Competencia metarrepresentacional en los primeros grados: representaciones externas de datos y sus componentes

Referencias

Carraher, D., Schliemann, A. y Schwartz, J. (2008). Early algebra is not the same as algebra early. En J. Kaput, D. Carraher y M. Blanton (Eds.). Algebra in the early grades (pp. 235-272). Nueva York, NY: Lawrence Erlbaum. https://doi.org/10.5860/choice.46-1024 Common Core State Standars (2012). Estándares Estatales Comunes de Matemáticas. Disponible en línea: . DiSessa, A. (2004). Meta-representation: Native competence and targets for instruction. Cognition and Instruction, 22(3), pp. 293-331. https://doi.org/10.1207/s1532690xci2203_2 DiSessa, A., Hammer, D., Sherin, B. y Kolpakowski, T. (1991). Inventing graphing: meta-representational expertise in children. Journal of Mathematical Behavior, 10, pp. 117-160. Disponible en línea: . DiSessa, A. y Sherin, B. (2000). Meta-representation: an introduction. Journal of Mathematical Behavior, 19, pp. 385-398. https://doi.org/10.1016/s0732-3123(01)00051-7 Duval, R. (2014). Commentary: Linking epistemology and semio-cognitive modeling in visualization. ZDM, 46(1), pp. 159-170. https://doi.org/10.1007/s11858-013-0565-8 Earnest, D. (2015). From number lines to graphs in the coordinate plane: investigating problem solving across mathematical representations. Cognition and Instruction, 33(1), pp. 46-87. https://doi.org/10.1080/07370008.2014.994634 English, L. (2012). Data modeling with first-grade students. Educational Studies in Mathematics, 81, pp. 15-30. https://doi.org/10.1007/s10649-011-9377-3 Estrella, S. (2014). El formato tabular: una revisión de literatura. Revista Actualidades Investigativas en Educación, 14(2), pp. 1-23. https://doi.org/10.15517/aie.v14i2.14817 Estrella, S. (2018). Data representations in Early Statistics: data sense, meta-representational competence and transnumeration. En A. Leavy, M. Meletiou y E. Paparistodemou (Eds.). Statistics in Early Childhood and Primary Education – Supporting early statistical and probabilistic thinking. Singapur: Springer. Estrella, S., Mena, A. y Olfos, R. (2017). Naturaleza del objeto matemático «Tabla». Magis: Revista Internacional de Investigación en Educación, 10(20), pp. 105-122. https://doi.org/10.11144/javeriana.m10-20.nomt Estrella, S., Olfos, R., Morales, S. y Vidal-Szabó, P. (2017). Argumentaciones de estudiantes de primaria sobre representaciones externas de datos: componentes lógicas, numéricas y geométricas. RELIME, Revista Latinoamericana de Investigación en Matemática Educativa, 20(3), pp. 345- 370. https://doi.org/10.12802/relime.17.2034 Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M. y Scheaffer, R. (2007). Guidelines for assessment and instruction in statistics education (GAISE) report. Alexandria, VA: American Statistical Association. Disponible en línea: . Ginsburg, H., Lee, J. y Boyd, J. (2008). Mathematics education for young children: what it is and how to promote it. Society for Research in Child Development, 22(1), pp. 3-24. https://doi.org/10.1037/e640072011-001 Kaufman, E., Lord, M., Reese, T. y Volkmann, J. (1949). The discrimination of visual number. The American Journal of Psychology, 62(4), pp. 498-525. https://doi.org/10.2307/1418556 Le Corre, M. y Carey, S. (2007). One, two, three, four, nothing more: an investigation of the conceptual sources of the verbal counting principles. Cognition, 105(2), pp. 395-438. https://doi.org/10.1016/j.cognition.2006.10.005 Leavy, A. y Hourigan, M. (2017). The role of perceptual similarity, context, and situation when selecting attributes: considerations made by 5–6-year-olds in data modeling environments. Educational Studies in Mathematics, 97(2), pp. 163-183. https://doi.org/10.1007/s10649-017-9791-2 Martí, E. (2009). Tables as cognitive tools in primary education. En C. Andersen et al. (Eds.). Representational systems and practices as learning tools (pp. 133-148). Rotterdam: Sense Publishers. Disponible en línea: . Martí, E. y Scheuer, N. (2015). Sistemas semióticos, cultura y conocimiento matemático temprano. Estudios de Psicología, 36(1), pp. 9-17. https://doi.org/10.1080/02109395.2014.1000008 Ministerio de Educación de Chile (2012). Bases Curriculares de la Educación Básica, Matemática. Santiago de Chile: Autor. Moore, D. (2009). Estadística Aplicada Básica. Barcelona: Antoni Bosch. Mulligan, J. (2015). Moving beyond basic numeracy: data modeling in the early years of schooling. ZDM, 47(4), pp. 653-663. https://doi.org/10.1007/s11858-015-0687-2 Mulligan, J., Mitchelmore, M., English, L. y Crevensten, N. (2013). Reconceptualizing early mathematics learning: the fundamental role of pattern and structure. En L. English y J. Mulligan (Eds.). Reconceptualizing early mathematics learning (pp. 47-66). Dordrecht, Holanda: Springer. https://doi.org/10.1007/978-94-007-6440-8_4 Papic, M., Mulligan, J. y Mitchelmore, M. (2011). Assessing the development of preschoolers’ mathematical patterning. Journal for Research in Mathematics Education, 42(3), pp. 237-269. https://doi.org/10.5951/jresematheduc.42.3.0237 Pérez-Echeverría, M. y Scheuer, N. (2009). External representations as learning tools: an introduction. En C. Andersen et al. (Eds.). Representational systems and practices as learning tools (pp. 1-18). Rotterdam: Sense Publishers. Disponible en línea: . Sarama, J. y Clements, D. (2009). «Concrete» computer manipulatives in mathematics education. Child Development Perspectives, 3(3), pp. 145-150. https://doi.org/10.1111/j.1750-8606.2009.00095.x Sawrey, K., Brizuela, B. y Blanton, M. (2015). Representaciones producidas por una alumna para interrumpir el flujo de una entrevista. Estudios de Psicología, 36(1), pp. 185-192. https://doi.org/10.1080/02109395.2014.1000033 Sfard, A. (2008). Thinking as communication: Human development, the growth of discourses, and mathematizing. Nueva York: Cambridge University Press. https://doi.org/10.1017/cbo9780511499944 Tippett, C. (2016). What recent research on diagrams suggests about learning with rather than learning from visual representations. Science International Journal of Science Education, 38(5), pp. 725- 746. https://doi.org/10.1080/09500693.2016.1158435