Comprensión y aprendizaje en matemáticas: perspectivas semióticas seleccionadas

dc.contributor.authorDuval, Raymond
dc.contributor.authorSáenz-Ludlow, Adalira
dc.contributor.orcidDuval, Raymond [0000-0003-3377-6318]spa
dc.date.accessioned2024-06-12T17:07:47Z
dc.date.available2024-06-12T17:07:47Z
dc.date.created2016
dc.descriptionEste libro está destinado al estudio, investigación y preparación profesional tanto de los doctorandos de nuestro énfasis, como de los estudiosos de todo el mundo. Dados sus contenidos trascendentales y ricos, el libro podría incluso ser leído por estudiantes de maestría en Didáctica de la matemática, por los colegas profesores de otras universidades y profesores de todos los niveles escolares que deseen tener una mayor competencia en estos importantes temas. Este es el propósito de los autores de este complejo pero interesante e iluminador volumen. Un libro de base para quienes deseen dar los primeros pasos en el estudio de la semiótica en los procesos de comprensión de aquel maravilloso mundo que involucra la enseñanza y el aprendizaje de la matemática. Del prólogo.spa
dc.description.abstractThis book is intended for the study, research and professional preparation of both doctoral students of our emphasis and scholars from around the world. Given its transcendental and rich contents, the book could even be read by master's students in Mathematics Didactics, by fellow professors from other universities and teachers of all school levels who wish to have greater competence in these important topics. This is the purpose of the authors of this complex but interesting and illuminating volume. A basic book for those who wish to take the first steps in the study of semiotics in the processes of understanding that wonderful world that involves the teaching and learning of mathematics. From the prologue.spa
dc.description.cityBogotáspa
dc.format.mimetypepdfspa
dc.identifier.editorialUniversidad Distrital Francisco José de Caldas. Doctorado Interinstitucional en Educación.spa
dc.identifier.isbn978-958-8972-31-2 Impresospa
dc.identifier.isbn978-958-8972-32-9 Digitalspa
dc.identifier.urihttp://hdl.handle.net/11349/36320
dc.relation.ispartofseriesÉnfasis; N° 14spa
dc.relation.referencesD’Amore, B., Fandiño-Pinilla, M.I., Iori, M. et al. (2015). Análisis de los antecedentes histórico-filosóficos de la “paradoja cognitiva de Duval”. Revista Latinoamericana de Investigación en Matemática Educativa, 18(2), 177-212. Recuperado de http://www.clame.org.mx/relime.htm DOI: 10.12802/relime.13.1822spa
dc.relation.referencesRadford L., D’Amore B. (eds.). (2006). Semiotics, Culture and Mathematical Thinking. Número especial trilingüe (inglés, francés y español), revista Relime, Cinvestav, México.spa
dc.relation.referencesBalacheff, N. (1988). Une étude des processus de preuve en mathématique chez des élèves de collège. (Tesis de doctorado). Université Joseph Fourrier, Grenoble, Francia. Disponible en http://tel.archives-ouvertes.fr/tel-00326426/en/spa
dc.relation.referencesBerthelot, R. y Salin, M-H. (1994). L’enseignement de la géométrie à l’école primaire. Grand N, 53, 39-56.spa
dc.relation.referencesBerthelot, R. y Salin, M-H. (2000). L’enseignement de l’espace à l’école primaire. Grand N, 65, 37-59.spa
dc.relation.referencesDupuis, C., Pluvinage, F. y Duval, R. (1978). Étude sur la géométrie en fin de troisième. En Géométrie au Premier Cycle, II (pp. 65-101). París: APMEP.spa
dc.relation.referencesDupuis, C., Pluvinage, F. y Duval, R. (1978). Étude sur la géométrie en fin de troisième. En Géométrie au Premier Cycle, II (pp. 65-101). París: APMEP.spa
dc.relation.referencesDupuis, C., Pluvinage, F. y Duval, R. (1978). Étude sur la géométrie en fin de troisième. En Géométrie au Premier Cycle, II (pp. 65-101). París: APMEP.spa
dc.relation.referencesDuval, R. (2000a). Basic issues for research in mathematics education. En T. Nakahara y M. Koyama (eds.), Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education (pp. 55-69). Hiroshima: Nishiki Print Co. Ltd.spa
dc.relation.referencesDuval, R. (2000b). Écriture, raisonnement et découverte de la démonstration en mathématiques. Recherches en Didactique des Mathématiques, 20(2), 135-170.spa
dc.relation.referencesDuval, R. (2001). Écriture et compréhension: pourquoi faire écrire des textes de démonstration par les élèves? En E. Barbin, R. Duval, I. Giogutti, J. Houdebine y C. Laborde (eds.), Produire et lire des textes de démonstration. París: Ellipses.spa
dc.relation.referencesDuval, R. y Egret, M.A. (1989). L’organisation déductive du discours: interactions entre structure profonde et structure de surface dans l’accès à la démonstration. Annales de Didactique et de Sciences Cognitives, 2, 41-65.spa
dc.relation.referencesEdwards, C.H. (1979). The historical development of calculus. Berlín: Springer.spa
dc.relation.referencesEuclides (1990). Les Éléments (Libros I a IV, trad. de B. Vitrac). París: PUF.spa
dc.relation.referencesGodin, M. (2004). De trois regards possibles sur une figure au regard «géométrique», à paraître. En Actes du séminaire national de didactique des mathématiques. ADIREM et IREM de Paris 7, pp. 39-70.spa
dc.relation.referencesIREM de Strasbourg, (1979). Mathématiques 4ème. París: Istraspa
dc.relation.referencesIREM de Strasbourg, (1986). Mathématiques 2ème. París: Istra.spa
dc.relation.referencesKant, E. (1976). Critique de la raison pure (trad. J. Barni en 1869). París: G. Baillière.spa
dc.relation.referencesLaborde, C. (1994). Enseigner la géométrie: permanences et révolutions. Bulletin APMEP, 396, 523-548.spa
dc.relation.referencesLepoivre, G. y Poirson, A. (1920). Cours de géométrie théorique et pratique I. Lille: Janny.spa
dc.relation.referencesPadilla, V. (1992). L’influence d’une acquisition de traitements purement figuraux pour l’apprentissage des mathématiques. Université Louis Pasteur, Institut de Recherche Mathématique Avancée. Estrasburgo, Francia.spa
dc.relation.referencesPeirce, C.S. (1978). Écrits sur le signe (elección de textos, traducción de G. Deledalle). París: Seuil.spa
dc.relation.referencesPiaget, J. (1972). La représentation de l’espace chez l’enfant. París: P.U.F.spa
dc.relation.referencesPoincaré, H. (1963). Pourquoi l’espace a trois dimensions. En Dernières pensées. París: Flammarion. Séminaire IUFM (1999). Conversion et articulation des représentations analogiques (editado por R. Duval). París: IUFM Nord-Pas-de-Calais.spa
dc.relation.referencesDescartes, R. (1954). The geometry of René Descartes (trads. D.E. Smith y M.L. Lantham en 1925). New York: Dover.spa
dc.relation.referencesDuval, R. (1983). L’obstacle du dédoublement des objets mathématiques. Educational Studies in Mathematics, 14(4), 385-414.spa
dc.relation.referencesDuval, R. (1988). Graphiques et équations: l’articulation de deux registres. Annales de Didactique et de Sciences Cognitives, 1, 235-253.spa
