Abstract
Building on the research of Vygotsky regarding the role of social interaction and the zone of proximal development (ZPD) in learning and development, this paper explored the relation between students' oral thought processes and written thought processes. It is argued that the practice of writing provides a context for a new learning zone: the ‘zone of proximal practice’ (ZPP). In this new zone, students independently organize their thinking about mathematical concepts and ideas. An interpretative case study of seven middle grade students is presented to support this contention. The case study describes the strategies and procedures students employed while solving mathematical problems and documents students' oral and written thought processes through interview protocols and writing samples. The position that students' mathematical understanding is further developed through writing as a communicative tool, while taking advantage of mediated social practices, is discussed to make clear the rationale for introducing a new learning zone.
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REFERENCES
Albert, L.: 1995, ‘A case study on the complexities of learning to teach problem solving: The effects writing process strategy model on seventh grade students’ Mathematics Performance’ Doctoral Dissertation, University of Illinois at Urbana-Champaign, 1995, Dissertation Abstracts International, 57, A1529.
Burkhalter, N.: 1995, ‘A Vygotsky-based curriculum for teaching persuasive writing in the elementary grades’ Language Arts 72, 192-199.
Bruner, J.S.: 1971, The Relevance of Education, Norton, New York.
Bruner, J.S.: 1973, Beyond the Information Given: Studies in the Psychology of Knowing, Norton, New York.
Bruner, J.S.: 1975, ‘The ontogenesis of speech acts’ Journal of Child Language 2, 1-21.
Bruner, J.S. and Haste: 1987, ‘Introduction’ in J. Bruner and H. Haste (eds.), Making Sense: The Child Construction of the World, Methuen, New York, pp. 1-25.
Bruner, J.S., Oliver, R. and Greenfield, P.: 1966, Studies in Cognitive Growth, Son, New York.
Cole, M.: 1996, Cultural Psychology: A Once and Future Disciplines, Harvard University Press, Cambridge, MA.
Creswell, J.W.: 1998, Qualitative Inquiry and Research Design: Choosing Among Five Traditions, Sage Publications, Thousand Oaks, CA.
DiCamilla, F.J. and Anton, M.: 1997, ‘Repetition in the collaborative discourse of L2learners: A Vygotskian perspective’ The Canadian Modern Language Review 53, 609-633.
Doolittle, P.E.: 1991, ‘Vygotsky and the socialization of literacy’ Eric Document ED 377 473.
Elbow, P.: 1981, Writing with Power, Oxford University Press, New York.
Emig, J.A.: 1983, The Web of Meaning, Boynton/Cook, Upper Montclair, NJ.
Ernest, P.: 1998, Social Constructivism as a Philosophy of Mathematics, State University of New York Press, New York.
Everson, B.J.: 1991, ‘Vygotsky and the teaching of writing’ The Quarterly of the National Writing Project and the Center for the Study of Writing 3, 8-11.
Freedman, S.W.: 1995, ‘Crossing the bridge to practice’ Written Communication 22, 74-92.
Graves, D.: 1983, Writing: Teachers and Children at Work, Heinemann Educational Books, Portsmouth, NH.
Hoel, T.L.: 1997, ‘Voices from the classroom’ Teaching and Teacher Education 13, 5-16.
John-Steiner, V.: 1985, Notebooks of the Mind, Harper and Row, New York.
Lave, J. and Wenger, E.: 1991, Situated Language: Legitimate Peripheral Participation, Cambridge University Press, Cambridge.
Lantolf, J.P. and Pavlenko, A.: 1995, ‘Sociocultural theory and second language acquisition’ Annual Review of Applied Linguistics 15, 108-124.
Lemke, J.: 1988, ‘Genres, semantics, and classroom education’ Linguistics and Education 1, 81-99.
Luria, A.R. and Yudovich, F.I.: 1971, Speech and the Development of Mental Processes in the Child, Penguin, Baltimore.
Mayher, J.S., Lester, N.B. and Pradle, G.M.: 1983, Learning to Write: Writing to Learn, Boynton Cook, Upper Montclair, NJ.
