Desarrollo de pensamiento relacional mediante trabajo con igualdades numéricas en aritmética básica

Referencias

Baroody, A.J., y H.P. Ginsburg (1983), “The Effects of Instruction on Children’s Understanding of the ‘Equals’ Sign”, The Elementary School Journal, vol. 84, núm. 2, pp. 199-212. Bastable, V., y D. Schifter (en prensa), “Classroom Stories: Examples of Elementary Students Engaged in Early-Algebra”, en J. Kaput, D. Carraher y M. Blanton (eds.), Employing Children’s Natural Power to Build Algebraic Reasoning in the Context of Elementary Mathematics, Englewood Cliffs, Laurence Erlbaum Associates. Behr, M., S. Erlwanger y E. Nichols (1980), “How Children View the Equal Sign”, Mathematics Teaching, núm. 92, pp. 13-15. Blanton, M., y J. Kaput (2004), “Elementary Grades Students’ Capacity for Functional Thinking”, en M. Johnsen y A. Berit (eds.), Proceedings of the 28th International Group for the Psychology of Mathematics Education, Bergen, vol. 2, pp. 135-142. Booth, L.R. (1999), “Children’s Difficulties in Beginning Algebra”, en B. Moses (ed.), Algebraic Thinking. Grades K-12, Readings from NCTM’S school-based journals and others publications, Reston, NCTM, pp. 299-307. Byers, V., y N. Herscovics (1977), “Understanding School Mathematics”, Mathematics Teaching, núm. 81, pp. 24-27. Carpenter, T. P., M. L. Franke y L. Levi (2003), Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School, Portsmouth, Heinemann. Carraher, D., A.D. Schliemann y B.M. Brizuela (2000), “Early-Algebra, Early Arithmetic: Treating Operations as Functions”, XXII Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education, Tucson, AZ. Confrey, J., y A. Lachance (2000), “Transformative Teaching Experiments Through Conjecture-driven Research Design”, en A.E. Kelly y R.A. Lesh (eds.), Research Design in Mathematics and Science Education, New Jersey, Lawrence Erlbaum Associates, pp. 231-265. Falkner, K.P., L. Levi y T.P. Carpenter (1999), “Children’s Understanding of Equality: A Foundation for Algebra”, Teaching Children Mathematics, núm. 6, pp. 232-236. Freiman, V., y L. Lee (2004), “Tracking Primary Students’ Understanding of the Equal Sign”, en M. Johnsen y A. Berit (eds.), Proceedings of the 28th International Conference of the International Group for the Psychology of Mathematics Education, Bergen, Bergen University College, vol. 2, pp. 415-422. Gallardo, A., y T. Rojano (1988), “Áreas de dificultades en la adquisición del lenguaje aritmético-algebraico”, Reserches en Didactique des Mathémathiques, vol. 9, núm. 2, pp. 155-188. Hejny, M., D. Jirotkova y J. Kratochvilova (2006), “Early Conceptual Thinking”, en J. Novotná, H. Moraová, M. Krátká y N. Stehlíková (eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education, Praga, República Checa, vol. 3, pp. 289-296. Kaput, J. (1995), A Research Base Supporting Long Term Algebra Reform?, North American Chapter of the International Group for the Psychology of Mathematics Education, Columbus. ————————– (1998), Teaching and Learning a New Algebra with Understanding, National Center for Improving Student Learning and Achievement in Mathematics and Science, Dartmouth, MA. ————————– (2000), Transforming Algebra from an Engine of Inequity to an Engine of Mathematical Power By “Algebrafying” the K-12 Curriculum, National Center for Improving Student Learning and Achievement in Mathematics and Science, Dartmouth, MA. Kieran, C. (1992), “The Learning and Teaching of School Algebra”, en D.A. Grouws (ed.), Handbook of Research on Mathematics Teaching and Learning (A Project of the NCTM), Nueva York, Macmillan, pp. 390-419. ————————– (1981), “Concepts Associated with the Equality Symbol”, Educational Studies in Mathematics, núm. 12, pp. 317-326. Kindt, M. (1980), “Als een kat om de hete algebrij”, Wiskrant, vol. 5, núm. 21. Knuth, E.J., M.W. Alibali, N.M. McNeil, A. Weinberg y A.C. Stephens (2005), “Middle School Students’ Understanding of Core Algebraic Concepts: Equivalence and Variable”, Zentralblatt für Didaktik der Mathematik [International Reviews on Mathematics Education], vol. 37, núm. 1, pp. 68-76. Koehler, J. (2002), Algebraic Reasoning in the Elementary Grades: Developing an Understanding of the Equal Sign as a Relational Symbol, Tesis de maestría inédita, Wisconsin, University of Wisconsin–Madison. ————————– (2004), Learning to Think Relationally: Thinking Relationally to Learn, Tesis doctoral inédita, Wisconsin, University of Wisconsin–Madison. Lee, L. (en prensa), “What is Algebra?”, en J. Kaput, D. Carraher y M. Blanton (eds.), Employing Children’s Natural Power to Build Algebraic Reasoning in the Context of Elementary Mathematics, Englewood Cliffs, Laurence Erlbaum Associates. Liebenberg, R., M. Sasman y A. Olivier (1999), From Numerical Equivalence to Algebraic Equivalence, Mathematics Learning and Teaching Initiative (MALATI), V Congreso Anual de la Asociación de Educación Matemática de Sudáfrica (AMESA), Puerto Elizabeth. Mevarech, Z.R., y D. Yitschak (1983), “Students’ Misconceptions of the Equivalence Relationship”, en R. Hershkowitz (ed.), Proceedings of the Seventh International Conference for the Psychology of Mathematics Education, Rehobot, Israel, Weizmann Institute of Science, pp. 313-318. Molina, M. (2006), Desarrollo de pensamiento relacional y comprensión del signo igual por alumnos de tercero de educación primaria, Tesis doctoral, Departamento de Didáctica de la Matemática, Granada, Universidad de Granada. Disponible en http://cumbia.ath.cx:591/pna/Archivos/MolinaM07-2822.PDF. National Council of Teacher of Mathematics (2000), Principles and Standards for School Mathematics, Reston, NCTM. Pirie, S., y L. Martin (1997), “The Equation, the Whole Equation and Nothing but the Equation! One Approach to the Teaching of Linear Equations”, Educational Studies in Mathematics, vol. 34, núm. 2, pp. 159-181. Sáenz-Ludlow, A., y C. Walgamuth (1998), “Third Graders’ Interpretations of Equality and the Equal Symbol”, Educational Studies in Mathematics, vol. 35, núm. 2, pp. 153-187. Sisofo, E. (2000), “Can the Instruction of the Davydov Curriculum Develop American Children’s Notion of the ‘=’ Symbol as a Relational Symbol Rather than an Operational ‘Do Something’ Symbol?”, Propuesta de tesis doctoral, descargado el 19 de abril de 2004 de http://ematusov.soe.udel.edu/educ820.00s/ Van Reeuwijk, M. (en prensa), “A Dutch Perspective”, en J. Kaput, D. Carraher y M. Blanton (eds.), Employing Children’s Natural Power to Build Algebraic Reasoning in the Context of Elementary Mathematics, Englewood Cliffs, Laurence Erlbaum Associates. Warren, E. (2003), “Unknowns Arithmetic to Algebra: Two Exemplars”, en A. Cockburn y E. Nardi (eds.), Proceedings of the 26th International Group for the Psychology of Mathematics Education, Inglaterra, vol. 4, pp. 362-369.