Generalización de patrones y formas de pensamiento algebraico temprano

Referencias

Arzarello, F. (2006). Semiosis as a multimodal process. Revista Latinoamericana de Investi-gación en Matemática Educativa. Special Issue on Semiotics, Culture, and Mathematical Thinking, 9(1), 267-300. Cole, M. y Wertsch, J. (1996). Beyond the individual-social antinomy in discussions of Pia-get and Vygotsky. Human Development, 39, 250-256. D’Amore, B., Fandiño, M. I. e Iori, M. (2013). La semiótica en la Didáctica de la Matemáti-ca. Bogotá, Colombia: Magisterio. D’Amore, B. y Maier, H. (1999). Investigating teachers’ work with pupils’ textual eigenpro-ductions. En I. Schwank (Ed.), Proceedings of the First Conference of the European So-ciety for Research in Mathematics Education (pp. 257-274). Osnabrück, Alemania: Euro-pean Society for Research in Mathematics Education. D’Amore, B. y Maier, H. (2003). Producciones escritas de los estudiantes sobre argumentos de matemáticas. Epsilon, 18(2), 53, 243-262. Davydov, V. V. (1981). Tipos de generalización en la enseñanza. La Habana, Cuba: Pueblo y Educación. Goldin, G. (1997). Observing mathematical problem solving through task-based interviews. Journal for Research in Mathematics Education. Monograph, chapter 4, 9, 40-62, 164-177. doi: 10.2307/749946 Goldin, G. (2000). A scientific perspectives on structured, task-based interviews in mathe-matics education research. En A. Kelly y R. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 517-545). New Jersey, NJ: LEA publishers. Hegel, G. (1837/2001). The philosophy of history. Kitchener, ON: Batoche Books. Ilyenkov, E. (1977). ‘The concept of the ideal’. In Philosophy in the USSR: Problems of dia-lectical materialism. Moscú, Rusia: Progress Publishers . Maybee, J. (2009). Picturing Hegel. Lanham, MD: Lexington Books. Miranda, I., Radford, L. y Guzmán, J. (2007). Interpretación de gráficas cartesianas sobre el movimiento desde el punto de vista de la teoría de la objetivación. Educación Matemática, 19(3), 5-30. Radford, L. (2003). Gestures, speech, and the sprouting of signs: A semiotic-cultural ap-proach to studens’ types of generalization. Mathematical Thinking and Learning, 5(1), 37-70. Radford, L. (2006). Elementos de una teoría cultural de la objetivación. Revista Latinoameri-cana de Investigación en Matemática Educativa. Special Issue on Semiotics, Culture, and Mathematical Thinking, 9(l), 267-299. Radford, L. (2008). Iconicity and contraction: A semiotic investigation of forms of algebraic generalizations of patterns in different contexts. ZDM. Mathematics Education, 40, 83-96. Radford, L. (2010a). Algebraic thinking from a cultural semiotic perspective. Research in Mathematics Education, 12(1), 1-19. Radford, L. (2010b). 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 y E. Knuth (Eds.), Early Algebraization. A global dialogue from multiple perspectives (pp. 303-322). Berlín, Alemania: Springer-Verlag. Radford, L. (2012a). Early algebraic thinking: Epistemological, semiotic, and developmental issues. En S. J. Cho (Ed.), Proceedings of the 12th International Congress on Mathemati-cal Education (ICME-12) (pp. 675-694). Seúl, Korea: National University of Education. Radford, L. (2012b). On the cognitive, epistemic, and ontological roles of artifacts. In G. Gueudet, B. Pepin y L. Trouche (Eds.), From text to ‘lived’ resources (pp. 238-288). New York, NY: Springer. Radford, L. (2013a). Three key concepts of the theory of objectification: Knowledge, know-ing, and learning. Journal of Research in Mathematics Education, 2(1), 7-44. doi: http://doi.dx.org/10.4471/redimat.2013.19 Radford, L. (2013b). En torno a tres problemas de la generalización. En L. Rico, M. C. Caña-das, J. Gutiérrez, M. Molina e I. Segovia (Eds.), Investigación en Didáctica de la Ma-temática. Homenaje a Encarnación Castro (pp. 3-12). Granada, España: Editorial Co-mares. Radford, L., Bardini, C. y Sabena, C. (2006). Perceptual semiosis and the microgenesis of algebraic generalizations. En M. Bosch (Ed.), Fourth Congress of the European Society for Research in Mathematics Education (CERME 4) (pp. 684-695). Sant Feliu de Guíxols, Spain: European Society for Research in Mathematics Education. Radford, L., Edwards, L. y Arzarello, F. (2009). Beyond words. Educational Studies in Mathematics, 70(3), 9-95. Vygotsky, L. (1929). The problem of the cultural development of the child. Journal of Genet-ic Psychology, 36, 415-434. Vygotsky, L. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press. You, H. (1994). Defining rhythm: Aspects of an anthropology of rhythm. Culture, Medicine and Psychiatry, 18, 361-384.