Sobre la emergencia del pensamiento algebraico temprano y su desarrollo en la educación primaria

dc.contributor.authorVergel Causado, Rodolfo
dc.contributor.orcidVergel Causado, Rodolfo [0000-0002-0925-3982]spa
dc.date.accessioned2024-06-13T14:09:39Z
dc.date.available2024-06-13T14:09:39Z
dc.date.created2015
dc.descriptionUna tradición curricular muy bien establecida nos ha llevado a pensar que la enseñanza del álgebra es un asunto de la escuela secundaria. La idea detrás de esta tradición es que, para entender álgebra, es necesario tener una base aritmética relativamente sólida. De hecho, muchos —y entre ellos incluimos no solamente a matemáticos y educadores matemáticos, sino también a filósofos, científicos y sicólogos del desarrollo, como Kant, Newton y Vygotsky, respectivamente— han considerado el álgebra como una extensión o generalización de la aritmética. ¿Cómo, dentro de esta línea de pensamiento, podría pensarse en enseñar álgebra si el estudiante no ha desarrollado suficiente- mente su base aritmética? (....)spa
dc.description.abstractA very well-established curricular tradition has led us to think that the teaching of algebra is a secondary school subject. The idea behind this tradition is that, to understand algebra, it is necessary to have a relatively solid arithmetic foundation. In fact, many—and among them we include not only mathematicians and mathematics educators, but also philosophers, scientists, and developmental psychologists, such as Kant, Newton, and Vygotsky, respectively—have considered algebra as an extension or generalization of arithmetic. How, within this line of thought, could we think about teaching algebra if the student has not sufficiently developed the arithmetic base of it? (....)spa
dc.description.cityBogotáspa
dc.format.mimetypepdfspa
dc.identifier.editorialUniversidad Distrital Francisco José de Caldas. Doctorado Interinstitucional en Educación.spa
dc.identifier.isbn978-958-8972-23-7spa
dc.identifier.isbn978-958-8972-24-4spa
dc.identifier.urihttp://hdl.handle.net/11349/36358
dc.relation.ispartofseriesTesis doctoral: N° 4spa
dc.relation.referencesAinley, J. (2001). Research Forum: Early Algebra. In Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 129-159). Utrecht University, The Netherlands.spa
dc.relation.referencesArzarello, F. & Robutti, O. (2001). From Body Motion to Algebra through Graphing. In Chick, H.; Stacey, K.; Vincent, J. & Vincent, J. (Eds.), Proceedings of the 12th ICMI Study Conference (Vol. 1, pp. 33-40). The University of Melbourne, Australia.spa
dc.relation.referencesBecker, J. & Rivera, F. (2006a). Establishing and justifying algebraic generalization at the sixth grade level. In Novotná, J.; Moraová, H.; Krátkná, M. & Stehlíková, N. (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 465-472). Prague, Czech Republic.spa
dc.relation.referencesBecker, J. & Rivera, F. (2006b). Sixth graders’ figural and numerical strategies for generalizing patterns in algebra. In Alatorre, S.; Cortina, J. L.; Sáiz, M. & Méndez, A. (Eds.), Proceedings of the 28th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 95-101). Mérida, México: Universidad Pedagógica Nacional.spa
dc.relation.referencesBednarz, N.; Kieran, C. & Lee, L. (1996). Approaches to algebra, perspectives for research and teaching. Dordrecht: Kluwer.spa
dc.relation.referencesCai, J. & Knuth, E. (2011). Early algebraization. New York: Springer.spa
dc.relation.referencesCarraher, D.; Schliemann, A. & Brizuela, B. (2001). Can young students operate on unknowns? In M. v. d. Heuvel-Panhuizen (Ed.), Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 130-140). Utretch University, The Netherlands.spa
dc.relation.referencesCarraher, D.; Schliemann, A. & Brizuela, B. (2001). Can young students operate on unknowns? In M. v. d. Heuvel-Panhuizen (Ed.), Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 130-140). Utretch University, The Netherlands.spa