Moffett, J.: 1981, Active Voices, Heinemann Educational Books, Portsmouth, NH.
National Council of Teachers of Mathematics: 1991, Professional Standards for Teaching Mathematics, National Council of Teachers of Mathematics, Reston, VA.
Newman, F. and Holzman, L.: 1993, Lev Vygotsky: Revolutionary Scientist, Routledge, New York.
Pellegrini, A.D.: 1981, ‘The development of preschoolers' private speech, Journal of Pragmatics, 5, 445-458.
Polya, G.: 1945, How to Solve It: A New Aspect of Mathematical Method, Princeton University Press, Princeton, NJ.
Rogoff, B. and Wertsch, J.V.: 1984, ‘Children learning in the 'zone of proximal development’ in B. Rogoff and J. Wertsch (eds.), New Directions for Child Development, Jossey-Bass, San Francisco.
Rogoff, B.: 1990, Apprenticeship in Thinking: Cognitive Development in Social Context, Oxford University Press, New York.
Russell, D.R.: 1997, ‘Writing and genre in higher education and workplaces: A review of studies that use cultural-historical activity theory’ Mind, Culture, and Activity 4(4), 224-237.
Scribner, S.: 1997, ‘Mind in action, a functional approach to thinking’ in M. Cole, Y. Engestrom and O. Vasquez (eds.), Mind, Culture, and Activity, Cambridge University Press, New York, pp. 354-368.
Scribner, S. and Cole, M.: 1981: The Psychology of Literacy, Harvard University Press, Cambridge, MA.
Smith, F.: 1988, Joining the Literacy Club, Heinemann Educational Books, Portsmouth, NH.
Stake, R.E.: 1994, ‘Case studies’ in N. Denzin and Y. Lincoln (eds.), Handbook of Qualitative Research, Sage, Thousand Oaks, CA, pp. 236-247.
Stenmark, J.K.: 1991, Mathematics Assessment: Myths, Models, Good Questions, and Practical Suggestions, National Council of Teachers of Mathematics, Reston, VA.
Tudge, J.: 1990, ‘Vygotsky, the zone of proximal development, and peer collaborations: Implications for classroom practice’ in L. Moll (ed.), Vygotsky and Education: Instructional Implications and Applications of Sociohistorical Psychology, Cambridge University Press, New York, pp. 155-172.
Vygotsky, L.S.: 1978, Mind in Society: The Development of Higher Psychological Processes, Harvard University, Cambridge, MA.
Vygotsky, L.S: 1981, ‘The genesis of higher mental functions’ in J. Wertsch (ed.), The Concept of Activity in Soviet Psychology, M. E. Sharpe, New York, pp. 144-188.
Vygotsky, L.S.: 1986, Thought and Language (A. Kozulin, Trans.), M. I. T. Press, Cambridge, MA (original work published 1934).
Wertsch, J.V.: 1979, ‘From social interaction to higher psychological processes: A clarification and application of Vygotsky's theory’ Human Development 22, 1-22.
Wertsch, J.V.: 1979, ‘The regulation of human action and the given-new organization of private speech’ in G. Zivin (ed.), The Development of Self-Regulation Through Private Speech, Wiley, New York, pp. 79-98.
Wertsch, J.V.: 1985, Vygotsky and the Social Formation of Mind, Harvard University Press, Cambridge, MA.
Wertsch, J.V.: 1991, Voices of the Mind: A Sociocultural Approach to Mediated Action, Harvard University Press, Cambridge, M.A.
Wertsch, J.V.: 1997, ‘Collective memory: A sociohistorical perspective’ in M. Cole, Y. Engestrom and O. Vasquez (eds.), Mind, Culture, and Activity, Cambridge University Press, New York, pp. 226-232.
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Albert, L.R. Outside-In – Inside-Out: Seventh-Grade Students' Mathematical Thought Processes. Educational Studies in Mathematics 41, 109–141 (2000). https://doi.org/10.1023/A:1003860225392
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DOI: https://doi.org/10.1023/A:1003860225392