Enseñanza y aprendizaje de las matemáticas: problemas semióticos, epistemológicos y prácticos

En este libro, Bruno D´Amore y Luis Radford ponen en evidencia a la luz de nuevos enfoques -sobre todo socioculturales-, que progresivamente se han venido imponiendo en el campo de la educación matemática, la necesidad de repensar hoy en día algunas nociones centrales de la didáctica, como aquellas...

Full description

Autores:
D´Amore, Bruno
Radford, Luis
Tipo de recurso:
Book
Fecha de publicación:
2017
Institución:
Universidad Distrital Francisco José de Caldas
Repositorio:
RIUD: repositorio U. Distrital
Idioma:
OAI Identifier:
oai:repository.udistrital.edu.co:11349/37879
Acceso en línea:
http://hdl.handle.net/11349/37879
Palabra clave:
Matemáticas
Conocimiento
Didáctica de la matemática
Constructivismo
Semiótica
Objetivación
Subjetividad
Noética
Matemáticas -- Enseñanza
Matemáticas -- Problemas, ejercicios, etc.
Semiología (Linguistica)
Mathematics
Knowledge
Mathematics teaching
Constructivism
Semiotics
Noetic
Objectification
Subjectivity
Rights
License
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
id UDISTRITA2_abd1e11a00857f4c0989b836ba357894
oai_identifier_str oai:repository.udistrital.edu.co:11349/37879
network_acronym_str UDISTRITA2
network_name_str RIUD: repositorio U. Distrital
repository_id_str
dc.title.spa.fl_str_mv Enseñanza y aprendizaje de las matemáticas: problemas semióticos, epistemológicos y prácticos
dc.title.alternative.spa.fl_str_mv Problemas semióticos, epistemológicos y prácticos
dc.title.titleenglish.spa.fl_str_mv Teaching and learning mathematics: semiotic, epistemological and practical problems
title Enseñanza y aprendizaje de las matemáticas: problemas semióticos, epistemológicos y prácticos
spellingShingle Enseñanza y aprendizaje de las matemáticas: problemas semióticos, epistemológicos y prácticos
Matemáticas
Conocimiento
Didáctica de la matemática
Constructivismo
Semiótica
Objetivación
Subjetividad
Noética
Matemáticas -- Enseñanza
Matemáticas -- Problemas, ejercicios, etc.
Semiología (Linguistica)
Mathematics
Knowledge
Mathematics teaching
Constructivism
Semiotics
Noetic
Objectification
Subjectivity
title_short Enseñanza y aprendizaje de las matemáticas: problemas semióticos, epistemológicos y prácticos
title_full Enseñanza y aprendizaje de las matemáticas: problemas semióticos, epistemológicos y prácticos
title_fullStr Enseñanza y aprendizaje de las matemáticas: problemas semióticos, epistemológicos y prácticos
title_full_unstemmed Enseñanza y aprendizaje de las matemáticas: problemas semióticos, epistemológicos y prácticos
title_sort Enseñanza y aprendizaje de las matemáticas: problemas semióticos, epistemológicos y prácticos
dc.creator.fl_str_mv D´Amore, Bruno
Radford, Luis
dc.contributor.author.none.fl_str_mv D´Amore, Bruno
Radford, Luis
dc.subject.spa.fl_str_mv Matemáticas
Conocimiento
Didáctica de la matemática
Constructivismo
Semiótica
Objetivación
Subjetividad
Noética
topic Matemáticas
Conocimiento
Didáctica de la matemática
Constructivismo
Semiótica
Objetivación
Subjetividad
Noética
Matemáticas -- Enseñanza
Matemáticas -- Problemas, ejercicios, etc.
Semiología (Linguistica)
Mathematics
Knowledge
Mathematics teaching
Constructivism
Semiotics
Noetic
Objectification
Subjectivity
dc.subject.lemb.spa.fl_str_mv Matemáticas -- Enseñanza
Matemáticas -- Problemas, ejercicios, etc.
Semiología (Linguistica)
dc.subject.keyword.spa.fl_str_mv Mathematics
Knowledge
Mathematics teaching
Constructivism
Semiotics
Noetic
Objectification
Subjectivity
description En este libro, Bruno D´Amore y Luis Radford ponen en evidencia a la luz de nuevos enfoques -sobre todo socioculturales-, que progresivamente se han venido imponiendo en el campo de la educación matemática, la necesidad de repensar hoy en día algunas nociones centrales de la didáctica, como aquellas del saber, del conocimiento y del aprendizaje... Lo que une [a los autores], y que yo percibo de forma particular al interior de la reflexión que ellos conducen, es la importancia que ambos conceden a la dimensión epistemológica y semiótica. (Prólogo)
publishDate 2017
dc.date.created.none.fl_str_mv 2017
dc.date.accessioned.none.fl_str_mv 2024-07-11T15:04:55Z
dc.date.available.none.fl_str_mv 2024-07-11T15:04:55Z
dc.type.spa.fl_str_mv book
dc.type.driver.none.fl_str_mv info:eu-repo/semantics/book
dc.type.coar.none.fl_str_mv http://purl.org/coar/resource_type/c_2f33
format http://purl.org/coar/resource_type/c_2f33
dc.identifier.isbn.spa.fl_str_mv 978-958-5434-47-9
978-958-5434-48-6
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/11349/37879
dc.identifier.editorial.spa.fl_str_mv Universidad Distrital Francisco José de Caldas. Doctorado Interinstitucional en Educación
identifier_str_mv 978-958-5434-47-9
978-958-5434-48-6
Universidad Distrital Francisco José de Caldas. Doctorado Interinstitucional en Educación
url http://hdl.handle.net/11349/37879
dc.relation.ispartofseries.spa.fl_str_mv Énfasis; N° 17
dc.relation.references.spa.fl_str_mv Eco, U. (1981). Lector in fabula. Barcelona: Lumen.
Bagni, G. T., & D’Amore, B. (2005). Epistemologia, sociologia, semiotica: la prospettiva socio-culturale. La matematica e la sua didattica, 19(1), 73–89.
Bales, R. (1950). Interaction process analysis: A method for the study of small groups. Cambridge, Mass.: Addison-Wesley.
Bales, R. (1970). Personality and interpersonal behavior. New York: Holt, Rinehart & Winston.
Bartolini Bussi, M. (1994). Theoretical and empirical approaches to classroom interaction. En R. Biehler, R. W. Scholz, R. Strässer, & B. Winkelmann (Eds.), Didactics of mathematics as a scientific discipline (pp. 121–132). Dordrecht: Kluwer Academic Publishers.
D’Amore, B. (1999). Elementi di didattica della matematica. Bologna: Pitagora.
D’Amore, B. (2006). Didáctica de la matemática (1ª edición italiana, 1999). Bogotá: Magisterio.
D’Amore, B. (2003). La complexité de la noétique en mathématiques ou les raisons de la dévolution manquée. For the learning of mathematics, 23(1), 47–51.
D’Amore, B. (2015). Saber, conocer, labor en didáctica de la matemática: una contribución a la teoría de la objetivación. En L. Branchetti (Ed.), Teaching and learning mathematics: Some past and current approaches to mathematics education [Número especial]. Isonomia-Epistemologica (pp. 151–171). Universidad de Urbino “Carlo Bo”. Recuperado de: http://isonomia.uniurb.it/archive_epistemologica_special/201509
D’Amore, B., & Fandiño Pinilla, M. I. (2015). Propuestas metodológicas que constituyeron ilusiones en el proceso de enseñanza de la matemática. Educación matemática [México DF, México], 27(3), 7-43.
Durkheim, E. (1964). The division of labor in society. New York: Free Press. (Trabajo original publicado en 1893).
Duval, R. (1993a). Registres de représentations sémiotiques et fonctionnement cognitif de la pensée. Annales de Didactique et de Science Cognitives, 5(1), 37–65.
Duval, R. (1993b). Argumenter, demontrer, expliquer: continuité ou rupture cognitive? Petit x, 31, 37–61.
Duval, R. (1999). Argumentar, demostrar, explicar: ¿continuidad o ruptura cognitiva? México: Grupo Editorial Iberoamérica.
Fandiño Pinilla, M. I. (2010). Múltiples aspectos del aprendizaje de la matemática. Prólogo de Giorgio Bolondi. Bogotá: Magisterio.
Godino, J. D., & Batanero, C. (1994). Significado institucional y personal de los objetos matemáticos. Recherches en didactiques des mathématiques, 14(3), 325–355.
Hardesty, D. (1977). Ecological anthropology. New York: Wiley.
Merton, R. (1968). Social theory and social structure. New York: Free Press.
Mills, T. (1967). The sociology of small groups. Englewood Cliffs, N.J.: Prentice Hall.
Radford, L. (1997). On psychology, historical epistemology and the teaching of mathematics: Towards a socio-cultural history of mathematics. For the Learning of Mathematics, 17(1), 26–33.
Radford, L. (2003a). On the epistemological limits of language: Mathematical knowledge and social practice in the Renaissance. Educational Studies in Mathematics, 52(2), 123–150. doi: 10.1023/A:1024029808871
Radford, L. (2003b). On culture and mind: A post-Vygotskian semiotic perspective, with an example from Greek mathematical thought. En M. Anderson, A. SáenzLudlow, S. Zellweger, & V. Cifarelli (Eds.), Educational Perspectives on Mathematics as Semiosis: From Thinking to Interpreting to Knowing (pp. 49–79). Ottawa: Legas Publishing.
Radford, L. (2014). De la teoría de la objetivación. Revista Latinoamericana de Etnomatemática, 7(2), 132-150.
Radford, L., & Demers, S. (2006). Comunicazione e apprendimento. Prólogo de Bruno D’Amore. Bologna: Pitagora.
Robertson, I. (1977). Sociobiology. New York: Worth Publishers Inc.
D’Amore, B. (2005). Pratiche e metapratiche nell’attività matematica della classe intesa come società: Alcuni elementi rilevanti della didattica della matematica interpretati in chiave sociologica. La matematica e la sua didattica, 19(3), 325–336.
D’Amore, B., Font, V., & Godino, J. D. (2007). La dimensión metadidáctica en los procesos de enseñanza y aprendizaje de la matemática. Paradigma, 28(2), 49–77.
D’Amore, B., Font, V., & Godino, D. J. (2008). La dimensione metadidattica dei processi di insegnamento e di apprendimento della matematica. La matematica e la sua didattica, 22(2), 207–235.
Font, V., Godino, D. J., & D’Amore, B. (2007). An onto-semiotic approach to rappresentations in mathematical education. For the learning of mathematics, 27(2), 2–7 and 14.
Artigue, M., Gras, R., Laborde, C., & Tavignot, P. (Eds.) (1994). Vingt ans de didactique des mathématiques en France: Hommage à Guy Brousseau et Gérard Vergnaud. Grenoble: La Pensée Sauvage.
Brousseau, G. (1986a). La relation didactique: le milieu. Actes de la IVème école d’été de didactique des mathématiques (pp. 54–68). Paris: IREM de Paris 7.
Brousseau, G. (1986b). Fondements et méthodes de la didactique des mathématiques. Recherches en didactique des mathématiques, 7(2), 33–115.
Campolucci, L., Fandiño Pinilla, M. I., & Maori, D. (2011). Frazioni. En B. D’Amore, M. I. Fandiño Pinilla, & S. Sbaragli (Eds.), Progetto “Matematica nella scuola primaria, percorsi per apprendere” (Vol. 8). Bologna: Pitagora.
Campolucci, L., Fandiño Pinilla, M. I., Maori, D., & Sbaragli, S. (2006). Cambi di convinzione sulla pratica didattica concernente le frazioni. La matematica e la sua didattica, 20(3), 353–400.
Chevallard, Y. (1988). Sur l’analyse didactique: Deux études sur les notions de contrat et de situation. Marseille: IREM d’Aix-Marseille.
D’Amore, B. (2003). Le basi filosofiche, pedagogiche, epistemologiche e concettuali della Didattica della Matematica. Bologna: Pitagora.
D’Amore, B. (2004). El papel de la epistemología en la formación de profesores de Matemática de la escuela secundaria, Epsilon 60, 20(3), 413–434.
D’Amore, B. (2005). Bases filosóficas, pedagógicas, epistemológicas y conceptuales de la didáctica de la matematica. México DF, México: Reverté-Relime. (Trabajo original publicado 2003).
D’Amore, B. (2006a). Didáctica de la matemática. Bogotá: Editorial Magisterio. (Trabajo original publicado 1999).
D’Amore, B. (2006b). Didattica della matematica “C”. En S. Sbaragli (Ed.), La matematica e la sua didattica, vent’anni di impegno. Actas del Congreso Internacional homónimo, Castel San Pietro Terme (BO), 23 septiembre 2006 (pp. 93–96). Roma: Carocci.
D’Amore, B. (2007). “Didattica disciplinare”, “Formazione in scienze naturali”, “Formazione in matemática”, “Scienza”. En F. Frabboni, G. Wallnöfer, N. Belardi, & W. Wiater (Eds.), Le parole della pedagogía: Teorie italiane e tedesche a confronto (pp. 72–75, 140–142, 145–147, 335-337). Torino: Bollati Boringhieri.
D’Amore, B., & Fandiño Pinilla, M. I. (2002). Un acercamiento analítico al “triángulo de la didáctica”. Educación Matemática, 14(1), 48–61.
D’Amore, B., & Fandiño Pinilla, M. I. (2004). Cambios de convicciones en futuros profesores de matemática de la escuela secundaria superior. Epsilon 58, 20(1), 25–43.
D’Amore, B., & Fandiño Pinilla, M. I. (2007). Le didattiche disciplinari. Prefación de Franco Frabboni. Trento: Erickson.
D’Amore, B., & Fandiño Pinilla, M. I. (2013). El paso más largo: Sobre la necesidad de no tirar por la borda (en el nombre de un modernismo vacío) las teorías de la educación matemática que explican, perfectamente, situaciones reales del aula. Acta Scientiae: Revista de Ensino de Ciências e Matemática, 15(2), 246–256. Recuperado de: http://www.periodicos.ulbra.br/index.php/acta/issue/view/36
D’Amore, B., & Fandiño Pinilla, M. I. (2015). Propuestas metodológicas que constituyeron ilusiones en el proceso de enseñanza de la matemática. Methodological proposals that constituted illusions in the process of teaching of mathematics. Educacion Matemática [México DF, México], 27(3), 7-43.