dc.relation.referencesDougherty, B. (2003). Voyaging From Theory to Practice in Learning: Measure Up. In Pateman, N. A.; Dougherty, B. J. & Zilliox, J. T. (Eds.), Proceedings of the 27th Conference of the International Group for the Pshychology of Mathematics Education (PME & PMENA) (Vol. 1, pp. 17-23). Honololu: University of Hawai’i.spa
dc.relation.referencesFilloy, E. & Rojano, T. (1984). La aparición del lenguaje aritmético-algebraico. L’Educazione Matematica, 5(3), 278-306.spa
dc.relation.referencesFilloy, E. & Rojano, T. (1989). Solving equations: The transition from arithmetic to algebra. For the Learning of Mathematics, 9(2), 19-25.spa
dc.relation.referencesKaput, J. (1998). Transforming algebra from an engine of inequity to an engine of mathematical power by “algebrafying” the K-12 curriculum. In The nature and role of algebra in the K-14 curriculum: Proceedings of a national symposium (pp. 25-26). Washington, D.C.: National Academic Press.spa
dc.relation.referencesKieran, C. (1989). A perspective on algebraic thinking. G Vernand, J., Rogalski, & M.Artigue (Eds). Proceedings of the 13th International Conference for the Psychology of Mathematics Education., 2, 163-171.spa
dc.relation.referencesMoss, J. & Beatty, R. (2006). Knowledge Building and Knowledge Forum: Grade 4 Students Collaborate to Solve Linear Generalizing Problems. In Novotná, J.; Moraová, H.; Krátká, M. & Stehlíková, N. (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 193-199). Prague, Czech Republic.spa
dc.relation.referencesRadford, L. (2006). Algebraic thinking and the generalization of patterns: A semiotic perspective. In Alatorre, S.; Cortina, J. L.; Sáiz, M. & Méndez, A. (Eds.), Proceedings of the 28th conference of the international group for the psychology of mathematics education, north american chapter (Vol. 1, pp. 2-21). Mérida, Mexico.spa
dc.relation.referencesRadford, L. (2014). The progressive development of early embodied algebraic thinking. Mathematics Education Research Journal, 26(2), 257-277.spa
dc.relation.referencesRivera, F. (2006). Sixth Graders’ ability to generalize patterns in algebra: issues and insights. In J. Novotná, H; Moraová, M; Krátká & N. Stehlíková (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, p. 320). Prague, Czech Republic.spa
dc.relation.referencesWagner, S., & Kieran, C. (1989). Research issues in the learning and teaching of algebra. Virginia: Lawrence Erlbaum & NCTM.spa
dc.relation.referencesWarren, E. (2006). Teacher actions that assist young students write generalizations in words and in symbols. In Novotná, J.; Moraová, H.; Krátká, M. & Stehlíková, N. (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 5, pp. 377-384). Prague, Czech Republic.spa
dc.relation.referencesAgudelo-Valderrama, C. (2000). Una innovación curricular que enfoca el proceso de transición entre el trabajo aritmético y el algebraico. Tunja: Universidad Pedagógica y Tecnológica de Colombia.spa
dc.relation.referencesAgudelo-Valderrama, C. & Vergel, R. (2009). Proyecto PROMICE - Promoción de un enfoque interdisciplinario y de resolución de problemas en el inicio del trabajo algebraico escolar: integrando contextos de ciencias y el uso de tecnología digital. Informe final del Proyecto PROMICE - Código 86 de 2007. Centro de documentación, IDEP: Bogotá.spa
dc.relation.referencesAlibali, M. W.; Kita, S. & Young, A. (2000). Gesture and the process of speech production: We think, therefore we gesture. Language and Cognitive Processes, 15, 593-613. doi:10.1080/016909600750040571.spa
dc.relation.referencesArzarello, F. (2006). Semiosis as a multimodal process. Revista Latinoamericana de Investigación en Matemática Educativa, Special Issue on Semiotics, Culture, and Mathematical Thinking (editores invitados: Radford, L. & D’Amore, B.), (pp. 267-299).spa