dc.relation.referencesDuval, R. (1991). Structure du raisonnement déductif et apprentissage de la démonstration. Educational Studies in Mathematics, 22(3), 233-261.spa
dc.relation.referencesDuval, R. (1993a). Registres de représentation sémiotique et fonctionnement cognitif de la pensée. Annales de Didactique et de Sciences Cognitives, 5, 37-65.spa
dc.relation.referencesDuval, R. (1993b). Argumenter, démontrer, expliquer: continuité ou rupture cognitive? Petit x, 31, 37-61.spa
dc.relation.referencesDuval, R. (1995a). Sémiosis et pensée humaine. Registres sémiotiques et apprentissages intellectuels. Berne: Peter Lang.spa
dc.relation.referencesDuval, R. (1995b). Geometrical pictures: Kinds of representation and specific processings. En R. Sutherland y J. Maison (eds.), Exploiting mental imagery with computers in mathematics education (pp. 142-157). Berlín: Springer.spa
dc.relation.referencesDuval, R. (1996a). Quel cognitif retenir en didactique des mathématiques? Recherches en Didactique des Mathématiques, 16(3), 349-382.spa
dc.relation.referencesDuval, R. (1996b). Les représentations graphiques: fonctionnement et conditions de leur apprentissage. En A. Antibi (ed.), Actes de la 46ème Rencontre Internationale de la CIEAEM (pp. 3-15). Toulouse: Université Paul Sabatier.spa
dc.relation.referencesDuval, R. (1998a). Signe et objet (I): trois grandes étapes dans la problématique des rapports entre représentation et objet. Annales de Didactique et de Sciences 93 Cognitives, 6, 139-163.spa
dc.relation.referencesDuval, R. (1998b). Geometry from a cognitive point a view. En C. Mammana y V. Villani (eds.), Perspectives on the teaching of geometry for the 21st century. An ICMI Study (pp. 37-51). Dordrecht: Kluwer Academic Publishers.spa
dc.relation.referencesDuval, R. (1999a). Semiosis y pensamiento humano: Registros semióticos y aprendizajes intelectuales (trad. M. Vega Restrepo). Cali: Artes Gráficas Univalle.spa
dc.relation.referencesDuval, R. (ed.) (1999b). Conversion et articulation des représentations analogiques. Séminaire I.U.F.M., D.R.E.D., Villeneuve d’Ascq.spa
dc.relation.referencesDuval, R. (2000a). Basic issues for research in mathematics education. En T. Nakahara y M. Koyama (eds.), Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education (pp. 55-69). Hiroshima: Nishiki Print Co. Ltd.spa
dc.relation.referencesDuval, R. (2000b). Écriture, raisonnement et découverte de la démonstration en mathématiques. Recherches en Didactique des Mathématiques, 20(2), 135-170.spa
dc.relation.referencesDuval, R. (2003). Langage(s) et représentation(s) dans l’enseignement des mathématiques: deux pratiques et une troisième. En M. Kourkoulos, G. Toulis y C. Tzanakis (eds.), Proceedings of 3rd Colloquium on the Didactics of Mathematics (pp. 13-33). Rethymnon: University of Crete.spa
dc.relation.referencesFrege, G. (1971). Sens et dénotation. En Écrits logiques et philosophiques (trad. al francés de Claude Imbert). París: Seuil. (Obra original publicada en alemán: Sinn und Bedeutung en 1892).spa
dc.relation.referencesHitt, F. (ed.) (2002). Representations and mathematics visualization. International Group for the Psychology of Mathematics Education North American Chapter. México: Cinvestav-IPN.spa
dc.relation.referencesHitt, F. (2003). Le caractère fonctionnel des représentations. Annales de Didactique et de Sciences Cognitives, 8, 255-271.spa
dc.relation.referencesMesquita, A.M. (1989). L’influence des aspects figuratifs dans l’argumentation des élèves en géométrie: éléments pour une typologie. Tesis de doctorado. Estrasburgo: IREM.spa
dc.relation.referencesPavlopoulou. K. (1993). Un problème décisif pour l’apprentissage de l’algèbre linéaire: la coordination des registres de représentation. Annales de Didactique et de Sciences Cognitives, 5, 67-93.spa
dc.relation.referencesPeirce, C.S. (1931). Collected Papers, II, Elements of Logic. Hartshorne y P. Weiss (eds.). Cambridge, Massachusetts: Belknap Press/Harvard University Press.spa
dc.relation.referencesPeirce, C.S. (1931-1966). Collected Papers (CP) (editado por C. Hartshorne y P. Weiss, vols. 1-6, y A.W. Burks, vols. 7-8). Cambridge, Massachusetts: Belknap Press/Harvard University Press.spa
dc.relation.referencesPiaget, J. (1923). Le langage et la pensée chez l’enfant. Neuchâtel: Delachaux et Niestlé.spa
dc.relation.referencesPiaget, J. (1926). La représentation du monde chez l’enfant. París: Alcan.spa
dc.relation.referencesPiaget, J. (1967a). Biologie et connaissance. París: Gallimard.spa
dc.relation.referencesPiaget, J. (1967b). Le jugement et le raisonnement chez l’enfant. Neuchâtel: Delachaux et Niestlé.spa
dc.relation.referencesPluvinage, F. (1990). Didactique de la résolution de problèmes. Annales de Didactique et de Sciences Cognitives, 3, 7-34.spa
dc.relation.referencesPluvinage, F. (1990). Didactique de la résolution de problèmes. Annales de Didactique et de Sciences Cognitives, 3, 7-34.spa
dc.relation.referencesSaussure, F. de (1973). Cours de linguistique générale. París: Payot. (Obra original publicada póstumamente por C. Bally y A. Sechehaye en 1916, sobre los cursos de 1906 a 1911).spa
dc.relation.referencesSchoenfeld, A.H. (1986). On having and using geometric knowledge. En J. Hiebert (ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 225-264). Hillsdale, NJ: Lawrence Erlbaum Associates.spa
dc.relation.referencesAnderson, J.R., Boyle, C.F., Farell, R. et al. (1987). Cognitive principles in the design of computer tutors. En P. Morris (Ed.), Cognition modeling (pp. 93-133). Nueva York: John Wiley & Sons Ltd.spa
dc.relation.referencesAristóteles (1964). Aristotelis analytica priora et posteriora (trad. W.D. Ross). Nueva York: Oxford University Press.spa
dc.relation.referencesBalacheff, N. (1987). Processus de preuve et situation de validation. Educational Studies in Mathematics, 18(2), 147-176.spa
dc.relation.referencesBalacheff, N. (1988). Une étude des processus de preuve en mathématique chez des élèves de collège. Tesis de doctorado, Université Joseph Fourier, Grenoble, Francia. Disponible en http://tel.archives-ouvertes.fr/tel-00326426/en/spa
dc.relation.referencesBourreau-Billerait, S., Dewitte, M.C. y Lion, I. (1998). Comment les réseaux peuvent-ils aider les élèves à mieux appréhender la démonstration en géométrie? Lille: IUFM Collection Mémoires Professionnels.spa
dc.relation.referencesCarnap, R. (1958). Meaning and necessity. A study in semantics and modal logic (2a ed.). Chicago: University of Chicago Press.spa
dc.relation.referencesDuval, R. (1991). Structure du raisonnement déductif et apprentissage de la démonstration. Educational Studies in Mathematics, 22(3), 233-261.spa
