Abstract
Cultural-historical activity theory—with historical roots in dialectical materialism and the social psychology to which it has given rise—has experienced exponential growth in its acceptance by scholars interested in understanding knowing and learning writ large. In education, this theory has constituted something like a well kept secret that is only in the process of gaining larger levels of acceptance. Mathematics educators are only beginning to realise the tremendous advantages that the theory provides over other theories. In this review essay, I articulate the theory as it may relate to the issues that concern mathematics education and educators with a particular focus on the way in which it addresses logical contradictions in existing theories.
Similar content being viewed by others
References
Bakhtin, M. (1981). The dialogic imagination. Austin: University of Texas Press.
Bakhtine, M. [Volochinov, V. N.] (1977). Le marxisme et la philosophie du langage: essai d’application de la méthode sociologique en linguistique [Marxism and the philosophy of language: Essay on the application of sociological method in linguistics] Paris, France: Les Éditions de Minuit.
Beswick, K., Watson, A., & de Geest, E. (2010). Comparing theoretical perspectives in describing mathematics departments: complexity and activity. Educational Studies in Mathematics, 75, 153–170.
Black, L., Williams, J., Hernandez-Martinez, P., Davis, P., Pampaka, M., & Wake, G. (2010). Developing a “leading identity”: the relationship between students’ mathematical identities and their career and higher education aspirations. Educational Studies in Mathematics, 73, 55–72.
Brown, T. (2011). Mathematics education and subjectivity: Cultures and cultural renewal. Dordrecht: Springer.
Carlsen, M. (2009). Reasoning with paper and pencil: the role of inscriptions in student learning of geometric series. Mathematics Education Research Journal, 21, 54–84.
Carlsen, M. (2010). Appropriating geometric series as a cultural tool: a study of student collaborative learning. Educational Studies in Mathematics, 74, 95–116.
Cobb, P. (1999). Individual and collective mathematical development: the case of statistical data analysis. Mathematical Thinking and Learning, 1, 5–43.
Cobb, P., Yackel, E., & Wood, T. (1992). A constructivist alternative to the representational view of mind in mathematics education. Journal for Research in Mathematics Education, 23, 2–33.
Corno, L., Cronbach, L. J., Kupermintz, H., Lohman, D. F., Mandinach, E. B., Porteus, A. W., et al. (2002). Remaking the concept of aptitude: Extending the legacy of Richard E. Snow. Mahwah: Lawrence Erlbaum Associates.
David, M. M., & Tomaz, V. S. (2011). The role of visual representations for structuring classroom mathematical activity. Educational Studies in Mathematics. doi:10.1007/s10649-011-9358-6.
Derrida, J. (1990). Le problème de la genèse dans la philosophie de Husserl. [The problem of genesis in the philosophy of Husserl]. Paris: Presses Universitaires de France.
Eckert, P. (1989). Jocks and burnouts: Social categories and identity in the high school. New York: Teachers College Press.
Falcade, R., Laborde, C., & Marlotti, M. A. (2007). Approaching functions: Cabri tools as instruments of semiotic mediation. Educational Studies in Mathematics, 66, 317–333.
Fried, M. N. (2011). Signs for you and signs for me: the double aspect of semiotic perspectives. Educational Studies in Mathematics, 77, 389–397.
Holzkamp, K. (1993). Lernen: Subjektwissenschaftliche Grundlegung [Learning: A subject-scientific grounding]. Frankfurt: Campus.
Husserl, E. (1939). Die Frage nach dem Ursprung der Geometrie als intentional-historisches Problem [The question of the origin of geometry as intentional-historical problem]. Revue Internationale de Philosophie, 1, 203–225.
Il’enkov, E. (1982). Dialectics of the abstract and the concrete in Marx’s Capital. Moscow: Progress.
Jurdak, M. E. (2006). Contrasting perspectives and performance of high school students on problem solving in real world situated, and school contexts. Educational Studies in Mathematics, 63, 283–301.
Lagrange, J.-B., & Erdogan, E. O. (2009). Teachers’ emergent goals in spreadsheet-based lessons: analyzing the complexity of technology integration. Educational Studies in Mathematics, 71, 65–84.
