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A Teacher’s Mediation of a Thinking-Aloud Discussion in a 6th Grade Mathematics Classroom

  • Betina Zolkower
  • Sam Shreyar
Article

Abstract

This article presents a Vygotsky-inspired analysis of how a teacher mediated a “thinking aloud” whole-group discussion in a 6th grade mathematics classroom. This discussion centered on finding patterns in a triangular array of consecutive numbers as a phase towards building recursive and direct algebraic formulas. By a “thinking aloud” discussion we mean a conversation wherein students exchange and further develop ideas-in-the-making with their peers under the teacher’s guidance. Drawing upon Halliday’s systemic functional linguistics (SFL), we treated the selected discussion as a text. We then analyzed how the teacher mediated the conjoined making of this text so that it served as an interpersonal gateway for students to practice searching for patterns and signifying these patterns in propositional form. This analysis was guided by the following questions: How did the discussion as a text-in-the-making mean what it did? What was the role of the teacher in the conjoined making of this text? Our study illustrates the power of SFL for capturing the inner grammar of instructional conversations thus illuminating the complexities and subtleties of the teacher’s role in mediating semiotic mediation in mathematics classrooms.

Key Words

interpersonal plane of learning teacher mediation text verbal semiotic mediation mathematics discussion 

References

  1. Bartolini Bussi, M.G.: 1998a, ‘Verbal interaction in the mathematics classroom,’ in H. Steinbring, M. Bartolini Bussi and A. Sierpinska (eds.), Language and Communication in the Mathematics Classroom, NCTM, Reston, VA, 65–84.Google Scholar
  2. Bartolini Bussi, M.G.: 1998b, ‘Joint activity in the mathematics classroom: A Vygotskian analysis’, in F. Seeger, J. Voigt and U. Waschescio (eds.), The Culture of the Mathematics Classroom: Analyses and Changes, Cambridge University Press, Cambridge, pp. 13–49.Google Scholar
  3. Carpay, J.: 1999, ‘The interdependence between forms of mutuality and the development of theoretical interest in the classroom’, Mind, Culture, and Activity 6(4), 314–324.CrossRefGoogle Scholar
  4. Christie, F.: 2000, Classroom Discourse Analysis: A Functional Perspective, Continuum, London and New York.Google Scholar
  5. Coulthard, M.: 1985, An Introduction to Discourse Analysis, 2nd edition, Longman, London and New York.Google Scholar
  6. Dewey, J.: 1910, How We Think, D.C. Heath, Boston.Google Scholar
  7. Dewey, J.: 1938, Logic: The Theory of Inquiry, Henry Holt, New York.Google Scholar
  8. Dörfler, W.: 1991, ‘Forms and means of generalization in mathematics’, in A.J. Bishop (ed.), Mathematical Knowledge: Its Growth through Teaching, Kluwer Academic Publishers, Dordrecht, pp. 63–85.Google Scholar
  9. Eggins, S.: 1994, Introduction to Systemic Functional Linguistics, Continuum, London.Google Scholar
  10. Forman, E.A., Larreamendy-Joerns, J., Stein, M.K. and Brown, C.: 1998, “You’re going to want to find out which and prove it’: Collective argumentation in a mathematics classroom”, Learning and Instruction 8(6), 527–548.CrossRefGoogle Scholar
  11. Freudenthal, H.: 1991, Revisiting Mathematics Education: China Lectures, Kluwer, Dordrecht.Google Scholar
  12. Halliday, M.A.K.: 1973, Explorations in the Functions of Language, Elsevier, New York, Oxford, and Amsterdam.Google Scholar
  13. Halliday, M.A.K.: 1978, Language as Social Semiotic: The Social Interpretation of Language and Meaning, Arnold, London.Google Scholar
  14. Halliday, M.A.K.: 1993, ‘Towards a language-based theory of learning’, Linguistics and Education 5, 93–116.CrossRefGoogle Scholar
  15. Halliday, M.A.K.: 1994, An Introduction to Functional Grammar, 2nd edition, Arnold, London.Google Scholar
  16. Halliday, M.A.K. and Hasan, R.: 1989, Language, Context, and Text: Aspects of Language is a Social-Semiotic Perspective, Oxford University Press, Oxford.Google Scholar