D’Amore, B., Fandiño Pinilla, M. I., & Iori, M. (2013). La semiotica en la didáctica de la matemática. Prefacios de Raymond Duval, Luis Radford. Prólogo a la edición en idioma español de Carlos Eduardo Vasco. Bogotá: Magisterio.
D’Amore, B., Fandiño Pinilla, M. I., & Sbaragli, S. (Eds.) (2011). Progetto “Matematica nella scuola primaria, percorsi per apprendere” (vols. 1-14). [Proyecto de enseñanza-aprendizaje de la matemática en la escuela primaria en 14 volúmenes]. Bologna: Pitagora.
D’Amore, B., Fandiño Pinilla, M. I., Marazzani, I., & Sarrazy, B. (2010). Didattica della matemática: Alcuni effetti del “contratto”. Prefación y postfación de Guy Brousseau. Bologna: Archetipolibri.
D’Amore, B., Fandiño Pinilla, M. I., Marazzani, I., & Sbaragli, S. (2008). La didattica e le difficoltà in matematica. Trento: Erickson.
D’Amore, B., Fandiño Pinilla, M. I., Marazzani, I., & Sbaragli, S. (2010). La didáctica y la dificultad en matemática. Bogotá: Magisterio. (Trabajo original publicado 2008).
D’Amore, B., & Frabboni, F. (1996). Didattica generale e didattiche disciplinari. Milano: Angeli.
D’Amore, B., & Frabboni, F. (2005). Didattica generale e didattica disciplinare. Milano: Bruno Mondadori.
D’Amore, B., & Sbaragli, S. (2011). Principi di base di didattica della matematica. En B. D’Amore, M. I. Fandiño Pinilla, & S. Sbaragli (Eds.), Progetto “Matematica nella scuola primaria, percorsi per apprendere” (Vol. 2). Bologna: Pitagora.
Da Ponte, J. P. (2009). Far ricerca sulla nostra pratica: una strategia di formazione e di costruzione della conoscenza professionale. La matematica e la sua didattica, 23(2), 157–189.
Dozza, L. (2006). Relazioni cooperative a scuola: Il lievito e gli ingredienti. Trento: Erickson.
Ellerani, P. (2012). La sfida della didattica: trasformare le classi in contesti di apprendimento continuo per formare competenze e capitale sociale. En G. Bolondi & M. I. Fandiño Pinilla (Eds.), Metodi e strumenti per l’insegnamento e l’apprendimento della matematica. Napoli: Edises.
Fandiño Pinilla, M. I. (2002). Curricolo e valutazione in matematica. Bologna: Pitagora.
Fandiño Pinilla, M. I. (2005). Frazioni, aspetti concettuali e didattici. Bologna: Pitagora.
Fandiño Pinilla, M. I. (2006). Currículo, evaluación y formación docente en matemática. Bogotá: Magisterio. (Trabajo original publicado 2002).
Fandiño Pinilla, M. I. (2009). Las fracciones: Aspectos conceptuales y didácticos. Bogotá: Magisterio. Prefacio de Athanasios Gagatsis. Prefacio a la edición en idioma español de Carlos Eduardo Vasco Uribe. (Trabajo original publicado 2005).
Fandiño Pinilla, M. I., & Sbaragli, S. (2011). Matematica di base per insegnare nella scuola primaria. En B. D’Amore, M. I. Fandiño Pinilla, & S. Sbaragli (Eds.), Progetto “Matematica nella scuola primaria, percorsi per apprendere” (Vol. 1). Bologna: Pitagora.
Godino, J. (1993). La metáfora ecológica en el estudio de la noosfera matemática. Quadrante, 2(2), 69–79.
Martini, B., & Sbaragli, S. (2005). Insegnare e apprendere la matematica. Napoli: Tecnodid.
Perrin-Glorian, M.-J. (1994). Théorie des situations didactiques: naissance, développement, perspectives. En M. Artigue, R. Gras, C. Laborde, & P. Tavignot (Eds.), Vingt ans de didactique des mathématiques en France: Hommage à Guy Brousseau et Gérard Vergnaud (pp. 97–147). Grenoble: La Pensée Sauvage.
Sbaragli, S. (Ed.) (2011). Buone pratiche d’aula. Bologna: Pitagora.
Sbaragli, S. (2012). Il ruolo delle misconcezione nella didattica della matematica. En G. Bolondi & M. I. Fandiño Pinilla (Eds.), Metodi e strumenti per l’insegnamento e l’apprendimento della matematica. Napoli: Edises.
Stenhouse, L. (1975). An introduction to curriculum research and development. London: Heineman Educational.
Zan, R. (2007). Difficoltà in matematica. Milano: Springer.
Zeichner, K., & Nofke, S. (2001). Practitioner research. En V. Richardson (Eds.), Handbook of research on teaching (pp. 298–330). Washington: AERA.
D’Amore, B., & Fandiño Pinilla, M. I. (2013). La didattica della didattica della matematica: Esperienze personali e spunti critici di discussione e ricerca. L’insegnamento della matematica e delle scienze integrate, 36B(4), 325–353.
Chevallard, Y. (1991). Dimension instrumentale, dimension sémiotique de l’acitivité mathématique. Actes du séminaire de didactique des mathématiques et de l’informatique (année 1990-1991, n. 122) (pp. 103–117). Grenoble: LSD-IMAG, Université Joseph Fourier.
Chevallard, Y. (1992). Concepts fondamentaux de la didactique: perspectives apportées par une approche antropologique. Recherches en didactique des mathématiques, 12(1), 73–111.
D’Amore, B. (1998). Objetos relacionales y registros representativos distintos: Dificultades cognitivas y obstáculos. Uno, 15, 63-78.
D’Amore, B. (1999a). Scolarizzazione del sapere e delle relazioni: effetti sull’apprendimento della matematica. L’insegnamento della Matematica e delle scienze integrate, 22A(3), 247–276.
D’Amore, B. (1999b). Elementi di didattica della matematica. Prefazione di Colette Laborde. Bologna: Pitagora.
D’Amore, B. (2001a). Concettualizzazione, registri di rappresentazioni semiotiche e noetica. La matematica e la sua didattica, 15(2), 150–173.
D’Amore, B. (2001b). Un contributo al dibattito su concetti e oggetti matematici: la posizione “ingenua” in una teoria “realista” vs il modello “antropologico” in una teoria “pragmatica”. La matematica e la sua didattica. 1, 4–30.
D’Amore, B. (2001c). Una contribución al debate sobre conceptos y objetos matemáticos. Uno, 27, 51–78.
D’Amore, B. (2004). Conceptualización, registros de representaciones semióticas y noética: interacciones constructivistas en el aprendizaje de los conceptos matemáticos e hipótesis sobre algunos factores que inhiben la devolución. Uno, 35, 90–106. (Trabajo original publicado 2001).
D’Amore, B. (2006a). Oggetti matematici e senso: Le trasformazioni semiotiche cambiano il senso degli oggetti matematici. La matematica e la sua didattica, 20(4), 557–583.
D’Amore, B. (2006b). Objetos, significados, representaciones semióticas y sentido. En L. Radford & B. D’Amore (Eds.), Semiotics, Culture and Mathematical Thinking [Número especial]. Revista Latinoamericana de Investigación en Matemática Educativa, 9(1), 177-195.
D’Amore, B. (2006c). Didáctica de la matemática. Con una carta de Guy Brousseau. Prefacio a la edición en idioma español de Luis Rico. Bogotá: Editorial Magisterio. (Trabajo original publicado en 1999).
D’Amore, B. (2007a). How the treatment or conversion changes the sense of mathematical objects. En E. P. Avgerinos & A. Gagatsis (Eds.), Current trends in Mathematics Education. Proceedings of 5th MEDCONF2007 (Mediterranean Conference on Mathematics Education) (pp. 77–82). Athens: New Technologies Publications.
D’Amore, B. (2007b). Mathematical objects and sense: How semiotic transformations change the sense of mathematical objects. Acta Didactica Universitatis Comenianae, 7, 23–45.
D’Amore, B. (2011). La ricerca in didattica della matematica: un esempio di ricerca. Oggetti matematici, trasformazioni semiotiche e senso. L’insegnamento della matematica e delle scienze integrate, 34AB(3), 255–266.
D’Amore, B., & Fandiño, M. I. (2007a). How the sense of mathematical objects changes when their semiotic representations undergo treatment and conversion. La matematica e la sua didattica, 21(1), 87–92.
D’Amore, B., & Fandiño, M. I. (2007b). Relationships between area and perimeter: Beliefs of teachers. En E. P. Avgerinos & A. Gagatsis (Eds.), Current trends in Mathematics Education. Proceedings of 5th MEDCONF2007 (Mediterranean Conference on Mathematics Education) (pp. 383–396). Athens: New Technologies Publications.
D’Amore, B., & Fandiño, M. I. (2008a). Change of the meaning of mathematical objects due to the passage between their different representations: How other disciplines can be useful to the analysis of this phenomenon. Roma, Symposium on the occasion of the 100th anniversary of ICMI, Marzo 2008. WG5: The evolution of theoretical framework in mathematics education. Recuperado de: www.unige.ch/math/EnsMath/Rome2008
D’Amore, B., & Fandiño, M. I. (2008b). The phenomenon of change of the meaning of mathematical objects due to the passage between their different representations: How other disciplines can be useful to the analysis. En A. Gagatsis (Ed.), Research in Mathematics Education. Proceedings of Conference of five cities: Nicosia, Rhodes, Bologna, Palermo, Locarno (pp. 13–22). Nicosia, Cyprus: University of Cyprus.
D’Amore, B., & Fandiño, M. I. (2008c). Change of the meaning of mathematical objects due to the passage between their different representations. En M. Menghini, F. Furinghetti, L. Giacardi & F. Arzarello (Eds.), The First Century of the International Commission on Mathematical Instruction (1908-2008). Reflecting and shaping the world of mathematics education. Actas del homónimo Congreso (pp. 304-305). Roma: Instituto de la Enciclopedia Italiana. Colección Scienza e Filosofia.
D’Amore, B., Fandiño Pinilla, M. I., Iori, M., & Matteuzzi, M. (2015). Análisis de los antecedentes histórico-filosóficos de la “paradoja cognitiva de Duval”. Revista Latinoamericana de Investigación en Matemática Educativa, 18(2), 177– 212. doi: 10.12802/relime.13.1822
De Saussure, F. (1915). Cours de linguistique générale (5a ed., 1960). Paris: Payot.
Duval, R. (1988a). Ecarts sémantiques et cohérence mathématique. Annales de Didactique et de Sciences cognitives, 1(1), 7–25.
Duval, R. (1988b). Approche cognitive des problèmes de géométrie en termes de congruence. Annales de Didactique et de Sciences cognitives, 1(1), 57–74.
Duval, R. (1988c). Graphiques et équations. Annales de Didactique et de Sciences cognitives, 1(1), 235–253.
Duval, R. (1993). Registres de représentations sémiotique et fonctionnement cognitif de la pensée. Annales de Didactique et de Sciences Cognitives, 5(1), 37–65.
Duval, R. (1995). Sémiosis et pensée humaine. Registres sémiotiques et apprentissages intellectuels. Berne: Peter Lang.
Duval, R. (1996). Quel cognitif retenir en didactique des mathématiques? Recherche en Didactique des Mathématiques, 16(3), 349–382.
Duval, R. (1998). Signe et object (I). Trois grandes étapes dans la problématique des rapports entre répresentation et objet. Annales de Didactique et de Sciences Cognitives, 6(1), 139–163.
Godino, J. D., & Batanero, C. (1994). Significado institucional y personal de los objetos matemáticos. Recherches en Didactique des Mathématiques, 14(3), 325–355.
Iori, M. (2015). La consapevolezza dell’insegnante della dimensione semio-cognitiva dell’apprendimento della matematica. (Tesis de Doctorado, Universidad de Palermo, Italia). Recuperado de: http://www.dm.unibo.it/rsddm/it/Phd/Iori/ Iori.htm
Iori, M. (2017). Objects, signs and representations in the semio-cognitive analysis of the processes involved in teaching and learning mathematics. A Duvalian perspective. Educational studies in mathematics, 94(3), 275-291. doi: 10. 1007 / s 10649-016-9726-3.
Moreno Armella, L. (1999). Epistemologia ed Educazione Matematica. La matematica e la sua didattica, 13(1), 43–59.
Perrin Glorian, M. J. (1994). Théorie des situations didactiques: naissance, développement, perspectives. En M. Artigue, R. Gras, C. Laborde, & P. Tavignot (Eds.), Vingt ans de didactique des mathématiques en France: Hommage à Guy Brousseau et Gérard Vergnaud (pp. 97–148). Grenoble: La Pensée Sauvage.
Piaget, J. (1937). La construction du réel chez l’enfant. Neuchâtel-Paris: Delachaux et Niestlé.
Piaget, J., & García, R. (1983). Psychogenèse et histoire des sciences. Paris: Flammarion.
Radford, 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.
Radford, L. (2003). Gestures, speech and the sprouting of signs: A semiotic-cultural approach to students’ types of generalization. Mathematical Thinking and Learning, 5(1), 37–70.
Radford, L. (2004). Cose sensibili, essenze, oggetti matematici ed altre ambiguità. La matematica e la sua didattica. 1, 4–23.
Rojas, P. (2014). Articulación de saberes matemáticos: representaciones semióticas y sentidos. Universidad Distrital Francisco José de Caldas: Bogotá (Colombia).
Santi, G. (2010). Changes in meaning of mathematical objects due to semiotic transformations: a comparison between semiotic perspectives (Tesis Doctoral), Universidad de Palermo (Italia).
Santi, G. (2011). Objectification and semiotic function. Educational studies in mathematics, 77 (2-3), 285-311.
Speranza, F. (1997). Scritti di epistemologia della matematica. Bologna: Pitagora.