Lave, J. (1988). Cognition in practice: Mind, mathematics and culture in everyday life. Cambridge: Cambridge University Press.
Lave, J. (1993). The practice of learning. In S. Chaiklin & J. Lave (Eds.), Understanding practice: Perspectives on activity and context (pp. 3–32). Cambridge: Cambridge University Press.
Leontjew, A. N. (1982). Tätigkeit, Bewusstsein, Persönlichkeit [Activity, consciousness, personality]. Köln: Pahl-Rugenstein.
Leontyev, A. N. (1981). Problems of the development of the mind. Moscow: Progress.
Livingston, E. (1986). The ethnomethodological foundations of mathematics. London: Routledge and Kegan Paul.
Luria, A. (1973). The working brain. New York: Basic Books.
Martin, D. B. (2007). Beyond missionaries or cannibals: why should teach mathematics to African American children? The High School Journal, 91(1), 6–28.
Marx, K., & Engels, F. (1962). Werke Band 23: Das Kapital [Works vol. 23: Capital]. Berlin, Germany: Dietz.
McDermott, R. P. (1993). The acquisition of a child by a learning disability. In S. Chaiklin & J. Lave (Eds.), Understanding practice: Perspectives on activity and context (pp. 269–305). Cambridge: Cambridge University Press.
Meira, L., & Lerman, S. (2001). The zone of proximal development as a symbolic space. London: South Bank University.
Merz, M., & Knorr-Cetina, K. (1997). Deconstruction in a “thinking” science: theoretical physicists at work. Social Studies of Science, 27, 73–111.
Mikhailov, F. T. (2001). The “other within” for the psychologist. Journal of Russian and East European Psychology, 39, 6–31.
Nancy, J.-L. (1993). Éloge de la mêlée. Transeuropéenne, 1, 8–18.
Nancy, J.-L. (1996). Être singulier pluriel [Being singular plural]. Paris: Galilée.
Núñez, R., Edwards, L., & Matos, J. F. (1999). Embodied cognition as grounding for situatedness and context in mathematics education. Educational Studies in Mathematics, 39, 45–65.
Nyamekye, F. (2010). Embracing mathematics identity in an African-centered school: Construction and interaction of racial and mathematical student identities. Dissertation, University of Maryland. Accessed October 27, 2010 at http://drum.lib.umd.edu/bitstream/1903/10939/1/Nyamekye_umd_0117E_11602.pdf.
Ozmantar, M. F., & Monaghan, J. (2007). A dialectical approach to the formation of mathematical abstractions. Mathematics Education Research Journal, 19, 89–112.
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.
Radford, L. (2011a). Classroom interaction: why is it good, really? Educational Studies in Mathematics, 76, 101–115.
Radford, L. (2011b). Vers une théorie socioculturelle de l’enseignement—apprentissage: la théorie de l’objectivation. Éléments, 1, 1–27.
Radford, L., & Puig, L. (2007). Syntax and meaning as sensuous, visual, historical forms of algebraic thinking. Educational Studies in Mathematics, 66, 145–164.
Radford, L., & Roth, W.-M. (2011). Beyond Kantian individualism: an activity perspective on classroom interaction. Educational Studies in Mathematics, 77, 227–245.
Radford, L., Schubring, G., & Seeger, F. (2011). Signifying and meaning-making in mathematical thinking, teaching, and learning. Educational Studies in Mathematics, 77, 149–156.
Rancière, J. (1999). Dis-agreement: Politics and philosophy. Minneapolis: University of Minnesota Press.
Roth, W.-M. (2004). Activity theory in education: an introduction. Mind, Culture, & Activity, 11, 1–8.
Roth, W.-M. (2005). Mathematical inscriptions and the reflexive elaboration of understanding: an ethnography of graphing and numeracy in a fish hatchery. Mathematical Thinking and Learning, 7, 75–109.
Roth, W.-M. (2007). Emotion at work: a contribution to third-generation cultural historical activity theory. Mind, Culture and Activity, 14, 40–63.
