Research Report #RR68). Filadelfia: CPRE. https://doi.org/10.12698/cpre.2011.rr68

Edgington, C., Wilson, P. H., Sztajn, P. y Webb, J. (2016). Translating learning trajectories into useable tools for teachers. Mathematics Teacher Educator, 5(1), 65-80. https://doi.org/10.5951/mathteaceduc.5.1.0065

Empson, S. B. (1999). Equal sharing and shared meaning: The development of fraction concepts in a first-grade classroom. Cognition and Instruction, 17(3), 283-342. https://doi.org/10.1207/S1532690XCI1703_3

Empson, S. y Levi, L. (2011). Extending children’s mathematics. Fractions and decimals. Portsmouth, New Hampshire: Heinemann.

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

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. https://doi.org/10.35763/aiem.v1i1.3

Grossman, P., Copton, C., Igra, D., Ronfeldt, M., Shahan, E. y Willianson, P. (2009). Teaching practice: A cross-professional perspective. Teachers College Record, 111(9), 2055-2100.

Gupta, D., Soto, M., Dick, L., Broderick, S. D. y Appelgate, M. (2018). Noticing and deciding the next steps for teaching: A cross-university study with elementary pre-service teachers. En J. Stylianides y K. Hino (Eds.), Research advances in the mathematical education of pre-service elementary teachers (pp. 261-275). Cham, Suiza: Springer. https://doi.org/10.1007/978-3-319-68342-3_18

Ivars, P., Fernández, C. y Llinares, S. (2020). A learning trajectory as a scaffold for pre-service teachers’ noticing of students’ mathematical understanding. International Journal of Science and Mathematics Education, 18(3), 529-548. https://doi.org/10.1007/s10763-019-09973-4

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.

Krupa, E. E., Huey, M., Lesseig, K., Casey, S. y Monson, D. (2017). Investigating secondary preservice teacher noticing of students’ mathematical thinking. En E. O. Schack, M. H. Fishery y J. A. Wilhelm (Eds.), Teacher Noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 49-72). Cham, Suiza: Springer. https://doi.org/10.1007/978-3-319-46753-5_4

Kurt, G. y Cakiroglu, E. (2009). Middle grade students’ performances in translating among representations of fractions: A Turkish perspective. Learning and Individual Differences, 19(4), 404-410. https://doi.org/10.1016/j.lindif.2009.02.005

Lai, M., Lam, K. M. y Lim, C. P. (2016). Design principles for the blend in blended learning: a collective case study. Teaching in Higher Education, 21(6), 716-729. https://doi.org/10.1080/13562517.2016.1183611

Larson, C. N. (1988). Teaching fraction terms to primary students. En M. J. Behr, C. B. Lacampagne y M. M. Wheeler (Eds.), Proceedings of the 10th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 100-106). Dekalb, IL: PME-NA.

Levin, D. M., Hammer, D. y Coffey, J. E. (2009). Novice teachers’ attention to student thinking. Journal of Teacher Education, 60(2), 142-154. https://doi.org/10.1177/0022487108330245

Mason, J. (2002). Researching your own practice. The discipline of noticing. Londres: Routledge. https://doi.org/10.4324/9780203471876

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

National Council of Teachers of Mathematics (2014). Principles to actions: Ensuring mathematics success for all. Reston, VA: NCTM.

Ni, Y. (2001). Semantic domains of rational numbers and the acquisition of fraction equivalence. Contemporary Educational Psychology, 26(3), 400-417. https://doi.org/10.1006/ceps.2000.1072

Sánchez-Matamoros, G., Fernández, C. y Llinares, S. (2015). Developing pre-service teachers’ noticing of students’ understanding of the derivative concept. International Journal of Science and Mathematics Education, 13(6), 1305-1329. https://doi.org/10.1007/s10763-014-9544-y

Sánchez-Matamoros, G., Moreno, M., Prez-Tyteca, P. y Callejo, M. L. (2018). Trayectoria de aprendizaje de la longitud y su medida como instrumento conceptual usado por futuros maestros de Educación Infantil. Revista Latinoamericana de Investigación en Matemática Educativa, 21(2), 203-228. https://doi.org/10.12802/relime.18.2124

