El futuro en la escuela del paso de la aritmética al álgebra para un psicólogo cognitivo: más investigación

Referencias

[1] Algebra Working Group to the National Council of Teachers of Mathematics (1995) A Framework for Constructing a Vision of Algebra: a Discussion Document. This document has been adapted from the Algebra in the K- 12 Curriculum: Dilemmas and Possibilities. [2] Booth, L. (1984) Algebra: Children’s Strategies and Errors, NFER-Nelson. [3] Campbell, S. (2001) Early mathematics education: A case of the blind leading the blind? Forum on exemplary practices and challenges in teacher preparation. American Association of Universities. Boston, MA. [4] Carpenter, T. & J. Moser (1983) The acquisition of addition and subtraction concepts. In R. Lesh and M. Landau (Eds.). Acquisition of Mathematics Concepts and Processes (7-43). Orlando, FL: Academic Press. [5] Carpenter, T., Franke, M. et al. (1998) A longitudinal study of invention and understanding in children’s multidigit addition and subtraction. Journal for Research in Mathematics Education, 29(1), 3-20. [6] Castro, E., Rico, L. y Castro, E. (1996) N´umeros y operaciones. Fundamentos para una aritm´etica escolar. Espa˜na. Editorial S´ıntesis [7] Charron, C. & Ducloy, N. (1996) How does addition contribute to the construction of natural numbers in 4 to 13 year old children. En Proceedings of the PME 20, Vol. 2, 209-216. Valencia, Espa˜na [8] Clement, J. (1982) Algebra word problem solutions: Thought processes underlying a common misconception, Journal for Research in Mathematics Education, 13, 16-30. [9] Cooper, T., Heirdsfield, A., et al.(1996) Children’s mental strategies for addition and subtraction word problems. In J. T. Mulligan and M. C. Mitchelmore (Eds.). Children’s Number Learning (pp. 147-161). Adelaide, Aus.: The Australian Association of Mathematics Teachers. [10] Costa, A. (1989) Prefacio. En: Resnick, L. & Klopfer, L. (Comp.) Curr´ıculum y Cognici´on. Buenos Aires, Argentina. Aique Grupo Editor S.A. p. 11-14 [11] Dehaene, S. (1997) The number sense. New York. Oxford University Press [12] Ebbutt, D. (1982) Educational action research: some general concerns and specific quibbles. TIQL, Cambrige, Cambrige Institute of Education. Citado por Walquer, R. (1989) M´etodos de investigaci´on para el profesorado. Ediciones Morata, p. 227 [13] Fern´andez, E. (1979) Estructura y did´actica de las ciencias. Madrid, Espa˜na. Servicio de Publicaciones del Ministerio de educaci´on [14] Fuson, K. (1988) Research on whole number addition and subtraction. En: Handbook of research on mathematics teaching and learning. New York: Macmillan Publishing Company. [15] Fuson, K. C., Wearne, D., et al.(1997) Children’s conceptual structures for multidigit numbers and methods of multidigit addition and subtraction. Journal for Research in Mathematics Education, 28(2), 130-162. [16] Fuson, K.; Richards, J. y Briars, D.(1982) The acquisition and elaboration of the number word sequence. En C. Brainer (ed.) Children’s logical and mathematical cognition. (pp. 33-92) New York: Springer-Verlag. [17] Gasc´on, J. (1999) La naturaleza prealgebraica de la matem´atica escolar, Educaci´on Matem´atica, 11(1), 77-88. [18] Gasc´on, J.; Bosch, M. y Bolea, P. (1998) ¿C´omo se construyen los problemas en did´actica de las matem´aticas? Parte (I) El ´algebra escolar en el Programa Cognitivo. (En prensa). [19] Giraldo, J. (2001) Problemas aritm´eticos verbales, Representaci´on Gr´afica y Resoluci´on de problemas en preescolar. I coloquio internacional y III regional de la c´atedra UNESCO para la lectura y la escritura en Am´erica latina. “Lectura y escritura para aprender a pensar”. Cartagena de Indias, Colombia; Diciembre 9 al 15 de 2001. [20] Greeno, J.