dc.relation.referencesDuval, R. (1993a). Registres de représentation sémiotique et fonctionnement cognitif de la pensée. Annales de Didactique et de Sciences Cognitives, 5, 37-65.spa
dc.relation.referencesDuval, R. (1993b). Argumenter, démontrer, expliquer: continuité ou rupture cognitive? Petit x, 31, 37-61.spa
dc.relation.referencesDuval, R. (1995a). Sémiosis et pensée humaine. Registres sémiotiques et apprentissages intellectuels. Berne: Peter Lang.spa
dc.relation.referencesDuval, R. (1995b). Geometrical pictures: Kinds of representation and specific processings. En R. Sutherland y J. Maison (eds.), Exploiting mental imagery with computers in mathematics education (pp. 142-157). Berlín: Springer.spa
dc.relation.referencesDuval, R. (1996a). Quel cognitif retenir en didactique des mathématiques? Recherches en Didactique des Mathématiques, 16(3), 349-382.spa
dc.relation.referencesDuval, R. (1996b). Les représentations graphiques: fonctionnement et conditions de leur apprentissage. En A. Antibi (ed.), Actes de la 46ème Rencontre Internationale de la CIEAEM (pp. 3-15). Toulouse: Université Paul Sabatier.spa
dc.relation.referencesDuval, R. (1998a). Signe et objet (I): trois grandes étapes dans la problématique des rapports entre représentation et objet. Annales de Didactique et de Sciences Cognitives, 6, 139-163.spa
dc.relation.referencesDuval, R. (1998b). Geometry from a cognitive point a view. En C. Mammana y V. Villani (eds.), Perspectives on the teaching of geometry for the 21st century. An ICMI Study (pp. 37-51). Dordrecht: Kluwer Academic Publishers.spa
dc.relation.referencesDuval, R. (2001). Écriture et compréhension: pourquoi faire écrire des textes de démonstration par les élèves? En E. Barbin, R. Duval, I. Giogutti et al. (eds.), Produire et lire des textes de démonstration. París: Ellipses.spa
dc.relation.referencesDuval, R. (2005). Les conditions cognitives de l’apprentissage de la géométrie: développement de la visualisation, différenciation des raisonnements et coordination de leurs fonctionnements. Annales de Didactique et de Sciences Cognitives, 10, 5-53.spa
dc.relation.referencesDuval, R. (2015). Figures et visualisation géométrique: «voir» en géométrie. Dans J. Baillé (dir.), Du mot au concept. Figur, p.147-182. Grenoble: Presses universitaires de Grenoble.spa
dc.relation.referencesDuval, R. y Egret, M.A. (1989). L’organisation déductive du discours: interactions entre structure profonde et structure de surface dans l’accès à la démonstration. Annales de Didactique et de Sciences Cognitives, 2, 41- 65.spa
dc.relation.referencesEgret, M.A. y Duval, R. (1989). Comment une classe de quatrième a pris conscience de ce qu’est une démarche de démonstration. A nnales de Didactique et de Sciences Cognitives, 2, 65-89.spa
dc.relation.referencesJohnson-Laird, P.N. (1983). Mental models. Nueva York: Cambridge University Press.spa
dc.relation.referencesLakatos, I. (1976) Proof and refutations: The logic of mathematical discovery. Nueva York: Cambridge University Press.spa
dc.relation.referencesLakatos, I. (1976) Proof and refutations: The logic of mathematical discovery. Nueva York: Cambridge University Press.spa
dc.relation.referencesLuengo, V. (1997). Cabri-Euclide: un micro-monde de preuve intégrant la réfutation. Principes didactiques et informatiques. Réalisation. Grenoble: Laboratoire Leibniz, Université Joseph Fourier.spa
dc.relation.referencesPiaget, J. (1967a). Biologie et connaissance. París: Gallimard.spa
dc.relation.referencesPiaget, J. (1967b). Le jugement et le raisonnement chez l’enfant. Neuchâtel: Delachaux et Niestlé.spa
dc.relation.referencesPiaget, J. e Inhelder, B. (1955). De la logique de l’enfant à la logique de l’adolescent. París: P.U.F.spa
dc.relation.referencesRips, L.J. (1988). Deduction. En R.J. Sternberg y E.E. Smith (eds.), The psychology of human thought (pp. 116-152). Nueva York: Cambridge University Press.spa
dc.relation.referencesSchoenfeld, A.H. (1986). On having and using geometric knowledge. En J. Hiebert (ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 225-264). Hillsdale, NJ: Lawrence Erlbaum Associates.spa
dc.relation.referencesToulmin, S.E. (1958). The use of arguments. Nueva York: Cambridge University Press.spa
dc.relation.referencesBauersfeld, H. (1995). “Language games” in mathematics classrooms: Their function and their effect. En P. Cobb y H. Bauersfeld (eds.), The emergence of mathematical meanings (pp. 271-291). Hillsdale, Nueva Jersey: Lawrence Erlbaum Associates.spa
dc.relation.referencesCobb, P. (2000a) Conducting teaching experiments in collaboration with teachers. En A.E. Kelly y R.A. Lesh (eds.), Handbook of research design in mathematics and science education (pp. 307-333). Mahwah, NJ: Lawrence Erlbaum.spa
dc.relation.referencesCobb, P. (2000b). From representations to symbolizing: Introductory comments on semiotics and mathematics learning. En P. Cobb, E. Yackel y K. McClain (eds.), Symbolizing and communicating in mathematics classrooms (pp. 17-36). Mahway, NJ: Lawrence Erlbaum Associates.spa
dc.relation.referencesCobb, P. y Steffe, L.P. (1983). The constructivist researcher as teacher and model builder. Journal for Research in Mathematics Education, 14(2), 83-94.spa
dc.relation.referencesCobb, P. y Yackel, E. (1995). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. En D.T. Owens, M.K. Reed y G.M. Millsaps (eds.), Proceedings of the Seventeenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 3-29). Columbus, OH: ERIC/CSMEE.spa
dc.relation.referencesConfrey, J. (1988). Multiplication and splitting: Their role in understanding exponential functions. En M. Behr, C. LaCampagne y M. Wheeler (eds.), Proceedings of the Tenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 250-259). DeKalb, IL: Northern Illinois University.spa
dc.relation.referencesConfrey, J. (1994). Splitting, similarity, and rate of change: A new approach to multiplication and exponential functions. En G. Harel y J. Confrey (eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 291-330). Albany, NY: State University of New York Press.spa
dc.relation.referencesCorrington, R.S. (1993). An introduction to C.S. Peirce. Boston: Rowman & Littlefield Publishers.spa
dc.relation.referencesErnest, P. (2002, julio). A semiotic perspective of mathematical activity. Ponencia presentada en el Grupo de Discusión “Semiotics in Mathematics Education Research” en 26th Conference of the International Group for the Psychology of Mathematics Education, Norwich, UK.spa
dc.relation.referencesForman, E.A. y Cazden, C. (1985). Exploring Vygotskian perspectives in education: The cognitive value of peer interaction. En J.V. Wertsch (ed.), Culture communication and cognition: Vygotskian perspectives (pp. 323-347). Nueva York: Cambridge University Press.spa