Vergnaud, G. (1990). La théorie des champs conceptuels. Recherches en Didactique des Mathématiques, 10(2-3), 133–170.
Vygotsky, L. (1962). Thought and language. Cambridge, MA: MIT Press.
Wertsch, J. (1993). Voces de la mente. Madrid: Visor.
Arendt, H. (1958). The modem concept of history. The Review of Politics, 20(4), 570-590. doi:10.1017/S0034670500034227.
Aristotle. (1998). Metaphysics. (H. Lawson-Tancred, Trans.). London: Penguin Books.
Campbell, S. (2002). Constructivism and the limits of reason: Revisiting the Kantian problematic. Studies in Philosophy and Education, 21,421-445.
Hegel, G. W. F. (1977). Phenomenology of spirit. Oxford: Oxford University Press (First edition, 1807).
Hegel, G. (2001). The philosophy of history. Kitchener, ON: Batoche Books. (Original work published 1837)
Hegel, G. (2009). Logic. (W. Wallace, Trans.). Pacifica, CA: MIA. (Original work published 1830)
Hirata, S., Morimura, N., & Houki, C. (2009). How to crack nuts: Acquisition process in captive chimpanzees (pan troglodytes) observing a model. Animal Cognition, 12, 87-101. doi: 10.1007/s10071-009-0275-3
Ilyenkov, E. V. (1977). Dialectical logic. Moscow: Progress Publishers.
Kant, I. (2003). Critique of pure reason. (N. K. Smith, Trans.) New York: St. Marin’s Press. (Original work published 1787)
Lawlor, R., & Lawlor, D. (1979). Theon of Smirna: Mathematics useful for understanding Plato. San Diego: Wizards Bookshelf.
Lefevre, W. (1981). Rechenstein und sprache [computing stones and language]. In P. Damerow & W. Lefevre (Eds.), Rechenstein, experiment, sprache. Historische fallstudien zur entstehung der exakten wissenschaften [Computing stones, experiment, language. Historical case studies on the emergence of the exact sciences] (pp. 115-169). Stuttgart: Klett-Cotta.
Lerman, S. (1996). Intersubjectivity in mathematics learning: A challenge to the radical constructivist paradigm? Journal for Research in Mathematics Education, 27(2), 133-150.
Manitius, K. (1888). Des hypsikles schrift anaphorikos nach iiberlieferung und inhalt kritisch behandelt [Hypsikles’ text “anaphorikos” according to transmission and content dealt with in a critical way]. Dresden: Lehmannsche Buchdruckerei.
Marx, K. (1973). Grundrisse: Introduction to the critique of political economy. Baltimore: Penguin Books.
Marx, K. (1998). The German ideology. New York: Prometheus Books.
Matsuzawa, T., Biro, D., Humle, T., Inoue-Nakamura, N., Tonooka, R., & Yamakoshi, G. (2001). Emergence of culture in wild chimpanzees: Education by masterapprenticeship. In T. Matsuzawa (Ed.), Primate origins of human cognition and behavior (pp. 557-574). Tokyo: Springer.
Maybee, J. (2009). Picturing Hegel. Lanham, MD: Lexington Books.
Mikhailov, F. T. (1980). The riddle of the self. Moscow: Progress Publishers.
Nicomachus of Gerasa. (1938). Introduction to arithmetic. (M. L. D’Ooge, Trans.). Ann Arbor: University of Michigan Press.
Otte, M. (1998). Limits of constructivism : Kant, Piaget and Peirce. Science & Education, 7, 425-450.
Radford, L. (2006a). Elementos de una teoría cultural de la objetivación. Revista Latinoamericana de Investigación en Matemática Educativa, Special Issue on Semiotics, Culture and Mathematical Thinking, 103-129 (available at: http://luisradford.ca)
Radford, L. (2006b). Variables, unknowns, and parameters of mathematical generality. In Mini-Workshop on studying original sources in mathematics education. Oberwolfach, April 30th-May 6th, 2006. Report No. 22/2006, 16-17.
Radford, L. (2014). De la teoría de la objetivación. Revista Latinoamericana de Etnomatemática, 7(2), 132-150.
Roth, W.-M. (2011). Possibility: At the limits of the constructivist metaphor. New York: Springer.
Sachs, J. (2015). Aristotle: Motion and its place in nature. In The internet encyclopedia of philosophy. http://www .iep.utm.edu/ (Accessed on April 9 2015).
Tarán, L. (1 969). Asclepius of Tralles: Commentary to Nichomacus’ Introduction to arithmetic (Vol. 59, part 4). Transactions of the American Philosophical Society.
Valero, M. (2004). Postmodernism as an attitude of critique to dominant mathematics education research. In P. Walshaw (Ed.), Mathematics education within the postmodern (pp. 35-54). Greenwich, CT: Information Age Publishing.
Ver Eecke, P. (1959). Diopante d’Alexandrie. Les six livres arithmetiques et le livre des nombres polygones [Diophantus of Alexandria: The six books on arithmetic and the book on polygonal numbers]. Liege: Desclee de Brower. (Original work published 1926).
Vygotsky, L. S. (1987-1999). Collected works. New York: Plenum Press.
Vygotsky, L. S., & Luria, A. (1994). Tool and symbol in child development. In R. van der Veer & J. Valsiner (Eds.), The Vygotsky reader (pp. 99-174). Oxford: Blackwell Publishers.
Zevenbergen, R. (1996). Constructivism as a liberal bourgeois discourse. Educational Studies in Mathematics, 31, 95-113.
Artigue, M. (1995). The role of epistemology in the analysis of teaching/learning relationships in mathematics education. In Y. M. Pothier (Ed.), Proceedings of the 1995 annual meeting of the Canadian mathematics education study group (pp. 7-21). University of Western Ontario.
Artigue, M. (2009). Didactical design in mathematics education. In C. Winslow (Ed.), Nordic research in mathematics education. Proceedings ofNORMA08. Rotterdam: Sense Publishers.
Gardener, S. (n.d.). Hegel: Glossary. Retrieved from http://philosophyfaculty.ucsd. edu/faculty/ewatkins/Hegel-Glossary.pdf.
Hegel, G. (2009). Logic. (W. Wallace, Trans.). Pacifica, CA: MIA. (Original work published 1830)
Heidegger, M. (2004). On the essence of language. New York: SUNY. (Original work published 1999)
Janet, P. (1929). L’evolution psychologique de la personnalite [The psychological evolution of personality]. Paris: Masson.
Lave, J. (1988). Cognition in practice. Cambridge: Cambridge University Press.
Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge: Cambridge University Press.
Leont’ev, A. N. (1978). Activity, consciousness, and personality. Englewood Cliffs, NJ: Prentice-Hall.
Mikhailov, F. T. (1980). The riddle of the self. Moscow: Progress Publishers.
Radford, L. (2007). Towards a cultural theory of learning. In D. Pitta-Pantazi & G. Philippou (Eds.), Proceedings of the fifth congress of the european society for research in mathematics education (CERME-5) (pp. 1782-1797). Lamaca, Cyprus.
Radford, L. (2008). Iconicity and contraction: A semiotic investigation of forms of algebraic generalizations of patterns in different contexts. ZDM - the International Journal on Mathematics Education, 40{ 1), 83-96. Doi:10.1007/sll858- 007-0061-0
Radford, L. (2010). Algebraic thinking from a cultural semiotic perspective. Research in Mathematics Education, 12(1), 1-19. Doi: 10.1080/14794800903569741
Radford, L. (2011). Embodiment, perception and symbols in the development of early algebraic thinking. In Proceedings of the 35th conference of the international group for the psychology of mathematics education (Vol. 4, pp. 17-24). Ankara: PME.
Radford, L., & Roth, W.-M. (2011). Intercorporeality and ethical commitment: An activity perspective on classroom interaction. Educational Studies in Mathematics, 77(2-3), 227-245. Doi: 10.1007/s10649-010-9282-1
Rogoff, B. (1990). Apprenticeship in thinking. Oxford: Oxford University Press.
Spinoza, B. (1989). Ethics including the improvement of the understanding. (R. Elwes, Trans.). Buffalo: Prometheus. (Original work published 1667)
Taylor, C. (1989). Sources of the self. Cambridge, MA: Harvard University Press.
Veresov, N. (1999). Undiscovered Vygotsky. Etudes on the pre-history of culturalhistorical psychology. Frankfurt: Peter Lang.
Vygotsky, L. (1929). The problem of the cultural development of the child. Journal of Genetic Psychology, 36, 415-434.
Vygotsky, L. S. (1978). Mind in society. Cambridge, Ma: Harvard University Press.
Arendt, H. (1958). The modern concept of history. The Review of Politics, 20(4), 570-590.
Baldino, R., & Cabral, T. (1998). Lacan and the school’s credit system. In A. Olivier & K. Newstead (Eds.), Proceedings of the 22nd conference of the international group for the psychology of mathematics education (Vol. 22, pp. 56-63). Stellenbosch, South Africa. University of Stellenbosch: PME.
Bakhtin, M. (1990). Art and answerability. Austin: University of Texas Press.
Beaud, M. (2004). A history of capitalism. Delhi: Aakar Books.
Brousseau, G. (1997). Theory of didactical situations in mathematics. Dordrecht: Kluwer.
Brousseau, G. (2003). Glossaire de quelques concepts de la théorie des situations didactiques en mathématiques [Glossary of some concepts of the theory of didactic situations in mathematics]. Retrieved on January 20, 2007, From http://dipmat.math.unipa.it/~grim/Gloss_fr_Brousseau.pdf.
Cambiano, G. (1993). Devenir homme. In J. Vernant (Ed.), L’homme grec (pp. 171- 215). Paris: Éditions du Seuil.
Cassirer, E. (1963). The individual and the cosmos in renaissance philosophy. (Original work published in 1927). New York: Harper Torchbooks.
Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31(3/4), 175-190.
Fischbach, F. (2012). Sans objet. Capitalisme, subjectivité, alienation [Sin objeto. Capitalismo, subjetividad, alienación]. Paris: Vrin.
Freire, P. (2004). Pedagogy of indignation. Boulder, Colorado: Paradigm Publishers.
Furinghetti, F., & Radford, L. (2008). Contrasts and oblique connections between historical conceptual developments and classroom learning in mathematics. In L. English (Ed.), Handbook of international research in mathematics education (2nd edition) (pp. 626 - 655). New York: Taylor and Francis.
Glasersfeld von, E. (1995). Radical constructivism: A way of knowing and learning. London: The Falmer Press.
Hegel, G. (2001). The philosophy of history. Kitchener, ON: Batoche Books. (Original work published 1837)
Heidegger, M. (1962). Being and time. (Translated by J. Macquarrie & E. Robinson). New York: Harper.
Husserl, E. (1970). The crisis of the European science. Evanston: Northwestern University Press.
Husserl, E. (1982). Cartesian meditations: An introduction to phenomenology. (D. Cairns, Trans.). The Hague: Martinus Nijhoff Publishers.
Illouz, E. (1997). Consuming the romantic utopia: Love and the cultural contradictions of capitalism. London: The University of California Press.
Lancy, D. F. (1983). Cross-cultural studies in cognition and mathematics. New York: Academic Press.
Le Goff, J. (1956). Marchands et banquiers du moyen age. (7th updated edition, 1986). Paris: Presses Universitaires de France.
Leont’ev, A. N. (1974). The problem of activity in psychology. Soviet Psychology, 13(2), 4-33.
Leont’ev [or Leontyev], A. N. (2009). Activity and consciousness. Pacifica, CA: MIA. Retrieved August 29, 2009, from http://www.marxists.org/archive/leontev/works/activity-consciousness.pdf.
Lévinas, E. (1982). Éthique et infini. Paris: Fayard.
Lizcano, E. (2009). Imaginario colectivo y creación matemática. Madrid: Gedisa.
Marx, K. (1988). Economic and philosophic manuscripts of 1844. Amherst, New York: Prometheus Books. (Original work published 1932).
Marx, K. (2007). Manuscrits économico-philosophiques de 1844 [Manuscritos económico-filosóficos de 1844]. (F. Fischbach, Trans.). Paris: Vrin. (Original work published 1932)
Owens, K. (2001). Indigenous mathematics: a rich diversity. Mathematics: Shaping Australia. Proceedings of the Eighteenth Biennial Conference of the Australian Association of Mathematics Teachers, 151–167. Retrieved Feburary 17, 2006, from: http://www.aamt.edu.au/ICSIMAN/resources/papers/owens.pdf.
Pais, A. (2011). Mathematics education and the political: An ideology critique of an educational research field. Ph. D. Dissertation. Aalborg, Denmark: Department of Learning and Philosophy. Aalborg University.
Piaget, J. (1973). To understand is to invent. The future of education. New York: Grossman.
Popkewitz, T. (2004). The alchemy of the mathematics curriculum: Inscriptions and the fabrication of the child. American Educational Research Journal, 41(1), 3-34.
Pumuge, H. M. (1975). The counting system of the pekai-alue tribe of the topopul village in the ialibu sub-district in the southern highlands district, papua new guinea. Science in New Guinea, 3(1), 19-25.
Radford, L. (2006). Elementos de una teoría cultural de la objetivación [Elements of a cultural theory of objectification]. Revista Latinoamericana de Investigación en Matemática Educativa, Special Issue on Semiotics, Culture and Mathematical Thinking, 103-129 (available at: http://www.laurentian.ca/educ/lradford/).
Radford, L. (2008). The ethics of being and knowing: Towards a cultural theory of learning. In L. Radford, G. Schubring, & F. Seeger (Eds.), Semiotics in mathematics education: Epistemology, history, classroom, and culture (pp. 215-234). Rotterdam: Sense Publishers.
Radford, L. (2012). Education and the illusions of emancipation. Educational Studies in Mathematics, 80(1), 101-118.
Radford, L. (2013). Sumisión, alienación y (un poco de) esperanza: hacia una visión cultural, histórica, ética y política de la enseñanza de las matemáticas. In A. Ramirez y Y. Morales (Eds). Memorias del I Congreso de Educación Matemática de América Central y El Caribe. Santo Domingo, República Dominicana, November 6-8, 2013 (disponible en la página: http://luisradford.ca)
Radford, L. (2014). De la teoría de la objetivación [on the theory of objectification]. Revista Latinoamericana de Etnomatemática, 7(2), 132-150.