(1983) Conceptual entities. En: Mental Models. New Jersey: Lawrence Erlbaum. [21] Hiebert, J. & Wearne, D. (1996) Instruction, understanding, and skill in multidigit addition and subtraction. Cognition and Instruction, 14(3), 251- 283. [22] ICMI (2001) The Future of the Teaching and Learning of Algebra. University of Melbourne (Australia) [23] Jones, G., Thornton, C., Putt, I., Hill, K., Mogill, T., Rich, B. & Van Zoest, L. (1996) Multidigit number sense: a framework for instruction and assessment. Journal for Research in Mathematics Education, Vol. 27, 3, 310 - 336 [24] Kamii, C.(1985) Place value: Children’s efforts to find a correspondence between digits and the number of objects. 10o JPS Symposium. Philadelphia. [25] Kaput, J. (1995) Transforming algebra from an engine of inequity to an engine of mathematical power by “algebrafying”the K-12 curriculum. Documento presentado en: NTCM meeting. San Francisco. pp. 11. [26] Kaput, J. (1996) ¿Una l´ınea de investigaci´on que sustente la reforma del ´algebra? I y II, UNO. Revista de Did´actica de las Matem´aticas, 9, 85-97 y 10, 89-103. [27] Kieran, C. y Filloy, E. (1989) El aprendizaje del ´algebra escolar desde una perspectiva psicol´ogica, Ense˜nanza de las Ciencias, 7 (3), 229-240. [28] Lakoff, G. & N´u˜nez, R. (2000) Where mathematics comes from. How the embodied mind brings mathematics into being. New York. Basic Books [29] Lakoff, G. y Johnson, M. (1980) Metaphors We Live By. The University of Chicago Press. Chicago. [30] Lamon, S. (1996) The development of unitizing: its role in children partitioning strategies. Journal for Research in Mathematics Education, Vol. 27, 2, 170 - 193 [31] Maza, C. (1991) Ense˜nanza de la suma y la resta. Espa˜na. Editorial S´ıntesis [32] McCloskey, M., Caramazza, A., Basili, A. (1985) Cognitive mechanisms in number processing and calculation: evidence from dyscalculia. Brain and Cognition 4, 171-196. [33] Miura, I. (1987). Mathematics achievement as a function of language. Journal of Educational Psychology, 79, 79-82. [34] Mulligan, J. T. & Mitchelmore, M.C., et al. (1997) Second grader’s representations and conceptual understanding of number: A longitudinal study. Paper presented to the 20th Conference of the Mathematics Education Research Group of Australasia (MERGA), Rotorua, New Zealand. [35] Orozco, M. & Hederich, C. (2002) Errores de los ni˜nos al escribir numerales dictados. On line www.matematicaycognition.cjb.net. [36] Orozco, M. (1997) La matem´atica en primaria. Actas 8vas JAEM. Jornadas para el aprendizaje y la ense˜nanza de las matem´aticas. Salamanca, Espa˜na: 447-449 [37] Resnick, L.(1983) A developmental theory of number understanding. En Ginsburg, H.(comp.), The development of mathematical thinking. (pp. 109- 155) New York: Academic Press. [38] Saxton, M. & Towse, J. (1998) Linguistic relativity: The case of place value in Multi-digit numbers. Journal of Experimental Child Psychology, 69, 66 - 79 [39] Serrano, J. y Denia, A.(1987) Estrategias de conteo implicadas en los procesos de adici´on y sustracci´on. Infancia y aprendizaje, 39-40. 57-69 [40] Sfard, A. (1998). On two metaphors for learning and the dangers of choosing just one. Educational Researcher, 27, 2, 4 -13 [41] Steffe, L., Cobb, P., et al. (1988) Construction of Arithmetical Meanings and Strategies. New York, Springer-Verlag. [42] Thomas, G. & Ward, J. (2001). An Evaluation of the Count me In Too Pilot Project. Wellington, NZ: Learning Media. [43] Vergnaud, G. (1988) Multiplicative structures. En J. Hiebert, J. and M. Behr, Number Concepts and Operations in the Middle Grades. Vol 2. Reston, Virginia: The National Council of Teachers of Mathematics, Inc., Second Printing 1989, 141-161. [44] Zapata, P. (2001) Educar cient´ıficamente en ciencias: Implicaciones para la formaci´on docente. Universidad Pedag´ogica Nacional y Programa de Doctorado en Educaci´on. ´Area Educaci´on en Ciencias. UPN. No publicado