dc.relation.referencesArzarello, F. & Edwards, L. (2005). Gesture and the construction of mathematical meaning. En: Chick, H. L. & Vincent, J. L. (Eds.), Proceedeings of the 29th Conference of the International Group for the Psychology of Mathematics Education (pp. 123-154). Melbourne: PME.spa
dc.relation.referencesBajtín, M. (1992). El marxismo y la filosofía del lenguaje. Madrid: Alianza Editorial. (Original publicado en 1929).spa
dc.relation.referencesBajtín, M. (2009). Estética de la creación verbal. México: Siglo XXI. (Original publicado en 1979).spa
dc.relation.referencesBlanton, M. & Kaput, J. (2005). Characterizing a Classroom Practice That Promotes Algebraic Reasoning. Journal for Research in Mathematics Education, 36 (5), 412-446.spa
dc.relation.referencesBruner, J. (2006). Actos de significado. Más allá de la revolución cognitiva. Madrid: Alianza Editorial.spa
dc.relation.referencesCalderón, D. (2005). Dimensión cognitiva y comunicativa de la argumentación en matemáticas. Tesis Doctoral no publicada. Universidad del Valle, Cali, Colombia.spa
dc.relation.referencesCalderón, D. (2005). Dimensión cognitiva y comunicativa de la argumentación en matemáticas. Tesis Doctoral no publicada. Universidad del Valle, Cali, Colombia.spa
dc.relation.referencesCarraher, D. W. & Schliemann, A. D. (2007). Early algebra and algebraic reasoning. En: Lester, F. K. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 669-705). Reston, VA: NCTM e IAP.spa
dc.relation.referencesCastañares, W. (1985). El signo: problemas semióticos y filosóficos. Tesis doctoral, Universidad Complutense de Madrid, Madrid. Recuperado el 8 de mayo de 2011 de http:// www.unav.es/gep/TesisDoctorales.htmlspa
dc.relation.referencesCastorina, J. A. & Carretero, M. (Comps.) (2012). Desarrollo cognitivo y educación. Procesos del conocimiento y contenidos específicos (Vol. II). Buenos Aires: Paidós.spa
dc.relation.referencesCole, M. (1999). Psicología Cultural. Madrid: Morata.spa
dc.relation.referencesCole, M. & Wertsch, J. (1996). Beyond the Individual-Social Antinomy in Discussions of Piaget and Vygotsky. Human Development, 39, 250-256.spa
dc.relation.referencesD´Amore, B. (2001). Cocepttualizzazione, registri di rappresentazioni semiotiche e noetica. La matemática e la sua didattica, 2, 150-173.spa
dc.relation.referencesD’Amore B. (2006). Objetos, significados, representaciones semióticas y sentido. In: Semiotics, Culture and Mathematical Thinking. Numero speciale della rivista Relime (Cinvestav, México DF., México), Radford L., D’Amore B. (eds.) (2006). 177-196.spa
dc.relation.referencesD’Amore, B., Radford, L., & Bagni, GT. (2007). Obstáculos epistemológicos y perspectiva socio-cultural de la matemática. Colección “Cuadernos del Seminario en educación”. Bogotá: Universidad Nacional de Colombia.spa
dc.relation.referencesD´Amore, B.; Fandiño, M. I. & Iori, M. (2013). La semiótica en la didáctica de la matemática. (M. Fandiño, Trad.). Bogotá: Magisterio.spa
dc.relation.referencesDavydov, V. V. (1981). Tipos de generalización en la enseñanza. La Habana: Pueblo y Educación.spa
dc.relation.referencesDescartes, R. (1954). The geometry. New York: Dover. (Original work published 1637).spa
dc.relation.referencesDuval, R. (1999). Semiosis y pensamiento humano: Registros semióticos y aprendizajes intelectuales (M. Vega, Trad.). Cali: Universidad del Valle. (Original publicado en 1995).spa
dc.relation.referencesEco, U. (1988). Le signe [the sign]. Bruxelles: Éditions Labor.spa
dc.relation.referencesEnglish, L. D. & Warren, E. (1998). Introducing the variable through pattern exploration. The Mathematics Teacher, 91(2), 166-171.spa