Schack, E. O., Fisher, M. H. y Wilhelm, J. A. (Eds.) (2017). Teacher Noticing: Bridging and broadening perspectives, contexts, and frameworks. Cham, Suiza: Springer. https://doi.org/10.1007/978-3-319-46753-5

Schoenfeld, A. H. (2011). How we think: A theory of goal-oriented decision making and its educational applications. Nueva York: Routledge. https://doi.org/10.4324/9780203843000

Sherin, M. G., Jacobs, V. R. y Philipp, R. A. (Eds.) (2011). Mathematics teacher noticing: Seeing through teachers’ eyes. Nueva York: Routledge. https://doi.org/10.4324/9780203832714

Simon, M. A. y Tzur, R. (2004). Explicating the role of mathematical tasks in conceptual learning: An elaboration of the hypothetical learning trajectory. Mathematical Thinking and Learning, 6(2), 91-104. https://doi.org/10.1207/s15327833mtl0602_2

Smith, T. (2003). Connecting theory and reflective practice through the use of personal theories. En N. Pateman, B. Dougherty y J. Zilliox (Eds.), Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education (vol. 4, pp. 215-222). Honolulu, HI: PME.

Smith, M. S. y Stein, M. K. (2011). 5 Practices for Orchestrating Productive Mathematics Discussions. Reston, VA: NCTM.

Son, J. W. y Crespo, S. (2009). Prospective teachers’ reasoning and response to a student’s non-traditional strategy when dividing fractions. Journal of Mathematics Teacher Education, 12(4), 235-261. https://doi.org/10.1007/s10857-009-9112-5

Son, J. W. y Sinclair, N. (2010). How prospective teachers interpret and respond to student geometric errors. School Science and Mathematics, 110(1), 31-46. https://doi.org/10.1111/j.1949-8594.2009.00005.x

Stahnke, R., Schueler, S. y Roesken-Winter, B. (2016). Teachers’ perception, interpretation, and decision-making: a systematic review of empirical mathematics education research. ZDM. Mathematics Education, 48(1-2), 1-27. https://doi.org/10.1007/s11858-016-0775-y

Steffe, L. y Olive, J. (2010). Children’s fractional knowledge. Nueva York: Springer. https://doi.org/10.1007/978-1-4419-0591-8

Sztajn, P., Confrey, J., Wilson, P. H. y Edgington, C. (2012). Learning trajectory based instruction toward a theory of teaching. Educational Researcher, 41(5), 147-156. https://doi.org/10.3102/0013189x12442801

Sztajn, P., Edgington, C., Wilson, P. H., Webb, J. y Myers, M. (2019). The Learning Trajectory Based Instruction Project. En P. Sztajn y P. Holt Wilson (Eds.), Learning Trajectories for teachers: Designing effective professional development for math instruction (pp. 15-47). Nueva York: Teachers’ College Press.

Sztajn, P. y Wilson, P. H. (2019). Learning trajectories for teachers: Designing effective professional development for math instruction. Nueva York: Teachers’ College Press.

Timinsky, A. M., Land, T. J., Drake, C., Zambak, V. S. y Simpson, A. (2014). Preservice elementary mathematics teachers’ emerging ability to write problems to build on children’s mathematics. En J. J. Lo, K. R. Leatham y L. R. Van Zoest (Eds.), Research trends in mathematics teacher education (pp. 193-218). Cham, Suiza: Springer. https://doi.org/10.1007/978-3-319-02562-9_11

van Es, E. (2011). A framework for learning to notice student thinking. En M. G. Sherin, V. R. Jacobs y R. Philipp (Eds.), Mathematics teacher noticing: Seeing through teachers’ eyes (pp. 134-151). Nueva York: Routledge.

Wager, A. A. (2014). Noticing children’s participation: Insights into teacher positionality toward equitable mathematics pedagogy. Journal for Research in Mathematics Education, 45(3), 312-350. https://doi.org/10.5951/jresematheduc.45.3.0312

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