dc.relation.referencesGodino, J. y Batanero, C. (2003). Semiotic functions in teaching and learning mathematics. En M. Anderson, A. Sáenz-Ludlow, S. Zellweger y V. Cifarelli (eds.), Educational perspectives on mathematics as semiosis: From thinking to interpreting to knowing (pp. 149-168). Ottawa, Ont.: Legas.spa
dc.relation.referencesHeath, T.L. (1956). The thirteen books of Euclid’s Elements (traducción del texto de Heiberg, con introducción y comentario; 2a ed. revisada). Nueva York: Dover Publications.spa
dc.relation.referencesMcLellan, J.A. y Dewey, J. (1908). The psychology of number and its applications to methods of teaching arithmetic. Nueva York: D. Appleton and Company.spa
dc.relation.referencesMoreno-Armella, L.E. y Waldegg, G.C. (2000). An epistemological history of number and variation. En V. Katz (ed.), Using history to teach mathematics: An international perspective (pp. 183-190). MAA Notes 51. Washington, DC: The Mathematical Association of America.spa
dc.relation.referencesMorris, C.V. (1938). Writings on the general theory of signs. Chicago: Chicago University Press.spa
dc.relation.referencesO’Halloran, K.L. (2003). Implications of mathematics as a multisemiotic discourse. En M. Anderson, A. Sáenz-Ludlow, S. Zellweger y V. Cifarelli (eds.), Educational perspectives on mathematics as semiosis: From thinking to interpreting to knowing (pp. 185-214). Ottawa, Ont.: Legas.spa
dc.relation.referencesOtte, M. (2001, julio). Mathematical epistemology from a semiotic point of view. Ponencia presentada en el Grupo de Discusión “Semiotics in Mathematics Education Research” en 25th International Conference for the Psychology of Mathematics Education, Utrecht, The Netherlands.spa
dc.relation.referencesOtte, M. (2006). Mathematical epistemology from a Peircean semiotic point of view. Educational Studies in Mathematics, 61(1-2), 11-38.spa
dc.relation.referencesParmentier, R.J. (1985). Signs’ place in medias res: Peirce’s concept of semiotic mediation. En E. Mertz y R.J. Parmentier (eds.), Semiotic mediation: Sociocultural and psychological perspectives (pp. 23-48). Orlando, FL: Academic Press.spa
dc.relation.referencesPeirce, C.S. (1867). Questions concerning certain faculties claimed by man. En J. Hoopes (ed.), Peirce on signs (1991, pp. 34-53). Chapel Hill: The University of North Carolina Press.spa
dc.relation.referencesPeirce, C. S. (1893-1913). The essential Peirce: Selected philosophical writings (vol. 2; editado por Peirce Edition Project). Bloomington, IN: Indiana University Press.spa
dc.relation.referencesPeirce, C.S. (1903). The three normative sciences. The essential Peirce (vol. 2, 1893-1913; editado por Peirce Edition Project, pp. 196-207). Bloomington, IN: Indiana University Press.spa
dc.relation.referencesPeirce, C.S. (1906a). Prolegomena to an apology for pragmaticism. En J. Hoopes (ed.), Peirce on signs (pp. 249-252). Chapel Hill, North Carolina: The University of North Carolina Press.spa
dc.relation.referencesPeirce, C.S. (1906b). Pragmatism in retrospect: A last formulation. En J. Buchler (ed.), Philosophical writings of Peirce (1955) (pp. 269-289). Nueva York: Dover Publications.spa
dc.relation.referencesPeirce, C.S. (1908). Excerpts from letters to Lady Welby. En Peirce Edition Project (ed.), The Essential Peirce (vol. 2, pp. 478-491). Bloomington, IN: Indiana University Press.spa
dc.relation.referencesPeirce, C.S. (1931). Collected Papers, vol. II, Elements of Logic. (editado por C. Hartshorne y P. Weiss). Cambridge, Massachusetts: Belknap Press/Harvard University Press.spa
dc.relation.referencesPeirce, C.S. (1931-1966). Collected Papers (CP) (editado por C. Hartshorne y P. Weiss, vols. 1-6, y A.W. Burks, vols. 7-8). Cambridge, Massachusetts: Belknap Press/Harvard University Press.spa
dc.relation.referencesPeirce, C.S. (1956). The essence of mathematics. En J.R. Newman (ed.), The World of Mathematics, (vol. 3, pp. 1773-1783). Nueva York: Simon and Schuster.spa
dc.relation.referencesPeirce, C.S. (1976). The new elements of mathematics (NEM), (vol. 4, Mathematical Philosophy, editado por Carolyn Eisele). The Hague: Mouton and Co. B. V. Publishers.spa
dc.relation.referencesPiaget, J. (1970). Genetic epistemology. Nueva York: Columbia University Press.spa
dc.relation.referencesSáenz-Ludlow, A. (1997). Iconic means in children’s understanding of the division algorithm. En C.W. Spinks y J. Deely (eds.), Semiotics (pp. 118-130). Toronto, Canada: Peter Lang.spa
dc.relation.referencesSáenz-Ludlow, A. (2002). Sign as a process of representation: A Peircean perspective. En F. Hitt (ed.), Representations and mathematics visualization (pp. 277-296). México, D.F.: Departamento de Matemática Educativa, Cinvestav-IPN.spa
dc.relation.referencesSáenz-Ludlow, A. y Walgamuth, C. (2001). Question-and diagram-mediated mathematical activity: A case in a fourth-grade classroom. Focus on Learning Problems in Mathematics, 23(4), 27-40.spa
dc.relation.referencesSebeok, T. (1995). Indexicality. En K.L. Ketner (ed.), Peirce and contemporary thought (pp. 222-242). Nueva York: Fordham University Press.spa
dc.relation.referencesSebeok, T. (1995). Indexicality. En K.L. Ketner (ed.), Peirce and contemporary thought (pp. 222-242). Nueva York: Fordham University Press.spa
dc.relation.referencesSteffe, L.P. (1983). The teaching-experiment methodology in a constructivist research program. En M. Zweng, T. Green, J. Kilpatrick, H. Pollak y M. Suydam (eds.), Proceedings of the Fourth International Congress on Mathematical Education (pp. 469-471). Boston, Massachusetts: Birkhäuser.spa
dc.relation.referencesSteffe, L.P. y Cobb, P. (1988). Construction of arithmetic meanings and strategies. Nueva York, New York: Springer-Verlag.spa
dc.relation.referencesSteffe, L.P. y Thompson, P. (2000). Teaching experiment methodology: Underlying principles and essential elements. En A. Kelly y R. Lesh (eds.), Handbook of research design in mathematics and science education (pp. 267-306). Mahwah, NJ: Lawrence Erlbaum.spa
dc.relation.referencesSteffe, L.P., von Glasersfeld, E., Richards, J. y Cobb, P. (1983). Children’s counting types: Philosophy, theory and applications. Nueva York: Praeger.spa
dc.relation.referencesThom, R. (1973). Modern mathematics: Does it exist? En G. Howson (ed.), Proceedings of the Second International Congress on Mathematical Education (pp. 194- 212). Cambridge: Cambridge University Press.spa
dc.relation.referencesVan Oers, B. (2001). Educational forms of initiation in mathematical culture. Educational Studies in Mathematics, 46(1), 59-85.spa
dc.relation.referencesVygotsky, L.S. (1986). Thought and language (edición revisada y editada nuevamente por A. Kozulin). Cambridge, Massachusetts: The MIT Press. (Obra original publicada póstumamente en ruso en 1934 y en inglés en 1962).spa
dc.relation.referencesWertsch, J.V. (1981). The concept of activity in Soviet psychology. Armonk, NY: Sharpe.spa