dc.relation.referencesErnest, P. (1991). The philosophy of Mathematics Education. London: Falmer Press.spa
dc.relation.referencesFairclough, N. (1995). Critical discourse analysis; the critical study of languages. New York, USA: Longman.spa
dc.relation.referencesGehlen, A. (1988). Man, his nature and place in the world. New York: Columbia University Press.spa
dc.relation.referencesGlaser, B. G. (1978). Theoretical Sensitivity. Advances in the Methodology of Grounded Theory. Mill Valley, CA: Sociology Press.spa
dc.relation.referencesGlaser, B. G. (2002). “Constructivist Grounded Theory?” Forum: Qualitative Sozial forschung/Forum: Qualitative Research (periódico on line), 3 (3). Disponible en: http:/ qualitative-research.net/fqs-texte/3-o2/3-02glaser-e.htm.spa
dc.relation.referencesGlaser, B. G. & Strauss, A. L. (1967). The Discovery of Grounded Theory. Strategies for Qualitative Research. Chicago: Aldine.spa
dc.relation.referencesGillin, J. (1948). The ways of men. New York, EU: Appleton-Century-Crofts.spa
dc.relation.referencesGoetz, J. & Lecompte, M. (1988). Etnografía y diseño cualitativo en investigación educativa. Madrid: Morata.spa
dc.relation.referencesGoldin, G. (1998). Observing Mathematical Problem Solving through Task-Based Interviews. In: Journal for Research in Mathematics Education, Monograph number 9. Qualitative Research Methods in Mathematics Education. Reston, Virginia, USA: National Council of Teachers of Mathematics.spa
dc.relation.referencesGoldin, G. (2000). A scientific perspectives on structured, task-based interviews in mathematics education research (pp. 517-545). En: Kelly, A. & Lesh, R. (Eds.). Handbook of Research Design in Mathematics and Science Education. New Jersey London: LEA, publishers.spa
dc.relation.referencesHegel, G. (2001). The philosophy of history. Kitchener, ON: Batoche Books. (Original publicado en 1837).spa
dc.relation.referencesHegel, G. (2004). Enciclopedia de las ciencias filosóficas. México: Porrúa. (Original publicado en 1817).spa
dc.relation.referencesHegel, G. (2009). Logic. (W. Wallace, Trans.). Pacifica, CA: MIA. (Original publicado en 1830).spa
dc.relation.referencesHerrero, C. (1992). “Mijail Bajtín y el principio dialógico en la creación literaria y en el discurso humano”. En: Revista Suplementos. Historia de la relación filosofía-literatura, 32 (mayo). Barcelona: Anthropos.spa
dc.relation.referencesHusserl, E. (1931). Ideas: General introduction to pure phenomenology (W. R. B. Gibson, Trans. Third Edition, 1958). London: Allen & Unwin.spa
dc.relation.referencesIlyenkov, E. (1977). ‘The concept of the ideal’. In: Philosophy in the USSR: Problems of Dialectical Materialism. Moscow: Progress Publishers.spa
dc.relation.referencesKaput, J. (1998). Teaching and learning a new algebra with understanding. Dartmouth, MA: National Center for Improving Student Learning and Achievement in Mathematics and Science.spa
dc.relation.referencesKaput, J. (1999). Teaching and learning a new algebra. In: Fennema, E. & Romberg, T. (Eds.), Mathematics classrooms that promote understanding (pp. 133-155). Mahwah, N.J: L. Erlbaum Associates, Publishers.spa
dc.relation.referencesKaput, J. (2000). Transforming algebra from an engine of inequity to an engine of mathematical power by “algebrafying” the K-12 curriculum. Dartmouth, MA: National Center for Improving Student Learning and Achievement in Mathematics and Science.spa
dc.relation.referencesKaput, J. & Blanton, M. (2001). Algebrafying the Elementary Mathematics Experience. Part I: Transforming Tasks Structures. In: Chick, H.; Stacey, K.; Vincent, J. & Vincent, J. (Eds.). The Future of the Teaching and Learning of Algebra (Proceedings of the 12th ICMI Study, Vol. 1, pp. 344-351). Melbourne: University of Melbourne.spa
