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When the Rules of Discourse Change, but Nobody Tells You: Making Sense of Mathematics Learning From a Commognitive Standpoint

By Anna Sfard

Abstract

In this article we introduce a research framework grounded in the assumption that thinking is a form of communication and that learning a school subject such as mathematics is modifying and extending one’s discourse. This framework is then applied in the study devoted to the learning of negative numbers. The analysis of data is guided by questions about (a) the discourse on negative numbers as such, and the features that set it apart from the mathematical discourse with which the students have been familiar when the learning began; (b) students’ and teacher’s efforts toward the necessary transition to the new meta-discursive rules, and (c) effects of the learning teaching process, that is, the extent of discursive change resulting from these efforts. Our findings lead to the conclusion that discursive change, rather than being necessitated by an extradiscursive reality, is spurred by communicational conflict, that is, by the situation that arises whenever different interlocutors seem to be acting according to differing discursive rules. Another conclusion is that school learning requires an active lead of an experienced interlocutor and is fuelled by a realistic communicational agreement between her and the learners

Year: 2007
OAI identifier: oai:eprints.ioe.ac.uk.oai2:4310

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Citations

  1. (2001). Adding it up: Helping children learn mathematics. Washington D.C.:
  2. (1994). Capturing and modeling the process of conceptual change. doi
  3. (1988). Cognition in practice. Cambridge:
  4. (2000). Council of Teachers of Mathematics
  5. (1997). Discourse and cognition.
  6. (1992). Discursive psychology.
  7. (2004). Doing wrong with words; What bars students’ access to arithmetical discourse.
  8. (1996). Intersubjectivity in mathematics learning: A challenge to the radical constructivist paradigm?
  9. (1992). Learning and teaching with understanding.
  10. (2002). Learning discourse: Discursive approaches to research in mathematics education.
  11. (1982). Michael Foucault: Beyond structuralism and hermeneutics.
  12. (1978). Mind in society: The development of higher psychological processes. doi
  13. (1999). New Perspectives on Conceptual Change.
  14. (2000). On reform movement and the limits of mathematical discourse.
  15. (2002). Orchestrating the Multiple Voices and Inscriptions of a Mathematics Classroom.
  16. (1985). Patterns and routines in classroom interaction.
  17. (1953). Philosophical investigations. doi
  18. (1962). Philosophie mathématique,
  19. (1995). Postmodern semiotics. Material culture and the forms of modern life.
  20. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. doi
  21. (2000). Steering (dis)course between metaphor and rigor: Using focal analysis to investigate the emergence of mathematical objects.
  22. (2000). Symbolizing mathematical reality into being: How mathematical discourse and mathematical objects create each other. In
  23. (1985). The child’s thought and geometry. In
  24. (1995). The discursive mind. Thousand Oaks:
  25. (1973). The structures of the life world. Evanston:
  26. (1997). Theory of didactical situations in mathematics. Dodrecht, The Netherlands:
  27. (2001). There is More to Discourse than Meets the Ears: Learning from mathematical communication things that we have not known before.
  28. (1987). Thinking and speech. In doi
  29. (2004). Why cannot children see as the same what grownups cannot see as different? Early numerical thinking revisited. doi

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