dc.relation.referencesWertsch, J.V. (1985). Vygotsky and the social formation of the mind. Cambridge, Massachusetts: Harvard University Press.spa
dc.relation.referencesWilder, R. (1968). Evolution of mathematical concepts. Milton Keynes, England: The Open University Press.spa
dc.relation.referencesWiley, N. (1994). The semiotic self. Chicago, Illinois: The University of Chicago Press.spa
dc.relation.referencesYackel, E. y Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458-477.spa
dc.relation.referencesBakhtin, M. (1986). The problem of speech genres. En C. Emerson y M. Holquist (eds.), Speech genres and other late essays (pp. 60-102). Austin, TX: University of Texas Press.spa
dc.relation.referencesBarnes, D. (1992). From communication to curriculum (2a ed.). Portsmouth, NH: Boynton/Cook Publishers. Bauersfeld, H. (1995). “Language games” in mathematics classrooms: Their function and their effect. En P. Cobb y H. Bauersfeld (eds.), The emergence of mathematical meanings (pp. 271-291). Hillsdale, Nueva Jersey: Lawrence Erlbaum Associates.spa
dc.relation.referencesBlumer, H. (1995). Symbolic interactionism. Berkeley, California: University of California Press.spa
dc.relation.referencesBourdieu, P. (1999). Language and symbolic power (trad. G. Raymond y M. Adamson). Cambridge, MA: Harvard University Press.spa
dc.relation.referencesBuchler, J. (1955). Philosophical writings of Peirce. Nueva York: Dover Publications.spa
dc.relation.referencesCajori, F. (1974). A history of mathematical notations: Notations in elementary mathematics (vol. 1). La Salle, IL: Open Court.spa
dc.relation.referencesCobb, P. (2000a) Conducting teaching experiments in collaboration with teachers. En A.E. Kelly y R.A. Lesh (eds.), Handbook of research design in mathematics and science education (pp. 307-333). Mahwah, NJ: Lawrence Erlbaum.spa
dc.relation.referencesCobb, P. (2000b). From representations to symbolizing: Introductory comments on semiotics and mathematics learning. En P. Cobb, E. Yackel y K. McClain (eds.), Symbolizing and communicating in mathematics classrooms (pp. 17-36). Mahway, NJ: Lawrence Erlbaum Associates.spa
dc.relation.referencesCobb, P. y Yackel, E. (1995). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. En D.T. Owens, M.K. Reed y G.M. Millsaps (eds.), Proceedings of the Seventeenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 3-29). Columbus, OH: ERIC/CSMEE.spa
dc.relation.referencesDewey, J. (1997/1916). Democracy and education: An introduction to the philosophy of education. New York: The Free Press.spa
dc.relation.referencesDewey, J. (1963/1938). Experience and education. Nueva York: Collier.spa
dc.relation.referencesDörfler, W. (2000). Means for meaning. En P. Cobb, E. Yackel y K. McClain (eds.), Symbolizing and communicating in mathematics classrooms (pp. 99-131). Hillsdale, NJ: Lawrence Erlbaum.spa
dc.relation.referencesDuval, R. (1999a). Semiosis y pensamiento humano: Registros semióticos y aprendizajes intelectuales (trad. M. Vega Restrepo). Cali: Artes Gráficas Univalle.spa
dc.relation.referencesDuval, R. (Ed.) (1999b). Conversion et articulation des représentations analogiques. Séminaire I.U.F.M., D.R.E.D., Villeneuve d’Ascq.spa
dc.relation.referencesDuval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1-2), 103-131.spa
dc.relation.referencesEdwards, D. y Mercer, N. (1987). Common knowledge: The development of understanding in the classroom. Nueva York: Routledge.spa
dc.relation.referencesEllerton, N. y Clements, M. (1991). Mathematics in language: A review of language factors in mathematics learning. Geelong, Victoria: Deakin University Press.spa
dc.relation.referencesErnest, P. (2003). The epistemic subject in mathematical activity. En M. Anderson, A. Sáenz-Ludlow, S. Zellweger y V. Cifarelli (eds.), Educational perspectives on mathematics as semiosis: From thinking to interpreting to knowing (pp. 81-106). Ottawa, Ontario: Legas.spa
dc.relation.referencesErnest, P. (2006). A semiotic perspective of mathematical activity: The case on number. Educational Studies in Mathematics, 61(1-2), 67-101.spa
dc.relation.referencesFreire, P. (2001/1970). Pedagogy of the oppressed. Nueva York: Continuum.spa
dc.relation.referencesFoucault, M. (1972). The archeology of knowledge. Londres: Tavistock.spa
dc.relation.referencesHabermas, J. (1984). The theory of communicative action. Boston: Beacon Press.spa
dc.relation.referencesHoffmann, M. (2004). How to get it. Diagrammatic reasoning as a tool of knowledge development and its pragmatic dimension. Foundation of Science, 9(3), 285-305.spa
dc.relation.referencesHoffmann, M. (2005). Signs as means for discoveries. Peirce and his concepts of “Diagrammatic Reasoning,” “Theorematic Deduction,” “Hypostatic Abstraction,” and “Theoric Transformation”. En M.H.G. Hoffmann, J. Lenhard y F. Seeger (eds.), Activity and sign: Grounding mathematics education (pp. 45-56). Nueva York: Springer.spa
dc.relation.referencesHoffmann, M. (2006). What is a “semiotic perspective”, and what could it be? Some comments on the contributions of this Special Issue. Educational Studies in Mathematics, 61(1-2), 279-291.spa
dc.relation.referencesKanes, C. (1998). Examining the linguistic mediation of pedagogical interaction in mathematics. En H. Steinbring, M.G. Bartolini-Bussi y A. Sierpinska (eds.), Language and communication in the mathematics classroom (pp. 120-139). Reston, VA: National Council of Teachers of Mathematics.spa
dc.relation.referencesLiszka, J.J. (1996). A general introduction to the semiotic of Charles Sanders Peirce. Bloomington, Indiana: Indiana University Press.spa
dc.relation.referencesMenninger, K. (1969). Number words and number symbols: A cultural history of numbers. Cambridge, MA: The MIT Press.spa
dc.relation.referencesNagel, E. (1956). Symbolic notation, haddocks’ eyes and the dog-walking ordinance. En J.R. Newman (ed.), The World of Mathematics (vol. 3, pp. 1576-1590). Nueva York: Simon and Schuster.spa
dc.relation.referencesNational Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.spa
dc.relation.referencesOtte, M. (1998). Limits of constructivism: Kant, Piaget, and Peirce. Science and Education, 7, 425-450.spa
dc.relation.referencesOtte, M. (2006). Mathematical epistemology from a Peircean semiotic point of view. Educational Studies in Mathematics, 61(1-2), 11-38.spa
dc.relation.referencesPeirce, C.S. (1867). Questions concerning certain faculties claimed by man. En J. Hoopes (ed.), Peirce on signs (1991, pp. 34-53). Chapel Hill: The University of North Carolina Press.spa
dc.relation.referencesPeirce, C.S. (1867). Questions concerning certain faculties claimed by man. En J. Hoopes (ed.), Peirce on signs (1991, pp. 34-53). Chapel Hill: The University of North Carolina Press.spa