dc.relation.referencesKendon, A. (1980). Gesticulation and speech: Two aspects of the process of the utterance. En: Key, M. R. The relationship of verbal and nonverbal communication (pp. 207-227). Inglaterra: Mouton.spa
dc.relation.referencesKendon, A. (1987). On gesture: Its complementary relationship with speech. En: Siegman, A. W. & Feldstein, S. (Eds.), Nonverbal behavior and communication (pp. 65- 97). New Jersey, E.U.: Lawrence Erlbaum.spa
dc.relation.referencesKieran, C. (1989). The early learning of algebra: A structural perspective. En: Wagner, S. y Kieran, C. Research agenda for mathematics education: Vol. 4. Research issues in the learning and teaching of algebra (pp.33-56). Hillsdale, NJ: Erlbaum.spa
dc.relation.referencesKieran, C. (2006). Research on the learning and the teaching of algebra: A broadening of sources of meaning. In: Handbook of research on the psychology of mathematics education: Past, present, future, ed. A. Gutiérrez and P. Boero, 23-49. Rotterdam, The Netherlands: Sense Publishers. Can be useful to the analysis of this phenomenon. ICMI, Rome, March 2008.spa
dc.relation.referencesKieran, C. (2007). Learning and Teaching Algebra at the Middle School Through College Levels. En: Lester, F. K. (Ed.), Second Handbook of Research on Mathematics Teaching and Learning. (pp. 707-762). Reston, Virginia: NCTM e IAP.spa
dc.relation.referencesKozulin, A. (2000). Instrumentos psicológicos: la educación desde una perspectiva cultural. Barcelona: Paidós.spa
dc.relation.referencesLamiell, J. T. (2003). Beyond individual and Group Differences. Thousand Oaks, Ca; Sage Lins, R. & Kaput, J. (2004). The early development of algebraic reasoning: the current state of the field. En: Stacey, K.; Chick, H. & Kendal, M. (Eds.) The teaching and learning of algebra. The 12th ICMI Study (pp.47-70). Norwell, MA: Kluwer Academic Publishers.spa
dc.relation.referencesMaddock, M. N. (1981). Science education: An anthropological viewpoint. Studies in Science Education, 8, 1-26.spa
dc.relation.referencesMarx, K. & Engels, F. (1970). The German Ideology, Edited with Introduction by C. J. Arthur, New York: International Publishers.spa
dc.relation.referencesMason, J. (1996). Expressing generality and roots of algebra. En N. Bednarz, C. Kieran y L. Lee (Eds.), Approaches to Algebra. Perspectives for Research and Teaching. London: Kluwer Academic Publishers.spa
dc.relation.referencesMason, J.; Burton, L. & Stacey, K. (1982). Mathematical thinking. London: Addison-Wesley.spa
dc.relation.referencesMason, J.; Graham, A.; Pimm, D. & Gowar, N. (1999). Raíces del álgebra/Rutas hacia el álgebra. Tunja: Universidad Pedagógica y Tecnológica de Colombia.spa
dc.relation.referencesMaybee, J. (2009). Picturing Hegel. Lanham, MD: Lexington Books.spa
dc.relation.referencesMcNeill, D. (1985). So you think gestures are nonverbal? Psychological Review, 92(3), 350-371.spa
dc.relation.referencesMerleau-Ponty, M. (1945). Phénomenologie de la perception. Paris: Gallimard.spa
dc.relation.referencesMinisterio de Educación Nacional de Colombia -MEN- (1998). Lineamientos Curriculares para Matemáticas. Bogotá: Magisterio.spa
dc.relation.referencesMinisterio de Educación Nacional de Colombia -MEN- (2006). Estándares Básicos de Competencias en Lenguaje, Matemáticas, Ciencias y Ciudadanas. Bogotá: Ministerio de Educación Nacional.spa
dc.relation.referencesMiranda, I. (2009). Objetivación de saberes científico-culturales relacionados con el movimiento lineal representado con gráficas cartesianas: una experiencia con estudiantes de Bachillerato. Tesis doctoral no publicada. Departamento de Matemática Educativa. Centro de Investigación y de Estudios Avanzados del IPN. México.spa
dc.relation.referencesMiranda, I.; Radford, L. & 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.spa