Roth, W.-M. (2008). Where are the cultural-historical critiques of “back to the basics”? Mind, culture, and activity, 15, 269–278.
Roth, W.-M. (2009). Learning in schools: A cultural-historical activity theoretic perspective. In B. Schwarz, T. Dreyfus, & R. Hershkovitz (Eds.), The guided construction of knowledge in classrooms (pp. 281–301). London: Routledge.
Roth, W.-M. (2011). Rules of bending, bending rules: the geometry of conduit bending in college and workplace. Educational Studies in Mathematics.
Roth, W.-M., & Barton, A. C. (2004). Rethinking scientific literacy. New York: Routledge.
Roth, W.-M., & Hwang, S.-W. (2006). Does mathematical learning occur in going from concrete to abstract or in going from abstract to concrete? The Journal of Mathematical Behavior, 25, 334–344.
Roth, W.-M., & Lee, Y. J. (2007). “Vygotsky’s neglected legacy”: cultural-historical activity theory. Review of Educational Research, 77, 186–232.
Roth, W.-M., & Radford, L. (2010). Re/thinking the zone of proximal development (symmetrically). Mind, culture, and activity, 17, 299–307.
Roth, W.-M., & Radford, L. (2011). A cultural-historical perspective on mathematics teaching and learning. Rotterdam: Sense Publishers.
Roth, W.-M., Lee, Y. J., & Boyer, L. (2008). The eternal return: Reproduction and change in complex activity systems. The case of salmon enhancement. Berlin: Lehmanns Media.
Saxe, G. B. (1991). Culture and cognitive development: Studies in mathematical understanding. Hillsdale: Lawrence Erlbaum Associates.
Seeger, F. (2011). On making meaning in mathematics education: social, emotional, semiotic. Educational Studies in Mathematics, 77, 207–226.
Triantafillou, C., & Potari, D. (2010). Mathematical practices in a technological workplace: the role of tools. Educational Studies in Mathematics, 74, 275–294.
Valero, P., & Stentoft, D. (2010). The “post” move of critical mathematics education. In A. O. Ravn & P. Valero (Eds.), Critical mathematics education: Past, present, future (pp. 183–195). Rotterdam: Sense.
von Glasersfeld, E. (1987). Learning as a constructive activity. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 3–17). Hillsdale: Lawrence Erlbaum Associates.
Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge: Harvard University Press.
Vygotsky, L. S. (1997). The historical meaning of the crisis in psychology: A methodological investigation. In W. R. Rieber & J. Wollock (Eds.), The collected work of L. S. Vygotsky vol. 6 (pp. 233–343). New York: Kluwer Academic Publishers. First published in 1927.
Vygotskij, L. S. (2002). Denken und Sprechen [Thought and language]. Weinheim: Beltz Verlag.
Vygotskij, L. S. (2005). ПCИXOЛOГИЯ PAЗBИTИЯ ЧEЛOBEКA [Psychology of human development]. Moscow: Eksmo.
Walkerdine, V. (1988). The mastery of reason. London: Routledge.
Williams, J., & Wake, G. (2007). Black boxes in workplace mathematics. Educational Studies in Mathematics, 64, 317–343.
Williams, J., Davis, P., & Black, L. (2007). Subjectivities in school: socio-cultural and activity theory perspectives. International Journal of Educational Research, 46, 1–7.
Willis, P. (1977). Learning to labor: How working class lads get working class jobs. New York: Columbia University Press.
Wittgenstein, L. (1997). Philosophische Untersuchungen / Philosophical investigations (2nd ed.). Oxford: Blackwell (First published in 1953).
Zevenbergen, R., & Lerman, S. (2008). Learning environments using interactive whiteboards: new learning spaces or reproduction of old technologies. Mathematics Education Research Journal, 20, 108–126.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Roth, WM. Cultural-historical activity theory: Vygotsky’s forgotten and suppressed legacy and its implication for mathematics education. Math Ed Res J 24, 87–104 (2012). https://doi.org/10.1007/s13394-011-0032-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13394-011-0032-1