Análisis de tareas de un libro de texto de primaria desde la perspectiva de los niveles de algebrización

Referencias

Aké, L. P., Godino, J. D., Gonzato, M. y Wilhelmi, M. R. (2013). Proto-algebraic Levels of Mathematical Thinking. En: A. 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: Leibniz-Institut. Alibali, M. W., Knuth, E. J., Hattikudur, S., McNeil, N. M. & Stephens, A. C. (2007). A Longitudinal Examination of Middle School Students’ Understanding of the Equal Sign and Equivalence Equations. Mathematical Thinking and Learning, 9 (3), pp. 221-247. Castro, E., Cañadas, M. C. & Molina, M. (2017). Pensamiento funcional mostrado por estudiantes de Educación Infantil. Edma 0-6: Educación Matemática en la Infancia, 6(2), 1-13. Blanton, M. L. & Kaput, J. J. (2011). Functional Thinking as a Route into Algebra in the Elementary Grades. En: J. Cai & E. Knuth (eds.). Early Algebraization: A Global Dialogue from Multiple Perspectives (pp. 5-23). Berlin, Germany: Springer. Branco, N. y Ponte, J. P. (2012). Developing Algebraic and Didactical Knowlendge in Pre-service Primary Teacher Education. En T. Y. Tso (ed.). Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education, - PME, Vol. 2 (pp. 75-82). Taipei, Taiwan: PME. Butto, C. & Rojano, T. (2004). Introducción temprana al pensamiento algebraico: Abordaje basado en la geometría. Educación Matemática, 16 (1), pp. 113-148. Cai, J. & Knuth, E. (2011). Early Algebraization: A Global Dialogue from Multiple Perspectives. Heidelberg, Germany: Springer-Verlag. Carpenter, T. P., Franke, M. L. & Levi, L. (2003). Thinking Mathematically. Integrating Arithmetic and Algebra in Elementary School. Portsmouth, New Hampshire: 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, North Carolina: Information Age Publishing, Inc. & NCTM. Carraher, D., Schliemann, A. D. & Brizuela, B. M. (2007). Early Algebra, Early Arithmetic: Treating Operations as Functions. En: M. L. Fernández (ed). Conferencia magistral presentada en el 22nd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education – PME-NA, Tucson, Arizona. Carraher, D. W., Schliemann, A. D., Brizuela, B. M. & Earnest, D. (2006). Arithmetic and Algebra in Early Mathematics Education. Journal for Research in Mathematics Education, 37(2), 87-115. Carraher, D. W., Schliemann, A. D. & Schwartz, J. L. (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). Mahwah, New Jersey: Erlbaum. Ellis, A. (2011). Algebra in the Middle School: Developing Functional Relationships Through Quantitative Reasoning. En: T. Rowland y K. Ruthven. (eds.). Mathematical Knowledge in Teaching (pp. 9-25). London: Springer. Filloy, E., Puig, L. y Rojano, T (2008). Educational Algebra. A Theorical and Empirical Approach. New York: Springer. Godino, J. D., Aké, L. P., Gonzato, M. & Wilhelmi, M. R. (2014). Niveles de algebrización de la actividad matemática escolar. Implicaciones para la formación de maestros. Enseñanza de las Ciencias, 32 (1), pp. 199-219. Godino, J.D., Neto, T. Wilhelmi, M.R., Aké, L., Etchegaray, S. & Lasa, A. (2015). Niveles de algebrización de las prácticas matemáticas escolares. Articulación de las perspectivas ontosemiótica y antropológica. Avances de Investigación en Educación Matemática, 8, 117–142. 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), pp. 127-135. Godino, J. D., Castro, W. F., Aké, L. P. & Wilhelmi, M. R. (2012). Naturaleza del razonamiento algebraico elemental. Boletim de Educação Matemática - BOLEMA, 26 (42B), 483-511. Hoch, M. & Dreyfus, T. (2004). Structure Sense in High School Algebra. The Effect of Brackets. En: M. J. Hoines & A. B. Fuglestad (eds). Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education - PME, Vol. 3, (pp. 49-56). Bergen, Norway: Bergen University College. Jamieson-Proctor, R. & Byrne, C. (2008). Primary Teachers’ Beliefs about the Use of Mathematics Textbooks. En: M. Goos, R. Brown & K. Makar (eds.). Proceedings of the 31st Annual Conference of the Mathematics Education: Meeting Research Group of Australasia-MERGA31: Navigating Currents and Charting Directions (pp. 295-302). Brisbane, Australia: MERGA. Jones, I. & Pratt, D. (2006). Three Utilities for the Equal Sign. En: H. L. Chick & J. L. Vincent (eds.). Proceedings of the 29th International Group for the Psychology of Mathematics Education - PME, Vol. 3 (pp.185-192). Melbourne, Australia: University of Melbourne. Kaput, J. (1998). Teaching and Learning a New Algebra. En: E. Fennema y T. A. Romberg (eds.). Mathematics Classrooms that Promote Understanding (pp. 133-155). Mahwah, New Jersey: Lawrence Erlbaum Associates. Kaput, J. & Blanton, M. L. (2002). Design Principles for Tasks that Support Algebraic Thinking in Elementary School Classrooms. En: A. D. Cockburn y E. Nardi (eds.). Proceedings of the 26th Annual Conference of the International Group for the Psy- chology of Mathematics Education - PME, Vol. 2 (pp. 105-112). Norwich, England: University of East Anglia. Kieran, K., Pang, J., Schifter, D. & Fong, S. (2016). Early Algebra. Research into its Nature, its Learning, its Teaching. Hamburg, Germany: Springer. Lins, R. & Kaput, J. J. (2004). The Early Development of Algebraic Reasoning: The Current State of the Field. En K. Stacey, H. Chick y M. Kendal (eds.). The Future of the Teaching and Learning of Algebra. The 12th ICMI Study (pp. 47-70). Massachusetts, USA: Kluwer Academic Publishers. National Council of Teachers of Mathematics (2000). Principles and Standards for School Mathematics. Reston, VA: NCTM National Governors Association Center for Best Practices and the Council of Chief State School Officers. (2011). Common Core State Standards for Mathematics-CCSSM. Disponible en http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf. Puig, L. & Rojano, T. (2004). The History of Algebra in Mathematics Education. En: K. Stacey, H. Chick y M. Kendal (eds.). Proceedings of the 12th International Commission on Mathematical Instruction-ICMI Study Conference: The Future of the Teaching and Learning of Algebra (pp. 189- 224). London: Kluwer Academic Publishers. Radford, L. (2003). Gestures, Speech, and the Sprouting of Signs: A Semiotic-cultural Approach to Students’ Types of Generalization. Mathematical Thinking and Learning, 5(1), pp. 37-70. Radford, L. (2010). The Eye as a Theoretician: Seeing Structures in Generalizing Activities. For the Learning of Mathematics, 30(2), 2-7. Radford, L. (2012). Early Algebraic Thinking: Epistemological, Semiotic, and Developmental Issues. En S. J. Cho (ed.). Proceedings of the 12th International Congress on Mathematical Education- ICME (pp. 675-694). Seúl, Korea: National University of Education. Rivera, (2013). Types and Levels of Pattern Generalization. Teaching and Learning Patterns in School Mathematics. Psychological and Pedagogical Considerations, 55-92. Springer: New York. Schliemann, A. D., Carraher, D. W. & Brizuela, B. (2007). Bringing Out the Algebraic Character of Arithmetic: From Children’s Ideas to Classroom Practice. Mahwah, New Jersey: Lawrence Erlbaum Associates. Secretaría de Educación Pública (2011). Plan de estudios 2011. Educación básica. México: SEP. Disponible en http://issuu.com/dgeb/docs/planedu2011?e=3503076/2622744. Secretaría de Educación Pública (2015). Desafíos matemáticos 2015. Libro para el alumno. Educación Básica Primaria. Primer grado. México: SEP. Vasilachis, I. (2009). Estrategias de investigación cualitativa. España: Gedisa. Warren, E. (2001). Algebraic Understanding and the Importance of Operation Sense. En: M. Heuvel-Penhuizen (ed.). Proceedings of the 25th International Group for the Psychology of Mathematics Education - PME, Vol. 4 (pp. 399-406). Utrecht, The Netherlands: Freudenthal Institute. Whitacre, I., Schoen, R. C., Champagne, Z. & Goddard, A. (2017). Relational Thinking: What’s the Difference? Teaching Children Mathematics, 23 (5), pp. 302-308.