dc.relation.referencesMolina, M. (2009). Una propuesta de cambio curricular: integración del pensamiento algebraico en educación primaria. PNA, 3 (3), 135-156.spa
dc.relation.referencesMontagu, A. (Ed.). (1968). Man’s adaptive dimension. New York, EU: Oxford University Press.spa
dc.relation.referencesNoel, G. (1995). La lógica de Hegel. (J. A. Díaz, Trad.). Bogotá: Editorial Universidad Nacional. (Original publicado en 1933).spa
dc.relation.referencesPopkewitz, T. (2004). The alchemy of the mathematics curriculum: Inscriptions and the fabrication of the child. American Educational Research Journal, 41 (1), 3-34.spa
dc.relation.referencesRadford, L. (1996). The Roles of Geometry and Arithmetic in the Development of Algebra: Historical Remarks from a Didactic Perspective. Cap.3, pp. 39-54. En: Bednarz, N. et al. (Eds.), Approaches to Algebra. Perspectives for Research and Teaching. Dordrecht: Kluwer.spa
dc.relation.referencesRadford, L. (1997). L’invention d’une idée mathématique: la deuxième inconnue en algèbre, Repères (Revue des instituts de Recherche sur l’enseignement des Mathématiques de France), juillet, 28, 81-96.spa
dc.relation.referencesRadford, L. (2000). Sujeto, objeto, cultura y la formación del conocimiento. Educación Matemática, 12(1), 51-69.spa
dc.relation.referencesRadford, L. (2002). The seen, the spoken and the written. A semiotic approach to the problem of objectification of mathematical knowledge. For the Learning of Mathematics, 22(2), 14-23.spa
dc.relation.referencesRadford, 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.spa
dc.relation.referencesRadford, L. (2004). Semiótica cultural y cognición. Conferencia plenaria Décima octava Reunión latinoamericana de Matemática Educativa. Universidad Autónoma de Chiapas.spa
dc.relation.referencesRadford, L. (2005). ¿Why do gestures matter? Gestures as semiotic means of Objectification. In Helen L. Chick, Jill L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education, University of Melbourne, Australia, Vol. 1, pp. 143-145.spa
dc.relation.referencesRadford, L. (2006a). The Anthropology of Meaning. Educational Studies in Mathematics, 61(1-2), 39-65.spa
dc.relation.referencesRadford, L. (2006b). Elementos de una teoría cultural de la objetivación. En: Revista Latinoamericana de Investigación en Matemática Educativa, número especial sobre semiótica, cultura y pensamiento matemático (editores invitados: Radford, L. & D’Amore, B.), pp. 267-299.spa
dc.relation.referencesRadford, L. (2006c). Algebraic Thinking and the Generalization of Patterns: A Semiotic Perspective. In S. Alatorre, J. L. Cortina, M. Sáiz, A. Méndez (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, North American Chapter, Mérida: Universidad Pedagógica Nacional, November 9-12, Vol. 1, pp. 2-21.spa
dc.relation.referencesRadford, L. (2008a). The ethics of being and knowing: towards a cultural theory of learning. In: Radford L.; Schubring G.; Seeger F. (Eds.), Semiotics in Mathematics Education (pp. 215-234). Rotterdam: Sense Publishers.spa
dc.relation.referencesRadford, L. (2008b). Iconicity and contraction: a semiotic investigation of forms of algebraic generalizations of patterns in different contexts. En: ZDM Mathematics Education, 40, 83-96.spa
dc.relation.referencesRadford, L. (2009). ‘‘No! He starts walking backwards!’’: interpreting motion graphs and the question of space, place and distance. ZDM - The International Journal on Mathematics Education, DOI 10.1007/s11858-009-0173-9.spa
dc.relation.referencesRadford, L. (2010a). Algebraic thinking from a cultural semiotic perspective. Research in Mathematics Education, 12(1), 1-19.spa
dc.relation.referencesRadford, L. (2010b). Layers of generality and types of generalization in pattern activities. PNA, 4(2), 37-62.spa
dc.relation.referencesRadford, L. (2010c). The eye as a theoretician: Seeing structures in generalizing activities, For the Learning of Mathematics, 30(2), 2-7.spa
