Instrumentation of a progression of strategies by prospective primary teachers
Abstract
The aim of this research work is to characterize how future teachers learn to use a progression of multiple-division problem-solving strategies to interpret children’s mathematical thinking. Sixty-one teachers in training participated in a teaching experiment whose purpose was to develop the teaching competence, and to take notice of the use of mathematical thinking by children from primary education when they solve problems of division-measure with fractions. Future teachers’ learning was analyzed using the instrumental approach to characterize how they identified and interpreted the strategies used by children. The results show that teachers in training made three different uses of the progression of strategies: as an artifact, generating instrumental action schemes and implementing the progression of strategies. From these results, we took notice of arising implications for teacher training.Keywords
Division-measure problems, Progression of strategies, Conceptual tool, Interpretation of progression stages, InstrumentationReferences
Ball, D. L. (1990). Pre-service elementary and secondary teachers’ understanding of division. Journal for Research in Mathematics Education, 21 (2), 132-144.
Carpenter, T., Fennema, E., Franke, M., Levi, L. y Empson, S. (1999). Children’s mathematics: Cognitively Guided Instruction. Porstmouth, NH: Heinemann.
Depaepe, F., Torbeyns, J., Vermeersch, N., Janssens, D., Janssen, R., Kelchtermans, G., Verschaffel, L. y Van Dooren, W. (2015). Teachers’ content and pedagogical content knowledge on rational numbers: A comparison of prospective elementary and lower secondary teachers. Teaching and Teacher Education, 47, 82-92.
Drijvers, P., Kieran, C. y Mariotti, M. A. (2010). Integrating technology into mathematics education: Theoretical perspectives. En C. Hoyles y J. B. Lagrange (Eds.), Mathematics education and technology: Rethinking the terrain (pp. 89-132). Nueva York: Springer.
Drijvers, P. y Trouche, L. (2008). From artifacts to instruments: A theoretical framework behind the orchestra metaphor. En G. W. Blume y M. K. Heid (Eds.), Research on technology and the teaching and learning of mathematics. Vol. 2. Cases and perspectives (pp. 363-392). Charlotte, NC: Information Age.
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. DOI: 10.5951/mathteaceduc.5.1.0065
Empson, S. B. (2011). On the idea of learning trajectories: Promises and pitfalls. The Mathematics Enthusiast, 8(3), 571-598.
Empson, S. B. y Jacobs, V. (2008). Learning to listen to children’s mathematics. En T. Wood y P. Sullivan (Eds.), International handbook of mathematics teacher education. Vol. 1. Knowledge and beliefs in mathematics teaching and teaching development (pp. 257-281). Rotterdan: Sense Publishers.
Empson, S. B. y Levi, L. (2011). Extending Children’s Mathematics: Fractions and Decimals. Portsmouth, NH: Heinemann.
Fernández, C., Callejo, M. L. y Márquez, M. (2012). Valoración de respuestas a problemas de división-medida con fracciones por estudiantes para maestro. En A. Estepa, A. Contreras, J. Deulofeu, M. C. Penalva, F. J. García y L. Ordóñez (Eds.), Investigación en Educación Matemática XVI (pp. 219-227). Jaén: SEIEM.
Fernández, C., Sánchez-Matamoros, G., Valls, J. y Callejo, M. L. (2018). Noticing students’ mathematical thinking: characterization, development and contexts. AIEM- Avances de Investigación en Educación Matemática, 13, 39-61.
Graeber, A., Tirosh, D. y Glover, R. (1986). Preservice teachers’ beliefs and performance on measurement and partitive division problems. En Proceedings of the Eighth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 262-267).
Grossman, P., Compton, C., Igra, D., Ronfeldt, M., Shahan, E. y Williamson, P. (2009). Teaching practice: A cross-professional perspective. Teachers College Record, 111(9), 2055-2100.
Ivars, P., Fernández, C. y Llinares, S. (2019). A learning trajectory as a scaffold for preservice teachers’ noticing of students’ mathematical understanding. International Journal of Science and Mathematics Education.
Jacobs, V., Lamb, L. y Philipp, R. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169-202.
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.
Li, Y. y Kulm, G. (2008). Knowledge and confidence of pre-service mathematics teachers: The case of fraction division. ZDM, 40(5), 833-843.
Llinares, S. (2014). Experimentos de enseñanza e investigación. Una dualidad en la práctica del formador de profesores de matemáticas. Educación Matemática, 26, 31-51.
Rabardel, P. (1995). Les hommes et les technologies: approche cognitive des instruments contemporains. París: Armand Colin.
Rabardel, P. (2002). People and Technology. A Cognitive Approach to Contemporary Instruments. Obtenido de http://ergoserv.psy.univ-paris8.fr. Visitada el 20-12-2005.
Sánchez-Matamoros, G., Moreno, M., Pérez-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.
Son, J. y Crespo, S. (2009). Prospective teachers’ reasoning and response to a student’s no traditional strategy when dividing fractions. Journal of Mathematics Teacher Education, 12(4), 235-261.
Steffe, L. P. (2004). On the construction of learning trajectories of children: The case of commensurate fractions. Mathematical Thinking and Learning, 6(2), 129-162. DOI 10.1207/s15327833mtl0602_4
Steinberg, R., Empson, S. y Carpenter, T. (2004). Inquiry into children mathematical thinking as a means to teacher change. Journal of Mathematics Teacher Education, 7(3), 237-267.
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. DOI 10.3102/0013189x12442801.
Trouche, L. (2004). Managing the complexity of human/machine interactions environments: Guiding student’s command process through instrumental orchestrations. International Journal of Computers for Mathematical Learning, 9(3), 281-307. DOI https://dx.doi.org/10.1007/s10758-004-3468-5
Vergnaud, G. (1994). Multiplicative conceptual field: What and why? En G. Harel y J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 41-60). Albany, NY: State University of New York Press.
Verillon, P. y Rabardel, P. (1995). Cognition and artifacts: A contribution to the study of thought in relation to instrument activity. European Journal of Psychology of Education, 10(1), 77-101. DOI https://dx.doi.org/10.1007/BF03172796
Wilson, P. H., Mojica, G. F. y Confrey, J. (2013). Learning trajectories in teacher education: Supporting teachers’ understandings of students’ mathematical thinking. The Journal of Mathematical Behavior, 32(2), 103-121. DOI 10.1016/j.jmathb.2012.12.003
Wilson, P. H., Sztajn, P., Edgington, C. y Myers, M. (2015). Teachers’ uses of a learning trajectory in student-centered instructional practices. Journal of Teacher Education, 66(3), 227-244.
Published
How to Cite
Downloads
Copyright (c) 2020 Autor
This work is licensed under a Creative Commons Attribution 4.0 International License.
