Distinción del pensamiento algebraico del aritmético en actividades matemáticas escolares

Referencias

Aké, L., Godino, J. D., Gonzato, M., & Wilhelmi, M. R. (2013). Proto-algebraic levels of mathematical thinking. En A. M. Lindmeier & A. Heinze (Eds.), Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education (PME), (Vol. 2, pp. 1-8). Kiel, Germany: PME. Arcavi, A. (2007). El desarrollo y el uso del sentido de los símbolos. Uno, Revista de Didáctica de las Matemáticas, 44, 59-75. Bednarz, N., Kieran, C., & Lee, L. (1996). Approaches to Algebra. Dordrecht: Kluwer Academic Publishers. Butto, C., & Rojano, T. (2004). Introducción temprana al pensamiento algebraico: Abordaje basado en la geometría. Educación Matemática, 16(1), 113-148. Distinción del pensamiento algebraico del aritmético en actividades matemáticas escolares Comunicación XIV CIAEM-IACME, Chiapas, México, 2015. 8 Cai, J. & Knuth, E. (2011). Early algebraization. A global dialogue from multiple perspectives. Berlin: Springer-Verlag. Carpenter, T. P., Frankle, M. L., & Levi, L. (2003). Thinking Mathematically. Integrating Arithmetic and Algebra in Elementary School. Portsmouth, NH: Heinemann. Carraher, D. W. & Schliemann, A. L. (2007). Early algebra and algebraic reasoning. En F. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (Vol. 2, pp. 669-705). Charlotte, N.C: Information Age Publishing, Inc. y NCTM. Davis, R. B. (1985). Algebraic thinking in the early grades. Journal of Mathematical Behavior, 4(2), 195- 208. Filloy, E., Puig, L., & Rojano, T (2008). Educational algebra. A theorical and empirical approach. New York: Springer. Freudenthal, H. (1983). Didactical Phenomenology of Mathematical Structures. Cap.6. Reidel, Dordrecht. Traducción de trabajo para uso interno. Luis Puig Espinosa. Universidad de Valencia. Godino, J. D. Aké, L., Gonzato, M., & Wilhelmi, M. R. (2014). Niveles de algebrización de la actividad matemática escolar. Implicaciones para la formación de maestros. Enseñanza de las Ciencias, 1(32), 199-219. Godino, J. D., Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education. Zentralblatt für Didaktik der Mathematik (ZDM): The International Journal on Mathematics Education, 39(1), 127-135. Kaput, J. J. (2000). Transforming algebra from an engine of inequity for an engine of mathematical power by "algebrafying" the K-12 curriculum: National Center of Improving Student Learning and Achievement in Mathematics and Science (NCISLA). Dartmouth, MA. Kaput, J. J. (2008). What is algebra? What is algebraic reasoning? En J. Kaput, D. W. Carraher, & M. L. Blanton (Eds), Algebra in the early grades (pp. 5-17). New York: Routledge. Kieran, C. (1992). The learning and teaching of school algebra. En D. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 390-419). New York: Macmillan Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels. Building meaning for symbols and their manipulation. En F. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (Vol. 2, pp.707-762). Charlotte, N.C: Information Age Publishing, Inc. & NCTM. Lamon, S. (1993). Ratio and proportion: Connecting and children’s thinking. Journal for Research in Mathematics Education, 24, 41-61. Puig, L., & Rojano, T. (2004). The history of algebra in mathematics education. En K. Stacey, H. Chick, & M. Kendal (Eds.), The teaching and learning of algebra: The 12th ICMI study (pp. 189-224). Norwood, MA: Kluwer Academic Publishers. Radford, L. (2010). Layers of generality and types of generalization in pattern activities. PNA, 4(2), 37- 62. Radford, L. (2011). Grade 2 Students’ Non-Symbolic Algebraic Thinking. En, J. Cai, E. Knuth (Eds.), Early algebraization. Advances in mathematics education. (pp. 303-320). Berlin: SpringerVerlag. Rivas, M., & Godino, J. D. (2009). Desarrollo del conocimiento del profesor mediante el estudio de configuraciones epistémicas y cognitivas de la proporcionalidad. Educere: Revista Venezolana de Educación, 48(14), 189-205. Distinción del pensamiento algebraico del aritmético en actividades matemáticas escolares Comunicación XIV CIAEM-IACME, Chiapas, México, 2015. 9 Santrock, J. W. (2001). Educational psychology. McGraw-Hill (Ed.), London 2001. Schliemann, A. D., Carraher, D. W., & Brizuela, B. (2007). Bringing out the algebraic character of arithmetic: From children's ideas to classroom practice. Hillsdale: Lawrence Erlbaum. Usiskin, Z. (1989). Conceptions of school algebra and uses of variables. En A. F. Coxford (Ed.), The Ideas of Algebra K-12 (pp. 8-19). Reston, VA: NCTM. Vergnaud G. (1988). Long terme et court terme dans l’apprentissage de l'algèbre. En C. Laborde, N. Balacheff (Eds.) Actes du Premier Colloque Franco-Allemand de Didactique des Mathématiques et de l’informatique, (pp. 189-199). La Pensée Sauvage, Grenoble, París. Wagner, S., & Kieran, C. (1989). Research issues in the learning and teaching of algebra. Reston, VA: National Council of Teachers of Mathematics; Hillsdale: Lawrence Erlbaum.