dc.relation.referencesPeirce, C.S. (1903). The three normative sciences. The essential Peirce (vol. 2, 1893-1913; editado por Peirce Edition Project, pp. 196-207). Bloomington, IN: Indiana University Press.spa
dc.relation.referencesPeirce, C.S. (1906a). Prolegomena to an apology for pragmaticism. En J. Hoopes (ed.), Peirce on signs (pp. 249-252). Chapel Hill, North Carolina: The University of North Carolina Press.spa
dc.relation.referencesPeirce, C.S. (1906b). Pragmatism in retrospect: A last formulation. En J. Buchler (ed.), Philosophical writings of Peirce (1955) (pp. 269-289). Nueva York: Dover Publications.spa
dc.relation.referencesPeirce, C.S. (1908). Excerpts from letters to Lady Welby. En Peirce Edition Project (ed.), The Essential Peirce (vol. 2, pp. 478-491). Bloomington, IN: Indiana University Press.spa
dc.relation.referencesPeirce, C.S. (1931). Collected Papers, vol. II, Elements of Logic. (editado por C. Hartshorne y P. Weiss). Cambridge, Massachusetts: Belknap Press/Harvard University Press.spa
dc.relation.referencesPeirce, C.S. (1931-1966). Collected Papers (CP) (editado por C. Hartshorne y P. Weiss, vols. 1-6, y A.W. Burks, vols. 7-8). Cambridge, Massachusetts: Belknap Press/Harvard University Press.spa
dc.relation.referencesPeirce, C.S. (1956). The essence of mathematics. En J.R. Newman (ed.), The World of Mathematics, (vol. 3, pp. 1773-1783). Nueva York: Simon and Schuster.spa
dc.relation.referencesPeirce, C.S. (1976). The new elements of mathematics (NEM), (vol. 4, Mathematical Philosophy, editado por Carolyn Eisele). The Hague: Mouton and Co. B. V. Publishers.spa
dc.relation.referencesPiaget, J. (1970). Genetic epistemology. Nueva York: Columbia University Press.spa
dc.relation.referencesPimm, D. (1987). Speaking mathematically: Communication in the classrooms. Londres: Routledge.spa
dc.relation.referencesRadford, L. (2003). Gestures, speech, and the sprouting of signs. Mathematical Thinking and Learning, 5(1), 37-70.spa
dc.relation.referencesRadford, L. (2003). Gestures, speech, and the sprouting of signs. Mathematical Thinking and Learning, 5(1), 37-70.spa
dc.relation.referencesRotman, B. (1988). Towards a semiotics of mathematics. Semiotica, 72(1-2), 1-36.spa
dc.relation.referencesSáenz-Ludlow, A. (1997). Iconic means in children’s understanding of the division algorithm. En C.W. Spinks y J. Deely (eds.), Semiotics (pp. 118-130). Toronto, Canada: Peter Lang.spa
dc.relation.referencesSáenz-Ludlow, A. (2003a). Classroom mathematics discourse as an evolving interpreting game. En M. Anderson, A. Sáenz-Ludlow, S. Zellweger y V. Cifarelli (eds.), Educational perspectives on mathematics as semiosis: From thinking to interpreting to knowing (pp. 253-284). Ottawa, Canada: Legas Press.spa
dc.relation.referencesSáenz-Ludlow, A. (2003b). A collective chain of signification in conceptualizing fractions: A case of a fourth-grade class. Journal of Mathematical Behavior, 22, 181- 211.spa
dc.relation.referencesSaussure, F. de (1959). Course of general linguistics (trad. W. Baskin). Nueva York: McGraw-Hill Book Company. (Obra original publicada póstumamente por C. Bally y A. Sechehaye en 1916, sobre los cursos de 1906 a 1911).spa
dc.relation.referencesSfard, A. (2000). Symbolizing mathematical reality into being – Or how mathematical discourse and mathematical objects create each other. En P. Cobb, E. Yackel y K. McClain (eds.), Symbolizing and communicating in mathematics classrooms (pp. 37-98). Mahwah, NJ: Lawrence Erlbaum Associates.spa
dc.relation.referencesSfard, A. (2001). There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematical learning. Educational Studies in Mathematics, 46(1), 13-57.spa
dc.relation.referencesSierpinska, A. (1994). Understanding in mathematics. Londres: The Falmer Press.spa
dc.relation.referencesSkemp, R. (1987). The psychology of learning mathematics. Hillsdale, NJ: Lawrence Erlbaum Associates.spa
dc.relation.referencesSteinbring, H. (2006). What makes a sign a mathematical sign? – An epistemological perspective on mathematical interaction. Educational Studies in Mathematics, 61(1-2), 133-162.spa
dc.relation.referencesSteinbring, H., Bartolini Bussi, M.G. y Sierpinska, A. (Eds.) (1998). Language and communication in the mathematics classroom. Reston, VA: National Council of Teachers of Mathematics.spa
dc.relation.referencesVan Oers, B. (2001). Educational forms of initiation in mathematical culture. Educational Studies in Mathematics, 46(1), 59-85.spa
dc.relation.referencesVile, A. (1997). From Peirce towards a semiotic of mathematical meaning. En J.F. Quesada (ed.), Logic, semiotic, social and computational perspectives on mathematical languages (pp. 64-76). Sevilla, España: SAEM Thales.spa
dc.relation.referencesVile, A. y Lerman, S. (1996). Semiotics as a descriptive framework in mathematical domains. En L. Puig y A. Gutiérrez (eds.), Proceedings of the 20th Conference of the International Group for the Psychology of Mathematics Education (vol. 4, pp. 389-402). Valencia, España: Universidad de Valencia.spa
dc.relation.referencesVygotsky, L.S. (1978). Mind in society (edit. y trad. por M. Cole, V. John-Steiner, S. Scribner y E. Souberman a partir de distintas obras originales publicadas en ruso de 1930 a 1960). Cambridge, Massachusetts: Harvard University Press.spa
dc.relation.referencesVygotsky, L.S. (1986/1934). Thought and language (edición revisada y editada nuevamente por A. Kozulin). Cambridge, Massachusetts: The MIT Press.spa
dc.relation.referencesWalkerdine, V. (1988). The mastery of reason. Londres: Routledge.spa
dc.relation.referencesWhitehead, A.N. (1985). Symbolism: Its meaning and effect. Nueva York: Fordham University Press.spa
dc.relation.referencesWhitson, J.A. (1997). Cognition as a semiosic process: From situated mediation to critical reflective transcendence. En D. Kirshner y J.A. Whitson (eds.), Situated cognition: Social, semiotic, and psychological perspectives (pp. 97-149). Mahwah, NJ: Lawrence Erlbaum.spa
dc.relation.referencesWilder, R. (1968). Evolution of mathematical concepts. Milton Keynes, Inglaterra: The Open University Press.spa
dc.relation.referencesWittgenstein, L. (1991/1944). Philosophical investigations. Oxford: Basil Blackwell.spa
dc.relation.referencesBauersfeld, H. (1995). “Language games” in mathematics classrooms: Their function and their effect. En P. Cobb y H. Bauersfeld (eds.), The emergence of mathematical meanings (pp. 271-291). Hillsdale, Nueva Jersey: Lawrence Erlbaum Associates.spa
dc.relation.referencesBehr, M., Khoury, H., Harel, G., Post, T. y Lesh, R. (1997). Conceptual units analysis of pre-service elementary school teachers’ strategies on rational-numberas-operator task. Journal for Research in Mathematics Education, 28(1), 48-69.spa