  17. Halliday, M.A.K. and Martin, J.: 1993, Writing Science: Literacy and Discursive Power, Falmer Press, London.Google Scholar
  18. Halliday, M.A.K. and Matthiessen, C.: 1999, Construing Experience through Meaning: A Language-Based Approach to Cognition, Cassell, London and New York.Google Scholar
  19. Hasan, R.: 1996, Ways of Saying, Ways of Meaning, Cassell, London and New York.Google Scholar
  20. Lee, L.: 1996, ‘An initiation into algebraic culture through generalization activities’, in N. Bednarz, C. Kieran and L. Lee (eds.), Approaches to Algebra: Perspectives for Research and Teaching, Kluwer Academic Publishers, Dordrecht, pp. 65–86.Google Scholar
  21. Martin, J.R.: 1984, ‘Language, register, and genre’, in F. Christie (ed.), Children Writing: A Reader, Deakin University Press, Geelong.Google Scholar
  22. Martin, J.R. and Veel, R. (eds.): 1998, Reading Science: Critical and Functional Perspectives on Discourses of Science, Routledge, London.Google Scholar
  23. Martin, T.S., McCrone, S.S., Wallace Bower, M.L. and Dindyal, J.: 2005, ‘The interplay of teacher and student actions in the teaching and learning of geometric proof’, Educational Studies in Mathematics 60, 95–124.CrossRefGoogle Scholar
  24. Morgan, C.: 2000, ‘Language in use in mathematics classrooms: Developing approaches to a research domain’, Educational Studies in Mathematics 41, 93–99.CrossRefGoogle Scholar
  25. O’Connor, M.C.: 2001, ‘Can any fraction be turned into a decimal?: A case study of a mathematical group discussion’, Educational Studies in Mathematics 46, 143–185.CrossRefGoogle Scholar
  26. O’Connor, M.C. and Michaels, S.: 1993, ‘Aligning academic task and participation status through revoicing: Analysis of a classroom discourse strategy’, Anthropology and Education Quarterly 24(4), 318–335.CrossRefGoogle Scholar
  27. Schleppegrell, M.: 2001, ‘Linguistic features of the language of schooling’, Linguistics and Education 12(4), 431–459.CrossRefGoogle Scholar
  28. Sfard, A. and Kieran, C.: 2001, ‘Cognition and communication: Rethinking learning-by-talking through multi-faceted analysis of students’ mathematical interactions’, Mind, Culture, and Activity 8(1), 42–76.CrossRefGoogle Scholar
  29. Steinbring, H., Bartolini Bussi, M. G. and Sierpinska, A. (eds.): 1998, Language and Communication in the Mathematics Classroom, National Council of Teachers of Mathematics, Reston, VA.Google Scholar
  30. Veel, R.: 1999, ‘Language, knowledge and authority in school mathematics’, in F. Christie (ed.), Pedagogy and the Shaping of Consciousness, Linguistics and Social Processes, Cassell, London and New York, pp. 185–216.Google Scholar
  31. Voigt, J.: 1985, ‘Patterns and routines in classroom interaction’, Recherches en Didactique des Mathématiques 6(1), 69–118.Google Scholar
  32. Vygotsky, L.S.: 1978, Mind in Society: The Development of Higher Psychological Functions, Harvard University Press, Cambridge, MA.Google Scholar
  33. Vygotsky, L.S.: 1986, Thought and Language, MIT Press, Cambridge, MA.Google Scholar
  34. Wells, G.: 1994, ‘The complementary contributions of Halliday and Vygotsky to a “Language-based theory of learning”’, Linguistics and Education 6, 41–90.CrossRefGoogle Scholar
  35. Wells, G.: 1999, Dialogic Inquiry: Toward a Socio-cultural Practice and Theory of Education, Cambridge University Press, Cambridge, UK.Google Scholar
  36. Zack V. and Graves, B.: 2001, ‘Making mathematical meaning through dialogue: Once you think of it, the z minus three seems pretty weird’, Educational Studies in Mathematics 46, 229–271.CrossRefGoogle Scholar
  37. Zazkis, R. and Liljedahl, P.: 2002, ‘Generalization of patterns: The tension between algebraic thinking and algebraic notation’, Educational Studies in Mathematics 49, 379–402.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.School of Education, Brooklyn CollegeCity University of New YorkBrooklynUSA
  2. 2.Lehman CollegeCity University of New YorkBrooklynUSA

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