Radford, L. (2015). Of love, frustration, and mathematics: A cultural-historical approach to emotions in mathematics teaching and learning. In B. Pepin & B. Roesken-Winter (Eds.), From beliefs to dynamic affect systems in mathematics education (pp. 25-49). New York: Springer.
Radford, L. (2016). On alienation in the mathematics classroom. International Journal of Educational Research, 79, 258-266. http://dx.doi.org/10.1016/j. ijer.2016.04.001.
Radford, L., & Roth, W. -M. (2011). Intercorporeality and ethical commitment: An activity perspective on classroom interaction. Educational Studies in Mathematics, 77(2-3), 227-245.
Shweder, R., & LeVine, R. (1984). Culture theory. Essays on mind, self, and emotion. Cambridge: Cambridge University Press.
Spinoza, B. (1989). Ethics including the improvement of the understanding. (R. Elwes, Trans.). Buffalo: Prometheus. (Original work published 1667)
Taylor, C. (1989). Sources of the self. Cambridge, Ma: Harvard University Press.
Thompson, P. (2014). Constructivism in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 96-100). New York: Springer.
Todorov, T. (2000). Éloge de l›individu [Elogio del individuo]. Paris: Adam Biro.
Valero, M. (2004). Postmodernism as an attitude of critique to dominant mathematics education research. In P. Walshaw (Ed.), Mathematics education within the postmodern (pp. 35-54). Greenwich, CT: Information Age Publishing.
Valero, P. (2009). Mathematics education as a network of social practices. In Proceedings of the 6th conference of European research in mathematics education (CERME 6). Lyon, France, Jan. 28th - Feb. 1, 2009. (Retrieved on December 10 2010 from) http://www.inrp.fr/publications/edition-electronique/cerme6/ plenary2-valero.pdf).
Vygotski, L. (1985). Pensée et langage. Paris: Messidor.
Vygotsky, L. S. (1987). Collected works (Vol. 1). R. W. Rieber and A. S. Carton (Eds.). New York: Plenum.
Vygotsky, L. S. (1999). Collected works (vol. 6). R. W. Rieber (Ed.). New York: Plenum.
Bachelard, G. (1938). La formation de l’esprit scientifique. Paris: VRIN.
Bagni, G. T. (2005). The historical roots of the limit notion: Cognitive development and development of representation registers. Canadian Journal of Science, Mathematics and Technology Education, 5(4), 453–468.
Bagni, G. T. (2006). Some cognitive difficulties related to the representations of two major concepts of set theory. Educational Studies in Mathematics, 62(3), 259–280. Doi: 10.1007/s10649-006-8545-3
Bagni, G. T., & D’Amore, B. (2005). Epistemologia, sociologia, semiotica: la prospettiva socio-culturale. La matematica e la sua didattica, 19(1), 73–89.
Balacheff, N. (1988). Le contrat et la coutume: deux registres des interactions didactiques. En C. Laborde (Ed.), Actes du premier colloque franco-allemand de didactique des mathématiques et de l’informatique (pp. 15–26). Grenoble: La Pensée Sauvage.
Barbin, E. (1994). Sur la conception des savoirs géométriques dans les Éléments de géométrie. Cahiers de didactique des Mathématiques, 14-15, 135–158. (http:// smf4.emath.fr/Publications/RevueHistoireMath/20/html/smf_rhm_20_253- 302.php)
Bauersfeld, H. (1995). “Language game” in the mathematics classroom: Their function and their effects. En P. Cobb & H. Bauersfeld (Eds.), The emergence of meaning: Interaction in classroom cultures (pp. 271–292). Hillsdale NJ: Lawrence Erlbaum Associates.
Bernhard, J. (1995). Child development, cultural diversity, and the professional training of early childhood educators. Canadian Journal of Education, 20(4), 415–436.
Brickhouse, N. (1990). Teachers’ beliefs about the nature of science and their relationship to classroom practice. Journal of teacher education, 41(3), 53–62.
Brousseau, G. (1976). Les obstacles épistémologiques et les problèmes en mathématiques. En W. Vanhamme & J. Vanhamme (Eds.), La problématique et l’enseignement des mathématiques, Actes de la XXVIIIème rencontre CIEAEM (pp. 101-117). Louvain la Neuve.
Brousseau, G. (1983). Les obstacles épistémologiques et les problèmes in mathématiques. Reserches en Didactique des Mathématiques, 4(2), 165–198.
Brousseau, G. (1989). Les obstacles épistémologiques et la didactique des mathématiques. En N. Bednarz & C. Garnier (Eds.), Constructions des savoirs, obstacles et conflits (pp. 41–64). Montreal: Agence d’Arc.
Castoriadis, C. (1987). The imaginary institution of society. Cambridge, Mass.: The MIT Press.
D’Amore, B. (2001a). Une contribution au débat sur les concepts et les objets mathématiques. Scientia Paedagogica Experimentalis, 38(1), 17–46.
D’Amore, B. (2001b). Conceptualisation, registres de représentations sémiotiques et noétique: interactions constructivistes dans l’apprentissage des concepts mathématiques et hypothèse sur quelques facteurs inhibant la dévolution. Scientia Paedagogica Experimentalis, 38(2), 143–168.
D’Amore, B. (2003a). Matemática em algumas culturas da America do Sul: Uma contribuição à Etnomatemática. Bolema. Boletim de Educação Matemática, 19, 73–89.
D’Amore, B. (2003b). Le basi filosofiche, pedagogiche, epistemologiche e concettuali della Didattica della Matematica. Bologna: Pitagora.
D’Amore, B. (2003c). The noetic in mathematics. Scientia Pedagogica Experimentalis, 39(1), 75–82.
D’Amore, B. (2003d). La complexité de la noétique en mathématiques ou les raisons de la dévolution manquée. For the learning of mathematics, 23(1), 47–51.
D’Amore, B. (2003e). La complejidad de la educación y de la construcción del saber. Suma, 43, 23–30.
D’Amore, B. (2004). Il ruolo dell’epistemologia nella formazione degli insegnanti di matematica nella scuola secondaria. La matematica e la sua didattica, 18(4), 4–30.
D’Amore, B. (2005a). Pratiche e metapratiche nell’attività matematica della classe intesa come società: Alcuni elementi rilevanti della didattica della matematica interpretati in chiave sociologica. La matematica e la sua didattica, 19(3), 325–336.
D’Amore, B. (2005b). Secondary school students’ mathematical argumentation and Indian logic (nyaya). For the learning of mathematics, 25(2), 26–32.
D’Amore, B., & Fandiño Pinilla, M. I. (2001). Matemática de la cotidianidad. Paradigma, 22(1), 59–72.
D’Amore, B., & Fandiño Pinilla, M. I. (2004). Cambi di convinzione in insegnanti di matematica di scuola secondaria superiore in formazione iniziale. La matematica e la sua didattica, 18(3), 27–50.
D’Amore, B., & Fandiño Pinilla, M. I. (2005). Storia ed epistemologia della matematica basi etiche. La matematica e la sua didattica, 19(4), 503–515.
D’Amore, B., & Godino, J. D. (2006). Punti di vista antropologico ed ontosemiotico in Didattica della Matematica. La matematica e la sua didattica, 20(1), 9–38.
D’Amore, B., & Sbaragli, S. (2005). Analisi semantica e didattica dell’idea di “misconcezione”. La matematica e la sua didattica, 19(2), 139–163.
D’Amore, B., & Speranza, F. (Eds.) (1989). Lo sviluppo storico della matematica: Spunti didattici (Vol. 1). Roma: Armando.
D’Amore, B., & Speranza, F. (Eds.) (1992). Lo sviluppo storico della matematica: Spunti didattici (Vol. 2). Roma: Armando.
D’Amore, B., & Speranza, F. (Eds.) (1995). La matematica e la sua storia: Alcuni esempi per spunti didattici. Milano: Angeli.
de Haan, M. (1999). Learning as a cultural practice. Amsterdam: Thela Thelis.
Eco, U. (1975). Trattato di semiotica generale. Milano: Bompiani.
Enriques, F. (1942). L’errore nelle matematiche. Periodico di matematiche, serie IV, 22, 57-65. [Bajo el pseudonimo A. Giovannini].
Fauvel, J., & Maanen, J. (2000). History in mathematics education: The ICMI study. Dordrecht - Boston, London: Kluwer.
Feyerabend, P. K. (2003). Contro il metodo. Milano: Feltrinelli. (Trabajo original publicado 1975).
Furinghetti, F., & Radford, L. (2002). Historical conceptual developments and the teaching of mathematics: From philogenesis and ontogenesis theory to classroom practice. En L. English (Ed.), Handbook of International Research in Mathematics Education (pp. 631–654). Hillsdale: Erlbaum.
Gadamer, H.-G. (1975). Truth and method (2nd ed., 1989). New York: Crossroad.
Godino, J. D. (2002). Un enfoque ontológico y semiótico de la cognición matemática. Recherches en Didactique des Mathématiques, 22(2-3), 237–284.
Godino, J. D., & Batanero, C. (1994). Significado institucional y personal de los objetos matemáticos. Recherches en didactiques des mathématiques, 14(3), 325–355.
Godino, J. D., & Llinares, S. (2000). El interaccionismo simbólico en educación matemática. Educación Matemática, 12(1), 70–92. Grugnetti, L., & Rogers, L. (2000). Philosophical, multicultural and interdisciplinary issues. En J. Fauvel & J. van Maanen (Eds.), History in Mathematics Education (pp. 39–62). Dodrecht: Kluwer.
Habermas, J. (2003). Truth and justification (trad. B. Fultner). Cambridge, MA: The MIT Press. (Trabajo original publicado 1999).
Hardesty, D. (1977). Ecological anthropology. New York: Wiley.
Hashweb, M. Z. (1996). Effects of science teachers’ epistemological beliefs in teaching. Journal of Research in Science Teaching, 33(1), 47–63.
Ilyenkov, E. (1977). The concept of the ideal. Philosophy in the USSR: Problems of dialectical materialism. Moscow: Progress Publishers.
Leontiev, A. A. (1981a). Sign and activity. En J. V. Wertsch (Ed.), The concept of activity in Soviet psychology (pp. 241–255). New York: Sharpe.
Leontiev, A. A. (1981b). The problem of activity in psychology. En J. V. Wertsch (Ed.), The concept of activity in Soviet psychology (pp. 37–71). New York: Sharpe.
McClain, K., & Cobb P. (1997). An analysis of the teacher’s role in guiding the evolution of sociomathematical norms. En E. Pekhonen (Ed.), Proceedings of the 21st PME International Conference (Vol. 3, pp. 224–231). Lahti: University of Helsinki.
Newton, M. (2002). Savage girls and wild boys: A history of feral children. London: Faber & Faber.
Piaget, J., & Garcia, R. (1983). Psychogenèse et histoire des sciences. Paris: Flammarion.
Perrin-Glorian, M.-J. (1994). Théorie des situations didactiques: naissance, développement, perspectives. En M. Artigue, R. Gras, C. Laborde, & P. Tavignot (Eds.), Vingt ans de didactique des mathématiques en France: Hommage à Guy Brousseau et Gérard Vergnaud (pp. 97–147). Grenoble: La Pensée Sauvage.
Radford, L. (1997). On psychology, historical epistemology and the teaching of mathematics: Towards a socio-cultural history of mathematics. For the Learning of Mathematics, 17(1), 26–33.
Radford, L. (2003a). On the epistemological limits of language: Mathematical knowledge and social practice in the Renaissance. Educational Studies in Mathematics, 52(2), 123–150. doi: 10.1023/A:1024029808871
Radford, L. (2003b). On culture and mind: A post-Vygotskian semiotic perspective, with an example from Greek mathematical thought. En M. Anderson, A. SáenzLudlow, S. Zellweger, & V. Cifarelli (Eds.), Educational Perspectives on Mathematics as Semiosis: From Thinking to Interpreting to Knowing (pp. 49–79). Ottawa: Legas Publishing.
Radford, L. (2004b). Syntax and meaning. En M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28 Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 161–166). Norway: Bergen University College.
Radford, L. (2006a). The anthropology of meaning. Educational Studies in Mathematics, 61(1-2), 9–65. doi: 10.1007/s10649-006-7136-7
Radford, L. (2006b). The cultural-epistemological conditions of the emergence of algebraic symbolism. En S. Kaijser, C. Tzanakis, & F. Furringhetti (Eds.), Proceedings of the 2004 History and Pedagogy of Mathematics Conference & ESU4 (pp. 509-524). Uppsala, Sweden. Recuperado de: http://laurentian.ca/ educ/lradford/PUBLIC.HTML
Radford, L. (2006c). Semiótica cultural y cognición. En R. Cantoral Uriza, O. Covián Chávez, R. M. Farfán, J. Lezama Andalón, & A. Romo Vázquez (Eds.), Investigaciones sobre enseñanza y aprendizaje de las matemáticas. Un reporte iberoamericano (pp. 669–689). Mexico: Diaz de Santos.
Radford, L., Boero, P., & Vasco, C. (2000). Epistemological assumptions framing interpretations of students understanding of mathematics. En J. Fauvel & J. van Maanen (Eds.), History in Mathematics Education (pp. 162–167). Dordrecht: Kluwer.
Robertson, I. (1977). Sociobiology. New York: Worth Publishers Inc.
Romberg, T. (1988). Necessary ingredients for a theory of mathematics education. En H. G. Steiner & A. Vermandel (Eds.), Foundations and methodology of the discipline Mathematics Education. Proceedings of the 2nd TME (pp. 97–112). Bielefeld, Antwerpen: IDM Publications.
Sfard, A., & Prusak, A. (2005). Identity that makes a difference: Substantial learning as closing the gap between actual and designated identities. En H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 37–52). Melbourne: PME.
Sierpinska, A., & Lerman, S. (1996). Epistemologies of mathematics and of mathematics education. En A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 827– 876). Dordrecht: Kluwer Academic Publishers.
Wartofsky, M. (1979). Models, representation and the scientific understanding. Dordrecht: Reidel.
Werner, H. (1948). Comparative psychology of mental development. New York: International University Press.
Wittgenstein, L. (1956), Bemerkungen über die Grundlagen der Mathematik. Oxford: Blackwell.
D’Amore, B., Radford, L. & Bagni, GT. (2007). Obstáculos epistemológicos y perspectiva socio-cultural de la matemática. Coleción “Cuadernos del Seminario en educación”. Bogotá: Universidad Nacional de Colombia.
dc.rights.*.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 Internacional
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.uri.*.fl_str_mv http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.acceso.spa.fl_str_mv Abierto (Texto Completo)
rights_invalid_str_mv Attribution-NonCommercial-NoDerivatives 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0/
Abierto (Texto Completo)
http://purl.org/coar/access_right/c_abf2
dc.format.mimetype.spa.fl_str_mv pdf
institution Universidad Distrital Francisco José de Caldas
bitstream.url.fl_str_mv https://repository.udistrital.edu.co/bitstreams/479d3bc7-3981-48b7-ad6c-ac80b92bd08f/download
https://repository.udistrital.edu.co/bitstreams/29df67e2-e222-469b-ae5d-3384cfccc76c/download
https://repository.udistrital.edu.co/bitstreams/913065ce-2317-4821-8468-e38c717cd8ed/download
https://repository.udistrital.edu.co/bitstreams/d0d921a6-8ab8-4647-a9d0-6248e23062ce/download
bitstream.checksum.fl_str_mv bed37e1a3f770906da6ed8caac817322
4460e5956bc1d1639be9ae6146a50347
997daf6c648c962d566d7b082dac908d
4ecf11cc745efe62645e900e748da97e
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
MD5
MD5
repository.name.fl_str_mv Repositorio Universidad Distrital
repository.mail.fl_str_mv repositorio@udistrital.edu.co
_version_ 1837007178275225600
spelling D´Amore, BrunoRadford, Luis2024-07-11T15:04:55Z2024-07-11T15:04:55Z2017978-958-5434-47-9978-958-5434-48-6http://hdl.handle.net/11349/37879Universidad Distrital Francisco José de Caldas. Doctorado Interinstitucional en EducaciónEn este libro, Bruno D´Amore y Luis Radford ponen en evidencia a la luz de nuevos enfoques -sobre todo socioculturales-, que progresivamente se han venido imponiendo en el campo de la educación matemática, la necesidad de repensar hoy en día algunas nociones centrales de la didáctica, como aquellas del saber, del conocimiento y del aprendizaje... Lo que une [a los autores], y que yo percibo de forma particular al interior de la reflexión que ellos conducen, es la importancia que ambos conceden a la dimensión epistemológica y semiótica. (Prólogo)In this book, Bruno D'Amore and Luis Radford highlight, in the light of new approaches - especially sociocultural - that have progressively been imposed in the field of mathematics education, the need to rethink some central notions today. of didactics, such as those of knowledge, knowledge and learning... What unites [the authors], and that I perceive in a particular way within the reflection that they lead, is the importance that both grant to epistemological and semiotic dimension. (Foreword)BogotápdfÉnfasis; N° 17Eco, U. (1981). Lector in fabula. Barcelona: Lumen.Bagni, G. T., & D’Amore, B. (2005). Epistemologia, sociologia, semiotica: la prospettiva socio-culturale. La matematica e la sua didattica, 19(1), 73–89.Bales, R. (1950). Interaction process analysis: A method for the study of small groups. Cambridge, Mass.: Addison-Wesley.Bales, R. (1970). Personality and interpersonal behavior. New York: Holt, Rinehart & Winston.Bartolini Bussi, M. (1994). Theoretical and empirical approaches to classroom interaction. En R. Biehler, R. W. Scholz, R. Strässer, & B. Winkelmann (Eds.), Didactics of mathematics as a scientific discipline (pp. 121–132). Dordrecht: Kluwer Academic Publishers.D’Amore, B. (1999). Elementi di didattica della matematica. Bologna: Pitagora.D’Amore, B. (2006). Didáctica de la matemática (1ª edición italiana, 1999). Bogotá: Magisterio.D’Amore, B. (2003). La complexité de la noétique en mathématiques ou les raisons de la dévolution manquée. For the learning of mathematics, 23(1), 47–51.D’Amore, B. (2015). Saber, conocer, labor en didáctica de la matemática: una contribución a la teoría de la objetivación. En L. Branchetti (Ed.), Teaching and learning mathematics: Some past and current approaches to mathematics education [Número especial]. Isonomia-Epistemologica (pp. 151–171). Universidad de Urbino “Carlo Bo”. Recuperado de: http://isonomia.uniurb.it/archive_epistemologica_special/201509D’Amore, B., & Fandiño Pinilla, M. I. (2015). Propuestas metodológicas que constituyeron ilusiones en el proceso de enseñanza de la matemática. Educación matemática [México DF, México], 27(3), 7-43.Durkheim, E. (1964). The division of labor in society. New York: Free Press. (Trabajo original publicado en 1893).Duval, R. (1993a). Registres de représentations sémiotiques et fonctionnement cognitif de la pensée. Annales de Didactique et de Science Cognitives, 5(1), 37–65.Duval, R. (1993b). Argumenter, demontrer, expliquer: continuité ou rupture cognitive? Petit x, 31, 37–61.Duval, R. (1999). Argumentar, demostrar, explicar: ¿continuidad o ruptura cognitiva? México: Grupo Editorial Iberoamérica.Fandiño Pinilla, M. I. (2010). Múltiples aspectos del aprendizaje de la matemática. Prólogo de Giorgio Bolondi. Bogotá: Magisterio.Godino, J. D., & Batanero, C. (1994). Significado institucional y personal de los objetos matemáticos. Recherches en didactiques des mathématiques, 14(3), 325–355.Hardesty, D. (1977). Ecological anthropology. New York: Wiley.Merton, R. (1968). Social theory and social structure. New York: Free Press.Mills, T. (1967). The sociology of small groups. Englewood Cliffs, N.J.: Prentice Hall.Radford, L. (1997). On psychology, historical epistemology and the teaching of mathematics: Towards a socio-cultural history of mathematics. For the Learning of Mathematics, 17(1), 26–33.Radford, L. (2003a). On the epistemological limits of language: Mathematical knowledge and social practice in the Renaissance. Educational Studies in Mathematics, 52(2), 123–150. doi: 10.1023/A:1024029808871Radford, L. (2003b). On culture and mind: A post-Vygotskian semiotic perspective, with an example from Greek mathematical thought. En M. Anderson, A. SáenzLudlow, S. Zellweger, & V. Cifarelli (Eds.), Educational Perspectives on Mathematics as Semiosis: From Thinking to Interpreting to Knowing (pp. 49–79). Ottawa: Legas Publishing.Radford, L. (2014). De la teoría de la objetivación. Revista Latinoamericana de Etnomatemática, 7(2), 132-150.Radford, L., & Demers, S. (2006). Comunicazione e apprendimento. Prólogo de Bruno D’Amore. Bologna: Pitagora.Robertson, I. (1977). Sociobiology. New York: Worth Publishers Inc.D’Amore, B. (2005). Pratiche e metapratiche nell’attività matematica della classe intesa come società: Alcuni elementi rilevanti della didattica della matematica interpretati in chiave sociologica. La matematica e la sua didattica, 19(3), 325–336.D’Amore, B., Font, V., & Godino, J. D. (2007). La dimensión metadidáctica en los procesos de enseñanza y aprendizaje de la matemática. Paradigma, 28(2), 49–77.D’Amore, B., Font, V., & Godino, D. J. (2008). La dimensione metadidattica dei processi di insegnamento e di apprendimento della matematica. La matematica e la sua didattica, 22(2), 207–235.Font, V., Godino, D. J., & D’Amore, B. (2007). An onto-semiotic approach to rappresentations in mathematical education. For the learning of mathematics, 27(2), 2–7 and 14.Artigue, M., Gras, R., Laborde, C., & Tavignot, P. (Eds.) (1994). Vingt ans de didactique des mathématiques en France: Hommage à Guy Brousseau et Gérard Vergnaud. Grenoble: La Pensée Sauvage.Brousseau, G. (1986a). La relation didactique: le milieu. Actes de la IVème école d’été de didactique des mathématiques (pp. 54–68). Paris: IREM de Paris 7.Brousseau, G. (1986b). Fondements et méthodes de la didactique des mathématiques. Recherches en didactique des mathématiques, 7(2), 33–115.Campolucci, L., Fandiño Pinilla, M. I., & Maori, D. (2011). Frazioni. En B. D’Amore, M. I. Fandiño Pinilla, & S. Sbaragli (Eds.), Progetto “Matematica nella scuola primaria, percorsi per apprendere” (Vol. 8). Bologna: Pitagora.Campolucci, L., Fandiño Pinilla, M. I., Maori, D., & Sbaragli, S. (2006). Cambi di convinzione sulla pratica didattica concernente le frazioni. La matematica e la sua didattica, 20(3), 353–400.Chevallard, Y. (1988). Sur l’analyse didactique: Deux études sur les notions de contrat et de situation. Marseille: IREM d’Aix-Marseille.D’Amore, B. (2003). Le basi filosofiche, pedagogiche, epistemologiche e concettuali della Didattica della Matematica. Bologna: Pitagora.D’Amore, B. (2004). El papel de la epistemología en la formación de profesores de Matemática de la escuela secundaria, Epsilon 60, 20(3), 413–434.D’Amore, B. (2005). Bases filosóficas, pedagógicas, epistemológicas y conceptuales de la didáctica de la matematica. México DF, México: Reverté-Relime. (Trabajo original publicado 2003).D’Amore, B. (2006a). Didáctica de la matemática. Bogotá: Editorial Magisterio. (Trabajo original publicado 1999).D’Amore, B. (2006b). Didattica della matematica “C”. En S. Sbaragli (Ed.), La matematica e la sua didattica, vent’anni di impegno. Actas del Congreso Internacional homónimo, Castel San Pietro Terme (BO), 23 septiembre 2006 (pp. 93–96). Roma: Carocci.D’Amore, B. (2007). “Didattica disciplinare”, “Formazione in scienze naturali”, “Formazione in matemática”, “Scienza”. En F. Frabboni, G. Wallnöfer, N. Belardi, & W. Wiater (Eds.), Le parole della pedagogía: Teorie italiane e tedesche a confronto (pp. 72–75, 140–142, 145–147, 335-337). Torino: Bollati Boringhieri.D’Amore, B., & Fandiño Pinilla, M. I. (2002). Un acercamiento analítico al “triángulo de la didáctica”. Educación Matemática, 14(1), 48–61.D’Amore, B., & Fandiño Pinilla, M. I. (2004). Cambios de convicciones en futuros profesores de matemática de la escuela secundaria superior. Epsilon 58, 20(1), 25–43.D’Amore, B., & Fandiño Pinilla, M. I. (2007). Le didattiche disciplinari. Prefación de Franco Frabboni. Trento: Erickson.D’Amore, B., & Fandiño Pinilla, M. I. (2013). El paso más largo: Sobre la necesidad de no tirar por la borda (en el nombre de un modernismo vacío) las teorías de la educación matemática que explican, perfectamente, situaciones reales del aula. Acta Scientiae: Revista de Ensino de Ciências e Matemática, 15(2), 246–256. Recuperado de: http://www.periodicos.ulbra.br/index.php/acta/issue/view/36D’Amore, B., & Fandiño Pinilla, M. I. (2015). Propuestas metodológicas que constituyeron ilusiones en el proceso de enseñanza de la matemática. Methodological proposals that constituted illusions in the process of teaching of mathematics. Educacion Matemática [México DF, México], 27(3), 7-43.D’Amore, B., Fandiño Pinilla, M. I., & Iori, M. (2013). La semiotica en la didáctica de la matemática. Prefacios de Raymond Duval, Luis Radford. Prólogo a la edición en idioma español de Carlos Eduardo Vasco. Bogotá: Magisterio.D’Amore, B., Fandiño Pinilla, M. I., & Sbaragli, S. (Eds.) (2011). Progetto “Matematica nella scuola primaria, percorsi per apprendere” (vols. 1-14). [Proyecto de enseñanza-aprendizaje de la matemática en la escuela primaria en 14 volúmenes]. Bologna: Pitagora.D’Amore, B., Fandiño Pinilla, M. I., Marazzani, I., & Sarrazy, B. (2010). Didattica della matemática: Alcuni effetti del “contratto”. Prefación y postfación de Guy Brousseau. Bologna: Archetipolibri.D’Amore, B., Fandiño Pinilla, M. I., Marazzani, I., & Sbaragli, S. (2008). La didattica e le difficoltà in matematica. Trento: Erickson.D’Amore, B., Fandiño Pinilla, M. I., Marazzani, I., & Sbaragli, S. (2010). La didáctica y la dificultad en matemática. Bogotá: Magisterio. (Trabajo original publicado 2008).D’Amore, B., & Frabboni, F. (1996). Didattica generale e didattiche disciplinari. Milano: Angeli.D’Amore, B., & Frabboni, F. (2005). Didattica generale e didattica disciplinare. Milano: Bruno Mondadori.D’Amore, B., & Sbaragli, S. (2011). Principi di base di didattica della matematica. En B. D’Amore, M. I. Fandiño Pinilla, & S. Sbaragli (Eds.), Progetto “Matematica nella scuola primaria, percorsi per apprendere” (Vol. 2). Bologna: Pitagora.Da Ponte, J. P. (2009). Far ricerca sulla nostra pratica: una strategia di formazione e di costruzione della conoscenza professionale. La matematica e la sua didattica, 23(2), 157–189.Dozza, L. (2006). Relazioni cooperative a scuola: Il lievito e gli ingredienti. Trento: Erickson.Ellerani, P. (2012). La sfida della didattica: trasformare le classi in contesti di apprendimento continuo per formare competenze e capitale sociale. En G. Bolondi & M. I. Fandiño Pinilla (Eds.), Metodi e strumenti per l’insegnamento e l’apprendimento della matematica. Napoli: Edises.Fandiño Pinilla, M. I. (2002). Curricolo e valutazione in matematica. Bologna: Pitagora.Fandiño Pinilla, M. I. (2005). Frazioni, aspetti concettuali e didattici. Bologna: Pitagora.Fandiño Pinilla, M. I. (2006). Currículo, evaluación y formación docente en matemática. Bogotá: Magisterio. (Trabajo original publicado 2002).Fandiño Pinilla, M. I. (2009). Las fracciones: Aspectos conceptuales y didácticos. Bogotá: Magisterio. Prefacio de Athanasios Gagatsis. Prefacio a la edición en idioma español de Carlos Eduardo Vasco Uribe. (Trabajo original publicado 2005).Fandiño Pinilla, M. I., & Sbaragli, S. (2011). Matematica di base per insegnare nella scuola primaria. En B. D’Amore, M. I. Fandiño Pinilla, & S. Sbaragli (Eds.), Progetto “Matematica nella scuola primaria, percorsi per apprendere” (Vol. 1). Bologna: Pitagora.Godino, J. (1993). La metáfora ecológica en el estudio de la noosfera matemática. Quadrante, 2(2), 69–79.Martini, B., & Sbaragli, S. (2005). Insegnare e apprendere la matematica. Napoli: Tecnodid.Perrin-Glorian, M.-J. (1994). Théorie des situations didactiques: naissance, développement, perspectives. En M. Artigue, R. Gras, C. Laborde, & P. Tavignot (Eds.), Vingt ans de didactique des mathématiques en France: Hommage à Guy Brousseau et Gérard Vergnaud (pp. 97–147). Grenoble: La Pensée Sauvage.Sbaragli, S. (Ed.) (2011). Buone pratiche d’aula. Bologna: Pitagora.Sbaragli, S. (2012). Il ruolo delle misconcezione nella didattica della matematica. En G. Bolondi & M. I. Fandiño Pinilla (Eds.), Metodi e strumenti per l’insegnamento e l’apprendimento della matematica. Napoli: Edises.Stenhouse, L. (1975). An introduction to curriculum research and development. London: Heineman Educational.Zan, R. (2007). Difficoltà in matematica. Milano: Springer.Zeichner, K., & Nofke, S. (2001). Practitioner research. En V. Richardson (Eds.), Handbook of research on teaching (pp. 298–330). Washington: AERA.D’Amore, B., & Fandiño Pinilla, M. I. (2013). La didattica della didattica della matematica: Esperienze personali e spunti critici di discussione e ricerca. L’insegnamento della matematica e delle scienze integrate, 36B(4), 325–353.Chevallard, Y. (1991). Dimension instrumentale, dimension sémiotique de l’acitivité mathématique. Actes du séminaire de didactique des mathématiques et de l’informatique (année 1990-1991, n. 122) (pp. 103–117). Grenoble: LSD-IMAG, Université Joseph Fourier.Chevallard, Y. (1992). Concepts fondamentaux de la didactique: perspectives apportées par une approche antropologique. Recherches en didactique des mathématiques, 12(1), 73–111.D’Amore, B. (1998). Objetos relacionales y registros representativos distintos: Dificultades cognitivas y obstáculos. Uno, 15, 63-78.D’Amore, B. (1999a). Scolarizzazione del sapere e delle relazioni: effetti sull’apprendimento della matematica. L’insegnamento della Matematica e delle scienze integrate, 22A(3), 247–276.D’Amore, B. (1999b). Elementi di didattica della matematica. Prefazione di Colette Laborde. Bologna: Pitagora.D’Amore, B. (2001a). Concettualizzazione, registri di rappresentazioni semiotiche e noetica. La matematica e la sua didattica, 15(2), 150–173.D’Amore, B. (2001b). Un contributo al dibattito su concetti e oggetti matematici: la posizione “ingenua” in una teoria “realista” vs il modello “antropologico” in una teoria “pragmatica”. La matematica e la sua didattica. 1, 4–30.D’Amore, B. (2001c). Una contribución al debate sobre conceptos y objetos matemáticos. Uno, 27, 51–78.D’Amore, B. (2004). Conceptualización, registros de representaciones semióticas y noética: interacciones constructivistas en el aprendizaje de los conceptos matemáticos e hipótesis sobre algunos factores que inhiben la devolución. Uno, 35, 90–106. (Trabajo original publicado 2001).D’Amore, B. (2006a). Oggetti matematici e senso: Le trasformazioni semiotiche cambiano il senso degli oggetti matematici. La matematica e la sua didattica, 20(4), 557–583.D’Amore, B. (2006b). Objetos, significados, representaciones semióticas y sentido. En L. Radford & B. D’Amore (Eds.), Semiotics, Culture and Mathematical Thinking [Número especial]. Revista Latinoamericana de Investigación en Matemática Educativa, 9(1), 177-195.D’Amore, B. (2006c). Didáctica de la matemática. Con una carta de Guy Brousseau. Prefacio a la edición en idioma español de Luis Rico. Bogotá: Editorial Magisterio. (Trabajo original publicado en 1999).D’Amore, B. (2007a). How the treatment or conversion changes the sense of mathematical objects. En E. P. Avgerinos & A. Gagatsis (Eds.), Current trends in Mathematics Education. Proceedings of 5th MEDCONF2007 (Mediterranean Conference on Mathematics Education) (pp. 77–82). Athens: New Technologies Publications.D’Amore, B. (2007b). Mathematical objects and sense: How semiotic transformations change the sense of mathematical objects. Acta Didactica Universitatis Comenianae, 7, 23–45.D’Amore, B. (2011). La ricerca in didattica della matematica: un esempio di ricerca. Oggetti matematici, trasformazioni semiotiche e senso. L’insegnamento della matematica e delle scienze integrate, 34AB(3), 255–266.D’Amore, B., & Fandiño, M. I. (2007a). How the sense of mathematical objects changes when their semiotic representations undergo treatment and conversion. La matematica e la sua didattica, 21(1), 87–92.D’Amore, B., & Fandiño, M. I. (2007b). Relationships between area and perimeter: Beliefs of teachers. En E. P. Avgerinos & A. Gagatsis (Eds.), Current trends in Mathematics Education. Proceedings of 5th MEDCONF2007 (Mediterranean Conference on Mathematics Education) (pp. 383–396). Athens: New Technologies Publications.D’Amore, B., & Fandiño, M. I. (2008a). Change of the meaning of mathematical objects due to the passage between their different representations: How other disciplines can be useful to the analysis of this phenomenon. Roma, Symposium on the occasion of the 100th anniversary of ICMI, Marzo 2008. WG5: The evolution of theoretical framework in mathematics education. Recuperado de: www.unige.ch/math/EnsMath/Rome2008D’Amore, B., & Fandiño, M. I. (2008b). The phenomenon of change of the meaning of mathematical objects due to the passage between their different representations: How other disciplines can be useful to the analysis. En A. Gagatsis (Ed.), Research in Mathematics Education. Proceedings of Conference of five cities: Nicosia, Rhodes, Bologna, Palermo, Locarno (pp. 13–22). Nicosia, Cyprus: University of Cyprus.D’Amore, B., & Fandiño, M. I. (2008c). Change of the meaning of mathematical objects due to the passage between their different representations. En M. Menghini, F. Furinghetti, L. Giacardi & F. Arzarello (Eds.), The First Century of the International Commission on Mathematical Instruction (1908-2008). Reflecting and shaping the world of mathematics education. Actas del homónimo Congreso (pp. 304-305). Roma: Instituto de la Enciclopedia Italiana. Colección Scienza e Filosofia.D’Amore, B., Fandiño Pinilla, M. I., Iori, M., & Matteuzzi, M. (2015). Análisis de los antecedentes histórico-filosóficos de la “paradoja cognitiva de Duval”. Revista Latinoamericana de Investigación en Matemática Educativa, 18(2), 177– 212. doi: 10.12802/relime.13.1822De Saussure, F. (1915). Cours de linguistique générale (5a ed., 1960). Paris: Payot.Duval, R. (1988a). Ecarts sémantiques et cohérence mathématique. Annales de Didactique et de Sciences cognitives, 1(1), 7–25.Duval, R. (1988b). Approche cognitive des problèmes de géométrie en termes de congruence. Annales de Didactique et de Sciences cognitives, 1(1), 57–74.Duval, R. (1988c). Graphiques et équations. Annales de Didactique et de Sciences cognitives, 1(1), 235–253.Duval, R. (1993). Registres de représentations sémiotique et fonctionnement cognitif de la pensée. Annales de Didactique et de Sciences Cognitives, 5(1), 37–65.Duval, R. (1995). Sémiosis et pensée humaine. Registres sémiotiques et apprentissages intellectuels. Berne: Peter Lang.Duval, R. (1996). Quel cognitif retenir en didactique des mathématiques? Recherche en Didactique des Mathématiques, 16(3), 349–382.Duval, R. (1998). Signe et object (I). Trois grandes étapes dans la problématique des rapports entre répresentation et objet. Annales de Didactique et de Sciences Cognitives, 6(1), 139–163.Godino, J. D., & Batanero, C. (1994). Significado institucional y personal de los objetos matemáticos. Recherches en Didactique des Mathématiques, 14(3), 325–355.Iori, M. (2015). La consapevolezza dell’insegnante della dimensione semio-cognitiva dell’apprendimento della matematica. (Tesis de Doctorado, Universidad de Palermo, Italia). Recuperado de: http://www.dm.unibo.it/rsddm/it/Phd/Iori/ Iori.htmIori, M. (2017). Objects, signs and representations in the semio-cognitive analysis of the processes involved in teaching and learning mathematics. A Duvalian perspective. Educational studies in mathematics, 94(3), 275-291. doi: 10. 1007 / s 10649-016-9726-3.Moreno Armella, L. (1999). Epistemologia ed Educazione Matematica. La matematica e la sua didattica, 13(1), 43–59.Perrin Glorian, M. J. (1994). Théorie des situations didactiques: naissance, développement, perspectives. En M. Artigue, R. Gras, C. Laborde, & P. Tavignot (Eds.), Vingt ans de didactique des mathématiques en France: Hommage à Guy Brousseau et Gérard Vergnaud (pp. 97–148). Grenoble: La Pensée Sauvage.Piaget, J. (1937). La construction du réel chez l’enfant. Neuchâtel-Paris: Delachaux et Niestlé.Piaget, J., & García, R. (1983). Psychogenèse et histoire des sciences. Paris: Flammarion.Radford, 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.Radford, L. (2003). Gestures, speech and the sprouting of signs: A semiotic-cultural approach to students’ types of generalization. Mathematical Thinking and Learning, 5(1), 37–70.Radford, L. (2004). Cose sensibili, essenze, oggetti matematici ed altre ambiguità. La matematica e la sua didattica. 1, 4–23.Rojas, P. (2014). Articulación de saberes matemáticos: representaciones semióticas y sentidos. Universidad Distrital Francisco José de Caldas: Bogotá (Colombia).Santi, G. (2010). Changes in meaning of mathematical objects due to semiotic transformations: a comparison between semiotic perspectives (Tesis Doctoral), Universidad de Palermo (Italia).Santi, G. (2011). Objectification and semiotic function. Educational studies in mathematics, 77 (2-3), 285-311.Speranza, F. (1997). Scritti di epistemologia della matematica. Bologna: Pitagora.Vergnaud, G. (1990). La théorie des champs conceptuels. Recherches en Didactique des Mathématiques, 10(2-3), 133–170.Vygotsky, L. (1962). Thought and language. Cambridge, MA: MIT Press.Wertsch, J. (1993). Voces de la mente. Madrid: Visor.Arendt, H. (1958). The modem concept of history. The Review of Politics, 20(4), 570-590. doi:10.1017/S0034670500034227.Aristotle. (1998). Metaphysics. (H. Lawson-Tancred, Trans.). London: Penguin Books.Campbell, S. (2002). Constructivism and the limits of reason: Revisiting the Kantian problematic. Studies in Philosophy and Education, 21,421-445.Hegel, G. W. F. (1977). Phenomenology of spirit. Oxford: Oxford University Press (First edition, 1807).Hegel, G. (2001). The philosophy of history. Kitchener, ON: Batoche Books. (Original work published 1837)Hegel, G. (2009). Logic. (W. Wallace, Trans.). Pacifica, CA: MIA. (Original work published 1830)Hirata, S., Morimura, N., & Houki, C. (2009). How to crack nuts: Acquisition process in captive chimpanzees (pan troglodytes) observing a model. Animal Cognition, 12, 87-101. doi: 10.1007/s10071-009-0275-3Ilyenkov, E. V. (1977). Dialectical logic. Moscow: Progress Publishers.Kant, I. (2003). Critique of pure reason. (N. K. Smith, Trans.) New York: St. Marin’s Press. (Original work published 1787)Lawlor, R., & Lawlor, D. (1979). Theon of Smirna: Mathematics useful for understanding Plato. San Diego: Wizards Bookshelf.Lefevre, W. (1981). Rechenstein und sprache [computing stones and language]. In P. Damerow & W. Lefevre (Eds.), Rechenstein, experiment, sprache. Historische fallstudien zur entstehung der exakten wissenschaften [Computing stones, experiment, language. Historical case studies on the emergence of the exact sciences] (pp. 115-169). Stuttgart: Klett-Cotta.Lerman, S. (1996). Intersubjectivity in mathematics learning: A challenge to the radical constructivist paradigm? Journal for Research in Mathematics Education, 27(2), 133-150.Manitius, K. (1888). Des hypsikles schrift anaphorikos nach iiberlieferung und inhalt kritisch behandelt [Hypsikles’ text “anaphorikos” according to transmission and content dealt with in a critical way]. Dresden: Lehmannsche Buchdruckerei.Marx, K. (1973). Grundrisse: Introduction to the critique of political economy. Baltimore: Penguin Books.Marx, K. (1998). The German ideology. New York: Prometheus Books.Matsuzawa, T., Biro, D., Humle, T., Inoue-Nakamura, N., Tonooka, R., & Yamakoshi, G. (2001). Emergence of culture in wild chimpanzees: Education by masterapprenticeship. In T. Matsuzawa (Ed.), Primate origins of human cognition and behavior (pp. 557-574). Tokyo: Springer.Maybee, J. (2009). Picturing Hegel. Lanham, MD: Lexington Books.Mikhailov, F. T. (1980). The riddle of the self. Moscow: Progress Publishers.Nicomachus of Gerasa. (1938). Introduction to arithmetic. (M. L. D’Ooge, Trans.). Ann Arbor: University of Michigan Press.Otte, M. (1998). Limits of constructivism : Kant, Piaget and Peirce. Science & Education, 7, 425-450.Radford, L. (2006a). Elementos de una teoría cultural de la objetivación. Revista Latinoamericana de Investigación en Matemática Educativa, Special Issue on Semiotics, Culture and Mathematical Thinking, 103-129 (available at: http://luisradford.ca)Radford, L. (2006b). Variables, unknowns, and parameters of mathematical generality. In Mini-Workshop on studying original sources in mathematics education. Oberwolfach, April 30th-May 6th, 2006. Report No. 22/2006, 16-17.Radford, L. (2014). De la teoría de la objetivación. Revista Latinoamericana de Etnomatemática, 7(2), 132-150.Roth, W.-M. (2011). Possibility: At the limits of the constructivist metaphor. New York: Springer.Sachs, J. (2015). Aristotle: Motion and its place in nature. In The internet encyclopedia of philosophy. http://www .iep.utm.edu/ (Accessed on April 9 2015).Tarán, L. (1 969). Asclepius of Tralles: Commentary to Nichomacus’ Introduction to arithmetic (Vol. 59, part 4). Transactions of the American Philosophical Society.Valero, M. (2004). Postmodernism as an attitude of critique to dominant mathematics education research. In P. Walshaw (Ed.), Mathematics education within the postmodern (pp. 35-54). Greenwich, CT: Information Age Publishing.Ver Eecke, P. (1959). Diopante d’Alexandrie. Les six livres arithmetiques et le livre des nombres polygones [Diophantus of Alexandria: The six books on arithmetic and the book on polygonal numbers]. Liege: Desclee de Brower. (Original work published 1926).Vygotsky, L. S. (1987-1999). Collected works. New York: Plenum Press.Vygotsky, L. S., & Luria, A. (1994). Tool and symbol in child development. In R. van der Veer & J. Valsiner (Eds.), The Vygotsky reader (pp. 99-174). Oxford: Blackwell Publishers.Zevenbergen, R. (1996). Constructivism as a liberal bourgeois discourse. Educational Studies in Mathematics, 31, 95-113.Artigue, M. (1995). The role of epistemology in the analysis of teaching/learning relationships in mathematics education. In Y. M. Pothier (Ed.), Proceedings of the 1995 annual meeting of the Canadian mathematics education study group (pp. 7-21). University of Western Ontario.Artigue, M. (2009). Didactical design in mathematics education. In C. Winslow (Ed.), Nordic research in mathematics education. Proceedings ofNORMA08. Rotterdam: Sense Publishers.Gardener, S. (n.d.). Hegel: Glossary. Retrieved from http://philosophyfaculty.ucsd. edu/faculty/ewatkins/Hegel-Glossary.pdf.Hegel, G. (2009). Logic. (W. Wallace, Trans.). Pacifica, CA: MIA. (Original work published 1830)Heidegger, M. (2004). On the essence of language. New York: SUNY. (Original work published 1999)Janet, P. (1929). L’evolution psychologique de la personnalite [The psychological evolution of personality]. Paris: Masson.Lave, J. (1988). Cognition in practice. Cambridge: Cambridge University Press.Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge: Cambridge University Press.Leont’ev, A. N. (1978). Activity, consciousness, and personality. Englewood Cliffs, NJ: Prentice-Hall.Mikhailov, F. T. (1980). The riddle of the self. Moscow: Progress Publishers.Radford, L. (2007). Towards a cultural theory of learning. In D. Pitta-Pantazi & G. Philippou (Eds.), Proceedings of the fifth congress of the european society for research in mathematics education (CERME-5) (pp. 1782-1797). Lamaca, Cyprus.Radford, L. (2008). Iconicity and contraction: A semiotic investigation of forms of algebraic generalizations of patterns in different contexts. ZDM - the International Journal on Mathematics Education, 40{ 1), 83-96. Doi:10.1007/sll858- 007-0061-0Radford, L. (2010). Algebraic thinking from a cultural semiotic perspective. Research in Mathematics Education, 12(1), 1-19. Doi: 10.1080/14794800903569741Radford, L. (2011). Embodiment, perception and symbols in the development of early algebraic thinking. In Proceedings of the 35th conference of the international group for the psychology of mathematics education (Vol. 4, pp. 17-24). Ankara: PME.Radford, L., & Roth, W.-M. (2011). Intercorporeality and ethical commitment: An activity perspective on classroom interaction. Educational Studies in Mathematics, 77(2-3), 227-245. Doi: 10.1007/s10649-010-9282-1Rogoff, B. (1990). Apprenticeship in thinking. Oxford: Oxford University Press.Spinoza, B. (1989). Ethics including the improvement of the understanding. (R. Elwes, Trans.). Buffalo: Prometheus. (Original work published 1667)Taylor, C. (1989). Sources of the self. Cambridge, MA: Harvard University Press.Veresov, N. (1999). Undiscovered Vygotsky. Etudes on the pre-history of culturalhistorical psychology. Frankfurt: Peter Lang.Vygotsky, L. (1929). The problem of the cultural development of the child. Journal of Genetic Psychology, 36, 415-434.Vygotsky, L. S. (1978). Mind in society. Cambridge, Ma: Harvard University Press.Arendt, H. (1958). The modern concept of history. The Review of Politics, 20(4), 570-590.Baldino, R., & Cabral, T. (1998). Lacan and the school’s credit system. In A. Olivier & K. Newstead (Eds.), Proceedings of the 22nd conference of the international group for the psychology of mathematics education (Vol. 22, pp. 56-63). Stellenbosch, South Africa. University of Stellenbosch: PME.Bakhtin, M. (1990). Art and answerability. Austin: University of Texas Press.Beaud, M. (2004). A history of capitalism. Delhi: Aakar Books.Brousseau, G. (1997). Theory of didactical situations in mathematics. Dordrecht: Kluwer.Brousseau, G. (2003). Glossaire de quelques concepts de la théorie des situations didactiques en mathématiques [Glossary of some concepts of the theory of didactic situations in mathematics]. Retrieved on January 20, 2007, From http://dipmat.math.unipa.it/~grim/Gloss_fr_Brousseau.pdf.Cambiano, G. (1993). Devenir homme. In J. Vernant (Ed.), L’homme grec (pp. 171- 215). Paris: Éditions du Seuil.Cassirer, E. (1963). The individual and the cosmos in renaissance philosophy. (Original work published in 1927). New York: Harper Torchbooks.Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31(3/4), 175-190.Fischbach, F. (2012). Sans objet. Capitalisme, subjectivité, alienation [Sin objeto. Capitalismo, subjetividad, alienación]. Paris: Vrin.Freire, P. (2004). Pedagogy of indignation. Boulder, Colorado: Paradigm Publishers.Furinghetti, F., & Radford, L. (2008). Contrasts and oblique connections between historical conceptual developments and classroom learning in mathematics. In L. English (Ed.), Handbook of international research in mathematics education (2nd edition) (pp. 626 - 655). New York: Taylor and Francis.Glasersfeld von, E. (1995). Radical constructivism: A way of knowing and learning. London: The Falmer Press.Hegel, G. (2001). The philosophy of history. Kitchener, ON: Batoche Books. (Original work published 1837)Heidegger, M. (1962). Being and time. (Translated by J. Macquarrie & E. Robinson). New York: Harper.Husserl, E. (1970). The crisis of the European science. Evanston: Northwestern University Press.Husserl, E. (1982). Cartesian meditations: An introduction to phenomenology. (D. Cairns, Trans.). The Hague: Martinus Nijhoff Publishers.Illouz, E. (1997). Consuming the romantic utopia: Love and the cultural contradictions of capitalism. London: The University of California Press.Lancy, D. F. (1983). Cross-cultural studies in cognition and mathematics. New York: Academic Press.Le Goff, J. (1956). Marchands et banquiers du moyen age. (7th updated edition, 1986). Paris: Presses Universitaires de France.Leont’ev, A. N. (1974). The problem of activity in psychology. Soviet Psychology, 13(2), 4-33.Leont’ev [or Leontyev], A. N. (2009). Activity and consciousness. Pacifica, CA: MIA. Retrieved August 29, 2009, from http://www.marxists.org/archive/leontev/works/activity-consciousness.pdf.Lévinas, E. (1982). Éthique et infini. Paris: Fayard.Lizcano, E. (2009). Imaginario colectivo y creación matemática. Madrid: Gedisa.Marx, K. (1988). Economic and philosophic manuscripts of 1844. Amherst, New York: Prometheus Books. (Original work published 1932).Marx, K. (2007). Manuscrits économico-philosophiques de 1844 [Manuscritos económico-filosóficos de 1844]. (F. Fischbach, Trans.). Paris: Vrin. (Original work published 1932)Owens, K. (2001). Indigenous mathematics: a rich diversity. Mathematics: Shaping Australia. Proceedings of the Eighteenth Biennial Conference of the Australian Association of Mathematics Teachers, 151–167. Retrieved Feburary 17, 2006, from: http://www.aamt.edu.au/ICSIMAN/resources/papers/owens.pdf.Pais, A. (2011). Mathematics education and the political: An ideology critique of an educational research field. Ph. D. Dissertation. Aalborg, Denmark: Department of Learning and Philosophy. Aalborg University.Piaget, J. (1973). To understand is to invent. The future of education. New York: Grossman.Popkewitz, T. (2004). The alchemy of the mathematics curriculum: Inscriptions and the fabrication of the child. American Educational Research Journal, 41(1), 3-34.Pumuge, H. M. (1975). The counting system of the pekai-alue tribe of the topopul village in the ialibu sub-district in the southern highlands district, papua new guinea. Science in New Guinea, 3(1), 19-25.Radford, L. (2006). Elementos de una teoría cultural de la objetivación [Elements of a cultural theory of objectification]. Revista Latinoamericana de Investigación en Matemática Educativa, Special Issue on Semiotics, Culture and Mathematical Thinking, 103-129 (available at: http://www.laurentian.ca/educ/lradford/).Radford, L. (2008). The ethics of being and knowing: Towards a cultural theory of learning. In L. Radford, G. Schubring, & F. Seeger (Eds.), Semiotics in mathematics education: Epistemology, history, classroom, and culture (pp. 215-234). Rotterdam: Sense Publishers.Radford, L. (2012). Education and the illusions of emancipation. Educational Studies in Mathematics, 80(1), 101-118.Radford, L. (2013). Sumisión, alienación y (un poco de) esperanza: hacia una visión cultural, histórica, ética y política de la enseñanza de las matemáticas. In A. Ramirez y Y. Morales (Eds). Memorias del I Congreso de Educación Matemática de América Central y El Caribe. Santo Domingo, República Dominicana, November 6-8, 2013 (disponible en la página: http://luisradford.ca)Radford, L. (2014). De la teoría de la objetivación [on the theory of objectification]. Revista Latinoamericana de Etnomatemática, 7(2), 132-150.Radford, L. (2015). Of love, frustration, and mathematics: A cultural-historical approach to emotions in mathematics teaching and learning. In B. Pepin & B. Roesken-Winter (Eds.), From beliefs to dynamic affect systems in mathematics education (pp. 25-49). New York: Springer.Radford, L. (2016). On alienation in the mathematics classroom. International Journal of Educational Research, 79, 258-266. http://dx.doi.org/10.1016/j. ijer.2016.04.001.Radford, L., & Roth, W. -M. (2011). Intercorporeality and ethical commitment: An activity perspective on classroom interaction. Educational Studies in Mathematics, 77(2-3), 227-245.Shweder, R., & LeVine, R. (1984). Culture theory. Essays on mind, self, and emotion. Cambridge: Cambridge University Press.Spinoza, B. (1989). Ethics including the improvement of the understanding. (R. Elwes, Trans.). Buffalo: Prometheus. (Original work published 1667)Taylor, C. (1989). Sources of the self. Cambridge, Ma: Harvard University Press.Thompson, P. (2014). Constructivism in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 96-100). New York: Springer.Todorov, T. (2000). Éloge de l›individu [Elogio del individuo]. Paris: Adam Biro.Valero, M. (2004). Postmodernism as an attitude of critique to dominant mathematics education research. In P. Walshaw (Ed.), Mathematics education within the postmodern (pp. 35-54). Greenwich, CT: Information Age Publishing.Valero, P. (2009). Mathematics education as a network of social practices. In Proceedings of the 6th conference of European research in mathematics education (CERME 6). Lyon, France, Jan. 28th - Feb. 1, 2009. (Retrieved on December 10 2010 from) http://www.inrp.fr/publications/edition-electronique/cerme6/ plenary2-valero.pdf).Vygotski, L. (1985). Pensée et langage. Paris: Messidor.Vygotsky, L. S. (1987). Collected works (Vol. 1). R. W. Rieber and A. S. Carton (Eds.). New York: Plenum.Vygotsky, L. S. (1999). Collected works (vol. 6). R. W. Rieber (Ed.). New York: Plenum.Bachelard, G. (1938). La formation de l’esprit scientifique. Paris: VRIN.Bagni, G. T. (2005). The historical roots of the limit notion: Cognitive development and development of representation registers. Canadian Journal of Science, Mathematics and Technology Education, 5(4), 453–468.Bagni, G. T. (2006). Some cognitive difficulties related to the representations of two major concepts of set theory. Educational Studies in Mathematics, 62(3), 259–280. Doi: 10.1007/s10649-006-8545-3Bagni, G. T., & D’Amore, B. (2005). Epistemologia, sociologia, semiotica: la prospettiva socio-culturale. La matematica e la sua didattica, 19(1), 73–89.Balacheff, N. (1988). Le contrat et la coutume: deux registres des interactions didactiques. En C. Laborde (Ed.), Actes du premier colloque franco-allemand de didactique des mathématiques et de l’informatique (pp. 15–26). Grenoble: La Pensée Sauvage.Barbin, E. (1994). Sur la conception des savoirs géométriques dans les Éléments de géométrie. Cahiers de didactique des Mathématiques, 14-15, 135–158. (http:// smf4.emath.fr/Publications/RevueHistoireMath/20/html/smf_rhm_20_253- 302.php)Bauersfeld, H. (1995). “Language game” in the mathematics classroom: Their function and their effects. En P. Cobb & H. Bauersfeld (Eds.), The emergence of meaning: Interaction in classroom cultures (pp. 271–292). Hillsdale NJ: Lawrence Erlbaum Associates.Bernhard, J. (1995). Child development, cultural diversity, and the professional training of early childhood educators. Canadian Journal of Education, 20(4), 415–436.Brickhouse, N. (1990). Teachers’ beliefs about the nature of science and their relationship to classroom practice. Journal of teacher education, 41(3), 53–62.Brousseau, G. (1976). Les obstacles épistémologiques et les problèmes en mathématiques. En W. Vanhamme & J. Vanhamme (Eds.), La problématique et l’enseignement des mathématiques, Actes de la XXVIIIème rencontre CIEAEM (pp. 101-117). Louvain la Neuve.Brousseau, G. (1983). Les obstacles épistémologiques et les problèmes in mathématiques. Reserches en Didactique des Mathématiques, 4(2), 165–198.Brousseau, G. (1989). Les obstacles épistémologiques et la didactique des mathématiques. En N. Bednarz & C. Garnier (Eds.), Constructions des savoirs, obstacles et conflits (pp. 41–64). Montreal: Agence d’Arc.Castoriadis, C. (1987). The imaginary institution of society. Cambridge, Mass.: The MIT Press.D’Amore, B. (2001a). Une contribution au débat sur les concepts et les objets mathématiques. Scientia Paedagogica Experimentalis, 38(1), 17–46.D’Amore, B. (2001b). Conceptualisation, registres de représentations sémiotiques et noétique: interactions constructivistes dans l’apprentissage des concepts mathématiques et hypothèse sur quelques facteurs inhibant la dévolution. Scientia Paedagogica Experimentalis, 38(2), 143–168.D’Amore, B. (2003a). Matemática em algumas culturas da America do Sul: Uma contribuição à Etnomatemática. Bolema. Boletim de Educação Matemática, 19, 73–89.D’Amore, B. (2003b). Le basi filosofiche, pedagogiche, epistemologiche e concettuali della Didattica della Matematica. Bologna: Pitagora.D’Amore, B. (2003c). The noetic in mathematics. Scientia Pedagogica Experimentalis, 39(1), 75–82.D’Amore, B. (2003d). La complexité de la noétique en mathématiques ou les raisons de la dévolution manquée. For the learning of mathematics, 23(1), 47–51.D’Amore, B. (2003e). La complejidad de la educación y de la construcción del saber. Suma, 43, 23–30.D’Amore, B. (2004). Il ruolo dell’epistemologia nella formazione degli insegnanti di matematica nella scuola secondaria. La matematica e la sua didattica, 18(4), 4–30.D’Amore, B. (2005a). Pratiche e metapratiche nell’attività matematica della classe intesa come società: Alcuni elementi rilevanti della didattica della matematica interpretati in chiave sociologica. La matematica e la sua didattica, 19(3), 325–336.D’Amore, B. (2005b). Secondary school students’ mathematical argumentation and Indian logic (nyaya). For the learning of mathematics, 25(2), 26–32.D’Amore, B., & Fandiño Pinilla, M. I. (2001). Matemática de la cotidianidad. Paradigma, 22(1), 59–72.D’Amore, B., & Fandiño Pinilla, M. I. (2004). Cambi di convinzione in insegnanti di matematica di scuola secondaria superiore in formazione iniziale. La matematica e la sua didattica, 18(3), 27–50.D’Amore, B., & Fandiño Pinilla, M. I. (2005). Storia ed epistemologia della matematica basi etiche. La matematica e la sua didattica, 19(4), 503–515.D’Amore, B., & Godino, J. D. (2006). Punti di vista antropologico ed ontosemiotico in Didattica della Matematica. La matematica e la sua didattica, 20(1), 9–38.D’Amore, B., & Sbaragli, S. (2005). Analisi semantica e didattica dell’idea di “misconcezione”. La matematica e la sua didattica, 19(2), 139–163.D’Amore, B., & Speranza, F. (Eds.) (1989). Lo sviluppo storico della matematica: Spunti didattici (Vol. 1). Roma: Armando.D’Amore, B., & Speranza, F. (Eds.) (1992). Lo sviluppo storico della matematica: Spunti didattici (Vol. 2). Roma: Armando.D’Amore, B., & Speranza, F. (Eds.) (1995). La matematica e la sua storia: Alcuni esempi per spunti didattici. Milano: Angeli.de Haan, M. (1999). Learning as a cultural practice. Amsterdam: Thela Thelis.Eco, U. (1975). Trattato di semiotica generale. Milano: Bompiani.Enriques, F. (1942). L’errore nelle matematiche. Periodico di matematiche, serie IV, 22, 57-65. [Bajo el pseudonimo A. Giovannini].Fauvel, J., & Maanen, J. (2000). History in mathematics education: The ICMI study. Dordrecht - Boston, London: Kluwer.Feyerabend, P. K. (2003). Contro il metodo. Milano: Feltrinelli. (Trabajo original publicado 1975).Furinghetti, F., & Radford, L. (2002). Historical conceptual developments and the teaching of mathematics: From philogenesis and ontogenesis theory to classroom practice. En L. English (Ed.), Handbook of International Research in Mathematics Education (pp. 631–654). Hillsdale: Erlbaum.Gadamer, H.-G. (1975). Truth and method (2nd ed., 1989). New York: Crossroad.Godino, J. D. (2002). Un enfoque ontológico y semiótico de la cognición matemática. Recherches en Didactique des Mathématiques, 22(2-3), 237–284.Godino, J. D., & Batanero, C. (1994). Significado institucional y personal de los objetos matemáticos. Recherches en didactiques des mathématiques, 14(3), 325–355.Godino, J. D., & Llinares, S. (2000). El interaccionismo simbólico en educación matemática. Educación Matemática, 12(1), 70–92. Grugnetti, L., & Rogers, L. (2000). Philosophical, multicultural and interdisciplinary issues. En J. Fauvel & J. van Maanen (Eds.), History in Mathematics Education (pp. 39–62). Dodrecht: Kluwer.Habermas, J. (2003). Truth and justification (trad. B. Fultner). Cambridge, MA: The MIT Press. (Trabajo original publicado 1999).Hardesty, D. (1977). Ecological anthropology. New York: Wiley.Hashweb, M. Z. (1996). Effects of science teachers’ epistemological beliefs in teaching. Journal of Research in Science Teaching, 33(1), 47–63.Ilyenkov, E. (1977). The concept of the ideal. Philosophy in the USSR: Problems of dialectical materialism. Moscow: Progress Publishers.Leontiev, A. A. (1981a). Sign and activity. En J. V. Wertsch (Ed.), The concept of activity in Soviet psychology (pp. 241–255). New York: Sharpe.Leontiev, A. A. (1981b). The problem of activity in psychology. En J. V. Wertsch (Ed.), The concept of activity in Soviet psychology (pp. 37–71). New York: Sharpe.McClain, K., & Cobb P. (1997). An analysis of the teacher’s role in guiding the evolution of sociomathematical norms. En E. Pekhonen (Ed.), Proceedings of the 21st PME International Conference (Vol. 3, pp. 224–231). Lahti: University of Helsinki.Newton, M. (2002). Savage girls and wild boys: A history of feral children. London: Faber & Faber.Piaget, J., & Garcia, R. (1983). Psychogenèse et histoire des sciences. Paris: Flammarion.Perrin-Glorian, M.-J. (1994). Théorie des situations didactiques: naissance, développement, perspectives. En M. Artigue, R. Gras, C. Laborde, & P. Tavignot (Eds.), Vingt ans de didactique des mathématiques en France: Hommage à Guy Brousseau et Gérard Vergnaud (pp. 97–147). Grenoble: La Pensée Sauvage.Radford, L. (1997). On psychology, historical epistemology and the teaching of mathematics: Towards a socio-cultural history of mathematics. For the Learning of Mathematics, 17(1), 26–33.Radford, L. (2003a). On the epistemological limits of language: Mathematical knowledge and social practice in the Renaissance. Educational Studies in Mathematics, 52(2), 123–150. doi: 10.1023/A:1024029808871Radford, L. (2003b). On culture and mind: A post-Vygotskian semiotic perspective, with an example from Greek mathematical thought. En M. Anderson, A. SáenzLudlow, S. Zellweger, & V. Cifarelli (Eds.), Educational Perspectives on Mathematics as Semiosis: From Thinking to Interpreting to Knowing (pp. 49–79). Ottawa: Legas Publishing.Radford, L. (2004b). Syntax and meaning. En M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28 Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 161–166). Norway: Bergen University College.Radford, L. (2006a). The anthropology of meaning. Educational Studies in Mathematics, 61(1-2), 9–65. doi: 10.1007/s10649-006-7136-7Radford, L. (2006b). The cultural-epistemological conditions of the emergence of algebraic symbolism. En S. Kaijser, C. Tzanakis, & F. Furringhetti (Eds.), Proceedings of the 2004 History and Pedagogy of Mathematics Conference & ESU4 (pp. 509-524). Uppsala, Sweden. Recuperado de: http://laurentian.ca/ educ/lradford/PUBLIC.HTMLRadford, L. (2006c). Semiótica cultural y cognición. En R. Cantoral Uriza, O. Covián Chávez, R. M. Farfán, J. Lezama Andalón, & A. Romo Vázquez (Eds.), Investigaciones sobre enseñanza y aprendizaje de las matemáticas. Un reporte iberoamericano (pp. 669–689). Mexico: Diaz de Santos.Radford, L., Boero, P., & Vasco, C. (2000). Epistemological assumptions framing interpretations of students understanding of mathematics. En J. Fauvel & J. van Maanen (Eds.), History in Mathematics Education (pp. 162–167). Dordrecht: Kluwer.Robertson, I. (1977). Sociobiology. New York: Worth Publishers Inc.Romberg, T. (1988). Necessary ingredients for a theory of mathematics education. En H. G. Steiner & A. Vermandel (Eds.), Foundations and methodology of the discipline Mathematics Education. Proceedings of the 2nd TME (pp. 97–112). Bielefeld, Antwerpen: IDM Publications.Sfard, A., & Prusak, A. (2005). Identity that makes a difference: Substantial learning as closing the gap between actual and designated identities. En H. L. Chick & J. L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 37–52). Melbourne: PME.Sierpinska, A., & Lerman, S. (1996). Epistemologies of mathematics and of mathematics education. En A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 827– 876). Dordrecht: Kluwer Academic Publishers.Wartofsky, M. (1979). Models, representation and the scientific understanding. Dordrecht: Reidel.Werner, H. (1948). Comparative psychology of mental development. New York: International University Press.Wittgenstein, L. (1956), Bemerkungen über die Grundlagen der Mathematik. Oxford: Blackwell.D’Amore, B., Radford, L. & Bagni, GT. (2007). Obstáculos epistemológicos y perspectiva socio-cultural de la matemática. Coleción “Cuadernos del Seminario en educación”. Bogotá: Universidad Nacional de Colombia.Attribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Abierto (Texto Completo)http://purl.org/coar/access_right/c_abf2MatemáticasConocimientoDidáctica de la matemáticaConstructivismoSemióticaObjetivaciónSubjetividadNoéticaMatemáticas -- EnseñanzaMatemáticas -- Problemas, ejercicios, etc.Semiología (Linguistica)MathematicsKnowledgeMathematics teachingConstructivismSemioticsNoeticObjectificationSubjectivityEnseñanza y aprendizaje de las matemáticas: problemas semióticos, epistemológicos y prácticosProblemas semióticos, epistemológicos y prácticosTeaching and learning mathematics: semiotic, epistemological and practical problemsbookinfo:eu-repo/semantics/bookhttp://purl.org/coar/resource_type/c_2f33ORIGINALensenanza_y_aprendizaje_de_las_matematicas_problemas_semioticos_epistemologicos_y_practicos.pdfensenanza_y_aprendizaje_de_las_matematicas_problemas_semioticos_epistemologicos_y_practicos.pdfEnseñanza y aprendizaje de las matemáticas: problemas semióticos, epistemológicos y prácticosapplication/pdf1845145https://repository.udistrital.edu.co/bitstreams/479d3bc7-3981-48b7-ad6c-ac80b92bd08f/downloadbed37e1a3f770906da6ed8caac817322MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805https://repository.udistrital.edu.co/bitstreams/29df67e2-e222-469b-ae5d-3384cfccc76c/download4460e5956bc1d1639be9ae6146a50347MD52LICENSElicense.txtlicense.txttext/plain; charset=utf-87167https://repository.udistrital.edu.co/bitstreams/913065ce-2317-4821-8468-e38c717cd8ed/download997daf6c648c962d566d7b082dac908dMD53THUMBNAILensenanza_y_aprendizaje_de_las_matematicas_problemas_semioticos_epistemologicos_y_practicos.pdf.jpgensenanza_y_aprendizaje_de_las_matematicas_problemas_semioticos_epistemologicos_y_practicos.pdf.jpgIM Thumbnailimage/jpeg13047https://repository.udistrital.edu.co/bitstreams/d0d921a6-8ab8-4647-a9d0-6248e23062ce/download4ecf11cc745efe62645e900e748da97eMD5411349/37879oai:repository.udistrital.edu.co:11349/378792024-11-28 14:18:24.007http://creativecommons.org/licenses/by-nc-nd/4.0/Attribution-NonCommercial-NoDerivatives 4.0 Internacionalopen.accesshttps://repository.udistrital.edu.coRepositorio Universidad Distritalrepositorio@udistrital.edu.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

Publicaciones similares