dc.relation.referencesRadford, L. (2012a). Early algebraic thinking: Epistemological, semiotic, and developmental issues. ICME-12 Regular Lecture. Seoul, South Korea. July 8-15, 2012.spa
dc.relation.referencesRadford, L. (2012b). On the cognitive, epistemic, and ontological roles of artifacts. In G. Gueudet, B. Pepin, & L. Trouche, (Eds.), From text to ‘lived’ resources (pp. 238-288). New York: Springer.spa
dc.relation.referencesRadford, 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.2013.19spa
dc.relation.referencesRadford, L. (2013b). En torno a tres problemas de la generalización. En: Rico, L.; Cañadas, M. C.; Gutiérrez, J.; Molina, M. & Segovia, I. (Eds.), Investigación en Didáctica de la Matemática. Homenaje a Encarnación Castro (pp. 3-12). Granada, España: Editorial Comares.spa
dc.relation.referencesRadford, L.; Edwards, L. & Arzarello, F. (2009). Beyond words. Educational Studies in Mathematics, 70(3), 91-95.spa
dc.relation.referencesRadford, L., Demers, S., Guzmán, J. & Cerulli, M. (2003). “Calculators, Graphs and the Production of Meaning”. En: Pateman, N.; Dougherty, B. & Zilliox, J. (eds.), Proceedings of the 27 Conference of the International Group for the Psychology of Mathematics Education (pme27 –pmena25), University of Hawaii, vol. 4, pp. 55-62.spa
dc.relation.referencesRadford, L. & Demers, S. (2004). Communication et apprentissage. Repères conceptuels et pratiques pour la salle de classe de mathématiques. Ottawa: Centre franco-ontarien des ressources pédagogiques, 206 p.spa
dc.relation.referencesRadford, L. & Roth, W. M. (2010). Intercorporeality and ethical commitment: an activity perspective on classroom interaction. Educational Studies in Mathematics, Online First. Doi 10.1007/s10649- 10010-19282-10641.spa
dc.relation.referencesRamos, S. (1936). El perfil del hombre y la cultura en México. (15 Ed.). México, D.F.: Espasa-Calpe.spa
dc.relation.referencesRancière, J. (1999). Dis-agreement: Politics and philosophy. Minneapolis: University of Minnesota Press.spa
dc.relation.referencesRatner, C. (2000). Outline of a coherent, comprehensive concept of culture. The problem of fragmentary notions of culture. Cross-Cultural Psychology Bulletin, Trinidad, USA.spa
dc.relation.referencesRosch, E. (1975). Universals and cultural specifics in human categorization. En: Cross-Cultural perspectives on learning. Brislin, R. W.; Bochner, Stephen & Lonner, Walter J. (Eds.), pp. 177-206. New York, Estados Unidos: John Wiley & Sons.spa
dc.relation.referencesRoth, M. & Radford, L. (2011). A Cultural-Historical Perspective on Mathematics Teaching and Learning. Ontario: Sense Publishers.spa
dc.relation.referencesSanti, G. (2010). Changes in meaning of mathematical objects due to semiotic transformations: a comparison between semiotic perspectives. Tesis doctoral no publicada. Universidad de Bologna, Bologna, Italia.spa
dc.relation.referencesSanti, G. (2011). Objectification and semiotic function. Educational Studies in Mathematics, 77, 285-311.spa
dc.relation.referencesSerfati, M. (1999). La dialectique de l’indéterminé, de viète à frege et russell. In M. Serfati (Ed.), La recherche de la vérité (pp. 145- 174). Paris: ACL - Les éditions du kangourou.spa
dc.relation.referencesSocas, M. (2011). La enseñanza del Álgebra en la Educación Obligatoria. Aportaciones de la investigación, 77, 5-34.spa
dc.relation.referencesSoneira, A. J. (2006). “La Teoría fundamentada en los datos de Glaser y Strauss”. En: Vasilachis de Gialdino, I. (Coord.), Estrategias de investigación cualitativa. (pp. 153- 173). Barcelona: Gedisa.spa
dc.relation.referencesValsiner, J. (2012). “La dialéctica en el estudio del desarrollo”. En: Castorina, J. & Carretero, M. (Comps.), Desarrollo cognitivo y educación. Procesos del conocimiento y contenidos específicos (Vol. II). (pp. 139-162). Buenos Aires: Paidós.spa