dc.relation.referencesBergeron, J. y Herscovics, N. (1987). Unit fractions of a continuous whole. En J. Bergeron, N. Herscovics y C. Kieran (eds.), Proceedings of the Eleventh International Conference on the Psychology of Mathematics Education (vol. 1, pp. 357-365). Montreal.spa
dc.relation.referencesCobb, P. (2000a). Conducting teaching experiments in collaboration with teachers. En A.E. Kelly y R.A. Lesh (eds.), Handbook of research design in mathematics and science education (pp. 307-333). Mahwah, NJ: Lawrence Erlbaum.spa
dc.relation.referencesCobb, P. (2000b). From representations to symbolizing: Introductory comments on semiotics and mathematics learning. En P. Cobb, E. Yackel y K. McClain (eds.), Symbolizing and communicating in mathematics classrooms (pp. 17-36). Mahway, NJ: Lawrence Erlbaum Associates.spa
dc.relation.referencesCobb, P. y Steffe, L.P. (1983). The constructivist researcher as teacher and model builder. Journal for Research in Mathematics Education, 14(2), 83-94.spa
dc.relation.referencesCobb, P. y Yackel, E. (1995). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. En D.T. Owens, M.K. Reed y G.M. Millsaps (eds.), Proceedings of the Seventeenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (vol. 1, pp. 3-29). Columbus, OH: ERIC/CSMEE.spa
dc.relation.referencesColapietro, V.M. (1993). Glossary of semiotics. Nueva York: Paragon House.spa
dc.relation.referencesConfrey, J. (1988). Multiplication and splitting: Their role in understanding exponential functions. En M. Behr, C. LaCampagne y M. Wheeler (eds.), Proceedings of the Tenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 250-259). DeKalb, IL: Northern Illinois University.spa
dc.relation.referencesDavydov, V.V. (1990/1972). Types of generalization in instruction: Logical and psychological problems in the structuring of the school curricula. Reston, VA: The National Council of Teachers of Mathematics.spa
dc.relation.referencesDeely, J. (1990). Basics of semiotics. Bloomington: University of Indiana Press.spa
dc.relation.referencesDeely, J. (1994). New beginnings: Early modern philosophy and postmodern thought. Toronto: University of Toronto Press.spa
dc.relation.referencesErnest, P. (2002, julio). A semiotic perspective of mathematical activity. Ponencia presentada en el Grupo de Discusión “Semiotics in Mathematics Education Research” en 26th Conference of the International Group for the Psychology of Mathematics Education, Norwich, UK.spa
dc.relation.referencesFreudenthal, H. (1991). Revisiting mathematics education. Boston: Kluwer Academic Publishers.spa
dc.relation.referencesGodino, J. y Batanero, C. (2003). Semiotic functions in teaching and learning mathematics. En M. Anderson, A. Sáenz-Ludlow, S. Zellweger y V. Cifarelli (eds.), Educational perspectives on mathematics as semiosis: From thinking to interpreting to knowing (pp. 149-168). Ottawa, Ont.: Legas.spa
dc.relation.referencesGravemeijer, K. (1994). Educational development and developmental research in mathematics education. Journal for Research in Mathematics Education, 25(5), 443-471.spa
dc.relation.referencesHeath, T.L. (1956). The thirteen books of Euclid’s Elements (traducción del texto 233 de Heiberg, con introducción y comentario; 2a ed. revisada). Nueva York: Dover Publications.spa
dc.relation.referencesHunting, R. (1980). The role of the discrete quantity partition knowledge in the child’s construction of fractional number. Disertación doctoral, The University of Georgia. Dissertation Abstracts International, University Microfilms No. 8107919, 430-A.spa
dc.relation.referencesHunting, R., Davis, G. y Pearn, C. (1996). Engaging whole number knowledge for rational number learning using a computer-based tool. Journal for Research in Mathematics Education, 27(3), 354-379.spa
dc.relation.referencesKieren, T. (1988). Personal knowledge of rational numbers: Its intuitive and formal development. En J. Hiebert y M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 162-181). Reston, VA: National Council of Teachers of Mathematics & Lawrence Erlbaum Associates.spa
dc.relation.referencesKieren, T. y Nelson, L.D. (1981). Partitioning and unit recognition in performances of rational numbers tasks. En Proceedings of the Third International Conference on the Psychology of Mathematics Education (pp. 91-102). Grenoble, France.spa
dc.relation.referencesLamon, S. (1996). The development of unitizing: Its role in children partitioning strategies. Journal for Research in Mathematics Education, 27(2), 170-193.spa
dc.relation.referencesMcLellan, J.A. y Dewey, J. (1908). The psychology of number and its applications to methods of teaching arithmetic. Nueva York: D. Appleton and Company.spa
dc.relation.referencesMerrell, F. (1995). Peirce’s semiotics now: A primer. Toronto, Canada: Canadian Scholars’ Press.spa
dc.relation.referencesMertz, E. (1985). Beyond symbolic anthropology: Introducing semiotic mediation. En E. Mertz y R.J. Parmentier (eds.), Semiotic mediation: Sociocultural and psychological perspectives (pp. 1-19). Orlando, FL: Academic Press.spa
dc.relation.referencesMoreno-Armella, L.E. y Waldegg, G.C. (2000). An epistemological history of number and variation. En V. Katz (Ed.), Using history to teach mathematics: An international perspective (pp. 183-190). MAA Notes 51. Washington, DC: The Mathematical Association of America.spa
dc.relation.referencesNöth, W. (1990). Handbook of semiotics. Bloomington, IN: Indiana University Press.spa
dc.relation.referencesO’Halloran, K.L. (2003). Implications of mathematics as a multisemiotic discourse. En M. Anderson, A. Sáenz-Ludlow, S. Zellweger y V. Cifarelli (Eds.), Educational perspectives on mathematics as semiosis: From thinking to interpreting to knowing (pp. 185-214). Ottawa, Ont.: Legas.spa
dc.relation.referencesParmentier, R.J. (1985). Signs’ Place in Medias Res: Peirce’s concept of semiotic mediation. En E. Mertz y R.J. Parmentier (eds.), Semiotic mediation: Sociocultural and psychological perspectives (pp. 23-48). Orlando, FL: Academic Press.spa
dc.relation.referencesPeirce, C.S. (1867). Questions concerning certain faculties claimed by man. En J. Hoopes (ed.), Peirce on signs (1991, pp. 34-53). Chapel Hill: The University of North Carolina Press.spa
dc.relation.referencesPeirce, C. S. (1893-1913). The essential Peirce: Selected philosophical writings (vol. 2; editado por Peirce Edition Project). Bloomington, IN: Indiana University Press.spa
dc.relation.referencesPeirce, C.S. (1903). The three normative sciences. The essential Peirce (vol. 2, 1893-1913; editado por Peirce Edition Project, pp. 196-207). Bloomington, IN: Indiana University Press.spa
dc.relation.referencesPeirce, C.S. (1906a). Prolegomena to an apology for pragmaticism. En J. Hoopes (ed.), Peirce on signs (pp. 249-252). Chapel Hill, North Carolina: The University of North Carolina Press.spa
