Is mathematical knowledge constructed? A cultural-historical critique of object oriented conceptions of learning activity
Palabras clave:
Activity Theory, Contradiction, Learning Paradox, Leading Activity, Mediation, Zone of Proximal Development, ProlepsisResumen
It has become a truism (ideology) to state that mathematical knowledge is constructed collectively, in communities of practice, and individually, on the part of students whileengaging in mathematical tasks. However, construction implies an image of the end result of the labor process, which allows people to build a house and compare each step to the plan. Students, on the other hand, do not know the end product of their learning process, the new knowledge. This knowledge, therefore, cannot be the transitive object towards which construction is oriented. In this study, I provide a cultural-historical critique of objectoriented notions of learning activity. Using classroom episodes as examples, I propose an alternative based on L. S. Vygotsky’s commitment to the primacy of the social, whereby any higher psychological function was a social relation first. This allows the final product to be available in the present, as relation, without the learner’s conscious awareness, and thereby determine learning and development. The idea of the future acting in the present is captured in M. Cole’s notion of prolepsis. Implications are discussed with respect to curriculum design in mathematics classrooms.
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Bakhtin, M. M. (1984). Problems of Dostoevsky’s poetics. Austin, TX: University of Texas Press.
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.
Chassapis, D. (1998). The mediation of tools in the development of formal mathematical concepts: he compass and the circle as an example. Educational Studies in Mathematics, 37, 275–293.
Cole, M. (1996). Cultural psychology: A once and future discipline. Cambridge, MA: Harvard University Press.
Cole, M., & Engeström, Y. (1993). A cultural historical approach to distributed cognition. In G. Salomon (Ed.), Distributed cognitions: Psychological and educational considerations (pp. 1–46). Cambridge: Cambridge University Press.
Goos, M., Galbraith, P., & Renshaw, P. (2002). Socially mediated metacognition: Creating collaborative zones of proximal development in small group problem solving. Educational Studies in Mathematics, 49, 193–223.
Grossen, M., & Perret-Clermont, A.-N. (1994). Psychosocial perspective on cognitive development: Construction of adult-child intersubjectivity in logic tasks. In W. de Graaf & R. Maier (Eds.), Sociogenesis reexamined (pp. 243–260). New York, NY: Springer.
Holzkamp, K. (1983). Grundlegung der Psychologie [The founding of psychology]. Frankfurt/M, Germany: Campus.
Holzkamp, K. (1993): Lernen: Subjektwissenschaftliche Grundlegung [Learning: Foundation in a science of the subject]. Frankfurt/M, Germany: Campus.
Hussain, M. A., Monaghan, J., & Threlfall, J. (2013). Teacher-student development in mathematics classrooms: Interrelated zones of free movement and promoted actions. Educational Studies in Mathematics, 82, 285–302.
Husserl, E. (1973). Husserliana Band I. Cartesianische Meditationen und Pariser Vorträge [Husserliana vol. I. Cartesian meditations and Paris lectures]. The Hague, Netherlands: Martinus Nijhoff.
Il’enkov, E. V. (1977). Dialectical logic: Essays on its history and theory. Moscow, USSR: Progress.
Jaworski, B., & Potari, D. (2009). Bridging the macro- and micro-divide: Using an activity theory model to capture sociocultural complexity in mathematics teaching and its development. Educational Studies in Mathematics, 72, 219–236.
Kieran, C. (2002). The mathematical discourse of 13-year-old partnered problem solving and its relation to the mathematics that emerges. Educational Studies in Mathematics, 46, 187–228.
Leont’ev, A. N. (1982). Tätigkeit, Bewusstsein, Persönlichkeit [Activity, consciounsness, personality]. Cologne, Germany: Pahl-Rugenstein.
Mariotti, M. A. (2000). Introduction to proof: The mediation of a dynamic software environment. Educational Studies in Mathematics, 44, 25–53.
Marx, K., & Engels, F. (1962). Werke Band 23 [Works vol. 23]. Berlin, Germany: Dietz.
Marx, K., & Engels, F. (1978). Werke Band 3 [Works vol. 3]. Berlin, Germany: Dietz.
Mikhailov, F. T. (2001). The “other within†for the psychologist. Journal of Russian and East European Psychology, 39(1), 6–31.
Mikhailov, F. T. (2004). Object-oriented activity—Whose?. Journal of Russian and East European Psychology, 42(3), 6–34.
Rorty, R. (1989). Contingency, irony, and solidarity. Cambridge, UK: Cambridge University Press.
Roth, W.-M. (2011). Passibility: At the limits of the constructivist metaphor. Dordrecht, The Netherlands: Springer.
Roth, W.-M. (2012). Mathematical learning, the unseen and the unforeseen. For the Learning of Mathematics, 32 (3), 15–21.
Roth, W.-M. (2016). Concrete human psychology. New York, NY: Routledge.
Roth, W.-M., & Lee, Y. J. (2007). “Vygotsky’s neglected legacyâ€: 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, The Netherlands: Sense Publishers.
Roth, W.-M., & Walshaw, M. A. (2015). Rethinking affect in education from a societal historical perspective: The case of mathematics anxiety. Mind, Culture and Activity, 22, 217–232.
Sheets-Johnstone, M. (2009). The corporeal turn: An interdisciplinary reader. Exeter, UK: Imprint Academic.
Van Oers, B. (2001). Educational forms of initiation in mathematical culture. Educational Studies in Mathematics, 46, 59–85.
VoloÅ¡inov, V. N. (1930). Marksizm i folosofija jazyka: osnovye problemy sociologiÄeskogo metoda b nauke o jazyke [Marxism and the philosophy of language: Main problems of the sociological method in linguistics]. Leningrad, USSR: Priboj.
Vygotskij, L. S. (2001). Lekcii po pedologii [Lectures on pedology]. Izhevsk, Russia: Udmurdskij University.
Vygotsky, L. S. (1978). Mind in society. Cambridge, MA: Harvard University Press.
Vygotsky, L. S. (1987). The collected works of L. S. Vygotsky, vol. 1: Problems of general psychology. New York, NY: Springer.
Vygotsky, L. S. (1989). Concrete human psychology. Soviet Psychology, 27(2), 53–77.
Vygotsky, L. S. (1997a). The collected works of L. S. Vygotsky vol. 3: Problems of the theory and history of psychology (R. W. Rieber & J. Wollock, Eds.). New York, NY: Plenum.
Vygotsky, L. S. (1997b). The collected works of L. S. Vygotsky, vol. 4: The history of the development of higher mental functions. New York, NY: Springer.
Vygotsky, L. S. (1998). The collected works of L. S. Vygotsky vol. 5: Child psychology. New York, NY: Kluwer Academic/Plenum Publishers.
Zavershneva, E. Iu. (2010a). The Vygotsky family archive (1912–1934): New findings. Journal of Russian and East European Psychology, 48(1), 14–33.
Zavershneva, E. Iu. (2010b). The Vygotsky family archive: New findings. Journal of Russian and East European Psychology, 48(1), 34–60.
Zavershneva, E. Iu. (2010c). The way to freedom. Journal of Russian and East European Psychology, 48(1), 61–90.
Yasnitsky, A., & van der Veer, R. (2016). Revisionist revolution in Vygotsky studies: The state of the Art. East Sussex, UK: Routledge.
Zolkower, B., & Shreyar, S. (2007). A teacher’s mediation of a thinking-aloud discussion in a 6th grade mathematics classroom. Educational Studies in Mathematics, 65, 177–202.
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