dc.relation.referencesValsiner, J. (2012). “La dialéctica en el estudio del desarrollo”. En: Castorina, J. & Carretero, M. (Comps.), Desarrollo cognitivo y educación. Procesos del conocimiento y contenidos específicos (Vol. II). (pp. 139-162). Buenos Aires: Paidós.spa
dc.relation.referencesViète, F. (1983). The analytic art. New York: Dover. (Trabajo original publicado en 1591).spa
dc.relation.referencesVygotsky, L. (1929). The problem of the cultural development of the child. Journal of Genetic Psychology, 36, 415-434.spa
dc.relation.referencesVygotsky, L. (1978). Mind in Society: The development of higher psychological processes. Cambridge, MA, E.U.: Harvard University Press.spa
dc.relation.referencesVygotski, L. (1987). Historia del desarrollo de las Funciones Psicológicas Superiores. La Habana: Científico-Técnica.spa
dc.relation.referencesVygotski, L. (1988). El desarrollo de los procesos psicológicos superiores. México: Grijalbo. Trad. de la versión inglesa, Mind in Society: The development of higher psycholgical processes. Cambridge, MA: Harvard University Press. La Habana: Ed. Científico-Técnica.spa
dc.relation.referencesVygotsky, L. (1989). El proceso de formación de la psicología marxista: Vygotsky, L.; Leontiev, A.; Luria, A. URSS: Progreso.spa
dc.relation.referencesVygotski, L. S. (2000). Obras escogidas (Vol. III) (L. Kuper, Trad.). Madrid: Visor. (Original publicado en 1931).spa
dc.relation.referencesVygotski, L. (2007). Pensamiento y habla (A. Ariel González, Trad.). Buenos Aires: Ediciones Colihue. (Original publicado en 1934).spa
dc.relation.referencesWertsch, J. (1988). Vygotsky y la formación social de la mente. Barcelona: Paidós. Versión original: Vygotsky and the social formation of mind, Cambridge: Harvard University Press, 1985.spa
dc.relation.referencesWertsch, J. (1991). Voces de la mente. Un enfoque sociocultural para el estudio de la acción mediada. Madrid: Visor.spa
dc.relation.referencesWertsch, J. (1998). La mente en acción. Madrid: Aique.spa
dc.relation.referencesWhite, L. A. (1959). The concept of culture. American Anthropologist, 61(2), 227-251.spa
dc.relation.referencesYou, H. (1994). Defining rhythm: aspects of an anthropology of rhythm. Culture, Medicine and Psychiatry, 18, 361-384.spa
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional*
dc.rights.accesoAbierto (Texto Completo)spa
dc.rights.accessrightsOpenAccessspa
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectPensamiento algebraicospa
dc.subjectObjetivaciónspa
dc.subjectSemióticaspa
dc.subjectRepresentación tabularspa
dc.subjectEducación primariaspa
dc.subject.keywordAlgebraic thinkingspa
dc.subject.keywordObjectificationspa
dc.subject.keywordSemioticspa
dc.subject.keywordtabular representationspa
dc.subject.lembÁlgebraspa
dc.subject.lembMatermáticas -- Enseñanza básicaspa
dc.subject.lembAnálisis matemáticospa
dc.subject.lembRazonamientospa
dc.subject.lembLógicaspa
dc.titleSobre la emergencia del pensamiento algebraico temprano y su desarrollo en la educación primariaspa
dc.title.alternativeAspectos a considerarspa
dc.title.titleenglishOn the emergence of early algebraic thinking and its development in primary educationspa
dc.typebookspa

Archivos

Bloque original

Mostrando 1 - 1 de 1
Cargando...
Miniatura
Nombre:
sobre_la_emergencia_del_pensamiento_algebraico_temprano0ay_su_desarrollo_en_la_educacion_primaria.pdf
Tamaño:
2.61 MB
Formato:
Adobe Portable Document Format
Descripción:
Sobre la emergencia del pensamiento algebraico temprano y su desarrollo en la educación primaria

Bloque de licencias

Mostrando 1 - 1 de 1
No hay miniatura disponible
Nombre:
license.txt
Tamaño:
7 KB
Formato:
Item-specific license agreed upon to submission
Descripción: