Methodological Aspects of the Theory of Objectification

  • Luis Radford Université Laurentienne, Canada
Palavras-chave: Theory of objectification, Methodology, Consciousness, Semiotics, Activity.


In this article, I focus on the methodology of a specific theory of teaching and learning: the theory of objectification. Inspired by dialectical materialism and Vygotsky’s psychology, the theory of objectification posits the goal of Mathematics Education as a dynamic political, societal, historical, and cultural endeavour aimed at the dialectical creation of reflexive and ethical subjects who critically position themselves in historically and culturally constituted and always evolving mathematical discourses and practices. In the first part, I briefly sketch the general lines of the theory. In the second part, emphasizing the semiotic and embodied nature of teaching and learning, I discuss the methodology of the theory, stressing in particular its task design, data collection, and data analysis components.


ARISTOTLE. (2015). Posterior analytics. Translated by G. R. G. Mure. Retrieved June 15 2015 from: . (Original work published around 350 B.C.)

ARTIGUE, M. Ingénierie didactique [Didactical engineering]. Recherches en Didactique des Mathématiques, v.9, n.3, p.281-308, 1988.

ARTIGUE, M. Didactical design in mathematics education. In: Winsløw, C. (Ed.). Nordic research in mathematics education. Proceedings of NORMA08. Rotterdam: Sense Publishers, 2009. p.7-16.

BACON, F. Francis Bacon's essays. London: Dent, 1906.

BROUSSEAU, G. Theory of didactical situations in mathematics. Dordrecht: Kluwer, 1997.

COBB, P. The tension between theories of learning and instruction in mathematics education. Educational Psychologist, v.23, n.2, p.87-103, 1988.

COULTHARD, M. An introduction to discourse analysis. London: Longman, 1977.

FAIRCLOUGH, N. Critical discourse analysis. London New York: Longman, 1995.

HARPER, D. Online Etymology Dictionary. 2013. Available at: <>. Accessed on: June 1 2013.

HEGEL, G. W. F. Hegel's phenomenology of spirit. Oxford: Oxford University Press, 1977. First edition, 1807.

HENRY, M. Marx. Paris: Gallimard, 1976.

ILYENKOV, E. Dialectics of the ideal. Historical Materialism, v.20, n.2, p.149-193, 2012.

LEONT’EV (OR LEONTYEV), A. N. Activity and consciousness. Pacifica, CA: MIA, 2009. Available on: <>. Accessed on: Aug. 29, 2009.

MARX, K. Manuscrits économico-philosophiques de 1844 [Economic and philosophic manuscripts of 1844]. Translated by F. Fischbach. Paris: Vrin, 2007. (Original work published 1932)

MOERMAN, M. Talking culture, ethnography and conversational analysis. Philadelphia: University of Pennsylvania Press, 1988.

POOVEY, M. A history of the modern fact: Problems of knowledge in the sciences of wealth and society. Chicago: University of Chicago Press, 1998.

RADFORD, L. The seen, the spoken and the written. A semiotic approach to the problem of objectification of mathematical knowledge. For the Learning of Mathematics, vol.22, no.2, 1p.4-23, 2002.

RADFORD, L. Connecting theories in mathematics education: Challenges and possibilities. ZDM - the International Journal on Mathematics Education, v.40, no.2, p.317-327, 2008a.

RADFORD, L. The ethics of being and knowing: Towards a cultural theory of learning. In: RADFORD, L.; SCHUBRING, G.; SEEGER, F. (Eds.). Semiotics in mathematics education: Epistemology, history, classroom, and culture. Rotterdam: Sense Publishers, 2008b. p.215-234.

RADFORD, L. The eye as a theoretician: Seeing structures in generalizing activities. For the Learning of Mathematics, v.30, n.2, p.2-7, 2010.

RADFORD, L. Cognição matemática: História, antropologia e epistemologia [mathematical cognition: History, anthropology, and epistemology]. São Paulo: Editora Livraria da Física, 2012a.

RADFORD, L. Education and the illusions of emancipation. Educational Studies in Mathematics, v.80, n.1, p.101-118, 2012b.

RADFORD, L. De la teoría de la objetivación [on the theory of objectification]. Revista Latinoamericana de Etnomatemática, v.7, n.2, p.132-150, 2014a.

RADFORD, L. On teachers and students: An ethical cultural-historical perspective. In: LILJEDAHL, P.; NICOL, C.; OESTERLE, S.; ALLAN, D. (Eds.). Proceedings of the joint meeting of PME 38 and PME-NA 36, v.1, p. 1-20, 2014b.

RADFORD, L. Towards an embodied, cultural, and material conception of mathematics cognition. ZDM - the International Journal on Mathematics Education, v.46, p.349-361, 2014c.

RADFORD, L. The progressive development of early embodied algebraic thinking. Mathematics Education Research Journal, v.26, p.257-277, 2014d.

RADFORD, L. (forthcoming). On alienation in the mathematics classroom. Sudbury: Laurentian University Faculty of Education Pre-prints.

RADFORD, L.; BARDINI, C.; SABENA, C. Perceiving the general: The multisemiotic dimension of students’ algebraic activity. Journal for Research in Mathematics Education, v.38, p.507-530, 2007.

RADFORD, L.; DEMERS, S. Communication et apprentissage. Repères conceptuels et pratiques pour la salle de classe de mathématiques [communication and learning. Conceptual and practical references for the mathematics classroom]. Ottawa: Centre franco-ontarien des ressources pédagogiques, 2004.

RADFORD, L.; DEMERS, I.; MIRANDA, S. Processus d'abstraction en mathématiques [Processes of abstraction in mathematics]. Ottawa: Centre franco-ontarien de ressources pédagogiques, Imprimeur de la Reine pour l'Ontario, 2009.

RADFORD, L.; SABENA, C. The question of method in a vygotskian semiotic approach. In: BIKNER-AHSBAHS, A.; KNIPPING, C.; PRESMEG, N. (Eds.). Approaches to qualitative research in mathematics education. New York: Springer, 2015. p.157-182.

VOLOSHINOV, V. N. Marxism and the philosophy of laguage. New York: Seminar Press, 1973.

VYGOTSKY, L. Consciousness as a problem in the psychology of behavior. Soviet Psychology, v.17, n.4, p.3-35, 1979.

VYGOTSKY, L. Collected works. Vol. 3. Problems of the theory and history of psychology. New York: Plenum, 1997.

Como Citar
RADFORD, L. Methodological Aspects of the Theory of Objectification. Perspectivas da Educação Matemática, v. 8, n. 18, 18 dez. 2015.