Generalización de patrones y formas de pensamiento algebraico temprano
DOI:
https://doi.org/10.30827/pna.v9i3.6220Keywords:
Algebraic generalization of patterns, Analyticity, Contextual algebraic thinking, Factual algebraic thinking, Hegelian particular, IndeterminacyAbstract
Este artículo aborda la emergencia de formas de pensamiento algebraico en estudiantes jóvenes y muestra evidencias sobre su evolución. En la primera parte se expone el problema, investigado a partir de la forma en que surgen y evolucionan nuevas relaciones entre el cuerpo, la percepción y el inicio del uso de símbolos a medida que los estudiantes participan en actividades sobre generalización de patrones. La segunda parte presenta algunos constructos analíticos de la teoría de la objetivación. En la tercera se expone la metodología, destacando la recolección de los datos y su análisis. En el resto del trabajo se discuten algunos resultados que alimentan reflexiones sobre el desarrollo del pensamiento algebraico.
Generalization of patterns and forms of early algebraic thinking
This paper addresses the emergence of algebraic thinking forms in young students and we show evidences of their evolution. First, we present the research problem, it is tackled from the way in which new relationships between the body, perception and initiation of use of symbols are emerged and evolved while students participate in activities about generalization of patterns. In the second part, we show some analytical constructs on the theory of objectification. In the third part, we present methodology, highlighting data collection and their analysis. Finally, we discuss some results that feed reflections on the development of algebraic thinking.
Handle: http://hdl.handle.net/10481/34991
Nº de citas en WOS (2017): 1 (Citas de 2º orden, 1)
Downloads
References
Arzarello, F. (2006). Semiosis as a multimodal process. Revista Latinoamericana de Investigación 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 Piaget and Vygotsky. Human Development, 39, 250-256.
D'Amore, B., Fandiño, M. I. e Iori, M. (2013). La semiótica en la Didáctica de la Matemática. Bogotá, Colombia: Magisterio.
D'Amore, B. y Maier, H. (1999). Investigating teachers' work with pupils' textual eigenproductions. En I. Schwank (Ed.), Proceedings of the First Conference of the European Society for Research in Mathematics Education (pp. 257-274). Osnabrück, Alemania: European 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 mathematics 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 dialectical 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 approach 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 Latinoamericana 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 Mathematical 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, knowing, 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. Cañadas, J. Gutiérrez, M. Molina e I. Segovia (Eds.), Investigación en Didáctica de la Matemática. Homenaje a Encarnación Castro (pp. 3-12). Granada, España: Editorial Comares.
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 Genetic 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.