dc.relation.referencesPeirce, C.S. (1906b). Pragmatism in retrospect: A last formulation. En J. Buchler (ed.), Philosophical writings of Peirce (1955) (pp. 269-289). Nueva York: Dover Publications.spa
dc.relation.referencesPeirce, C.S. (1908). Excerpts from letters to Lady Welby. En Peirce Edition Project (ed.), The Essential Peirce (vol. 2, pp. 478-491). Bloomington, IN: Indiana University Press.spa
dc.relation.referencesPeirce, C.S. (1931). Collected Papers, vol. II, Elements of Logic. (editado por C. Hartshorne y P. Weiss). Cambridge, Massachusetts: Belknap Press/Harvard University Press.spa
dc.relation.referencesPeirce, C.S. (1931-1966). Collected Papers (CP) (editado por C. Hartshorne y P. Weiss, vols. 1-6, y A.W. Burks, vols. 7-8). Cambridge, Massachusetts: Belknap Press/Harvard University Press.spa
dc.relation.referencesPeirce, C.S. (1956). The essence of mathematics. En J.R. Newman (ed.), The World of Mathematics, (vol. 3, pp. 1773-1783). Nueva York: Simon and Schuster.spa
dc.relation.referencesPeirce, C.S. (1976). The new elements of mathematics (NEM), (vol. 4, Mathematical Philosophy, editado por Carolyn Eisele). The Hague: Mouton and Co. B. V. Publishers.spa
dc.relation.referencesPeirce, C.S. (1978). Écrits sur le signe (elección de textos, traducción de G. Deledalle). París: Seuil.spa
dc.relation.referencesSáenz-Ludlow, A. (1994). Michael’s fraction schemes. Journal for Research in Mathematics Education, 25(1), 50-85.spa
dc.relation.referencesSáenz-Ludlow, A. (1995). Ann’s fraction schemes. Educational Studies in Mathematics, 28(1), 101-132.spa
dc.relation.referencesSáenz-Ludlow, A. (1997). Iconic means in children’s understanding of the division algorithm. En C.W. Spinks y J. Deely (eds.), Semiotics (pp. 118-130). Toronto, Canada: Peter Lang.spa
dc.relation.referencesSáenz-Ludlow, A. (1998). Symbolic activity in mathematics classrooms: A semiotic perspective. En C.W. Spinks y J. Deely (Eds.), Semiotics (pp. 156-170). Toronto, 235 Canadá: Peter Lang.spa
dc.relation.referencesSáenz-Ludlow, A. (1998). Symbolic activity in mathematics classrooms: A semiotic perspective. En C.W. Spinks y J. Deely (Eds.), Semiotics (pp. 156-170). Toronto, 235 Canadá: Peter Lang.spa
dc.relation.referencesSáenz-Ludlow, A. y Walgamuth, C. (2001). Question-and diagram-mediated mathematical activity: A case in a fourth-grade classroom. Focus on Learning Problems in Mathematics, 23(4), 27-40.spa
dc.relation.referencesSteffe, L.P. (1983). The teaching-experiment methodology in a constructivist research program. En M. Zweng, T. Green, J. Kilpatrick, H. Pollak y M. Suydam (eds.), Proceedings of the Fourth International Congress on Mathematical Education (pp. 469-471). Boston, Massachusetts: Birkhäuser.spa
dc.relation.referencesSteffe, L.P. (1983). The teaching-experiment methodology in a constructivist research program. En M. Zweng, T. Green, J. Kilpatrick, H. Pollak y M. Suydam (eds.), Proceedings of the Fourth International Congress on Mathematical Education (pp. 469-471). Boston, Massachusetts: Birkhäuser.spa
dc.relation.referencesSteffe, L.P., von Glasersfeld, E., Richards, J. et al. (1983). Children’s counting types: Philosophy, theory and applications. Nueva York: Praeger.spa
dc.relation.referencesStreefland, L. (1991). Fractions in realistic mathematics education. Dordrecht, The Netherlands: Kluwer Academic Publishers.spa
dc.relation.referencesVan Oers, B. (2001). Educational forms of initiation in mathematical culture. Educational Studies in Mathematics, 46(1), 59-85.spa
dc.relation.referencesVon Glasersfeld, E. (1981). An attentional model for the conceptual construction of units and number. Journal for Research in Mathematics Education, 12(2), 83-94.spa
dc.relation.referencesVon Glasersfeld, E. y Richards, J. (1983). The creation of units as a prerequisite for number: A philosophical review. En L.P. Steffe, E. von Glasersfeld, J. Richards et al. (eds.), Children’s counting types: Philosophy, theory and applications (pp. 1-20). Nueva York: Praeger.spa
dc.relation.referencesYackel, E. y Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458-477.spa
dc.relation.referencesArtigue, M. (2011). Le sfide dell’insegnamento della matematica nell’educazione di base. La matematica nella società e nella cultura. rivista della Unione Matematica Italiana, 4(2) 211-259. Brousseau, G., D’Amore, B. (2008). I tentativi di trasformare analisi di carattere meta in attività didattica. Dall’empirico al didattico. En D’Amore B., Sbaragli F. (eds.) (2008). Didattica della matematica e azioni d’aula. Atti del XXII Convegno Nazionale: Incontri con la matematica. Castel San Pietro Terme (Bo), 7-8-9 novembre 2008. Bolonia: Pitagora. 3-14. ISBN: 88-371-1746-9.spa
dc.relation.referencesD’Amore, B. (2005). La argumentación matemática de jóvenes alumnos y la lógica hindú (nyaya). Uno,38, 83-99. D’Amore, B. (2005). Secondary school students’ mathematical argumentation and Indian logic (nyaya). For the learning of mathematics, 25(2), 26-32.spa
dc.relation.referencesD’Amore B., Fandiño-Pinilla, M. I., Iori, M. (2013). La semiótica en la didáctica de la matemática. Prefacios de Raymond Duval, Luis Radford. Prólogo a la edición en español de Carlos Eduardo Vasco. Bogotá: Magisterio.spa
dc.relation.referencesD’Amore, B., Fandiño-Pinilla, M. I., Iori, M. et al. (2015). Análisis de los antecedentes histórico-filosóficos de la “paradoja cognitiva de Duval”. Revista Latinoamericana de Investigación en Matemática Educativa. 18(2), 177-212. Recuperado de http://www.clame.org.mx/relime.htm Doi: 10.12802/relime.13.1822.
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.subjectMatemáticasspa
dc.subjectFuncionamiento cognitivospa
dc.subjectDiagramas numéricosspa
dc.subjectJuegos de interpretación
dc.subjectGeometría
dc.subject.keywordMathematicsspa
dc.subject.keywordCognitive functioningspa
dc.subject.keywordNumerical diagramsspa
dc.subject.keywordInterpretation gamesspa
dc.subject.keywordGeometry
dc.subject.lembMatemáticas -- Enseñanzaspa
dc.subject.lembGeometría -- Enseñanzaspa
dc.subject.lembMatemáticas -- Problemas, ejercicios, etc.spa
dc.subject.lembSemióticaspa
dc.titleComprensión y aprendizaje en matemáticas: perspectivas semióticas seleccionadasspa
dc.title.alternativeComprensión y aprendizaje en matemáticasspa
dc.title.titleenglishUnderstanding and learning in mathematics: semiotic perspectives selectedspa
dc.typebookspa
dc.type.coarhttp://purl.org/coar/resource_type/c_2f33
dc.type.driverinfo:eu-repo/semantics/book

Archivos

Bloque original

Mostrando 1 - 1 de 1
Cargando...
Miniatura
Nombre:
comprension_y_aprendizaje_en_matematicas_perspectivas_semioticas_seleccionadas.pdf
Tamaño:
3.06 MB
Formato:
Adobe Portable Document Format
Descripción:
Comprensión y aprendizaje en matemáticas: perspectivas semióticas seleccionadas

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: