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Improving Teachers’ Mathematical Content Knowledge Through Scaffolded Instruction

  • Lillie R. Albert
Chapter

Abstract

Recent research on scaffolded instruction has focused increasingly on the potential of support to promote collaborative learning of content. Sociocultural historic theories have been introduced from associated fields to suggest that cognition and learning takes place at individual and group levels. The concept of a scaffolded instruction model, the Field of Social Interaction, was developed to explain how multiple individuals share meanings and understandings of mathematics’ content. Applying a mixed-methods design, this study examined the concept of shared meanings through the language of scaffolding among practicing middle school mathematics teachers during a professional development program designed to increase mathematical content knowledge. Findings suggest that when learners work in collaborative situations, scaffolded instruction may provide opportunities for those learners to be the knowledgeable others, especially when linked to intentional and deliberate pedagogy. This research provides a fresh perspective on the role of learning and understanding mathematical content within a collaborative context in which teachers’ metacognitive processes evolve and influence their role as teachers of mathematics.

Keywords

Professional Development Content Knowledge Common Denominator Partial Product Proximal Development 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Albert, L. R. (2000). Outside in, inside out: Seventh grade students’ mathematical thought processes. Educational Studies in Mathematics, 41, 109–142.CrossRefGoogle Scholar
  2. Albert, L. R. (2002). Bridging the achievement gap in mathematics: Sociocultural historic theory and dynamic cognitive assessment. Journal of Thought, 37, 65–82.Google Scholar
  3. Albert, L. R., Mayotte, G., & Phelan, C. (2004). The talk of scaffolding: Communication that brings adult learners to deeper levels of mathematical understanding. In D. E. McDougal & J. A. Ross (Eds.), Proceeding of the twenty-sixth annual meeting of the American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1137–1138). Toronto, Canada: OISE/UT.Google Scholar
  4. Albert, L. R., & McKee, K. (2001). In their own words: Achieving intersubjectivity through complex instruction. In V. Spiridonov, I. Bezmenova, O. Kuoleva, E. Shurukht, & S. Lifanova (Eds.), The summer psychology conference 2000, the zone of proximal development (pp. 6–23). Moscow: Institute of Psychology of the Russian State University for the Humanities.Google Scholar
  5. Andrade, A. D. (2009). Interpretive research aiming at theory building: Adopting and adapting the case study design. The Qualitative Report, 14, 42–60.Google Scholar
  6. Bakhtin, M. (1984). Problems of Dostoevsky’s poetics. Minneapolis, MN: University of Minnesota Press.Google Scholar
  7. Bauersfeld, H. (1995). Language games’ in the mathematics classroom: Their function and their effects. In P. Cobb & H. Bauersfeld (Eds.), The emergence of mathematical meaning: Interaction in classroom cultures (pp. 271–289). Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
  8. Bruner, J. (1987). Prologue. In L. Vygotsky, the collected works of L. S. Vygotsky (M. Cole, S. Scribner, V. John-Steiner, & E. Souberman, Trans.). Cambridge, MA: Harvard University Press.Google Scholar
  9. Chaiklin, S. (2003). The zone of proximal development in Vygotsky’s analysis of learning and instruction. In A. Kozulin, B. Gindis, V. Ageyev, & S. Miller (Eds.), Vygotsky’s educational theory in cultural context (pp. 39–64). New York: Cambridge University Press.CrossRefGoogle Scholar
  10. Cobb, P. (1994). Where is the mind? Constructivist and sociocultural perspectives on mathematical development. Educational Researcher, 23(7), 13–20.Google Scholar
  11. Cohen, E. (1994). Designing group work: Strategies for the heterogeneous classroom. New York: Teachers College Press.Google Scholar
  12. Cohen, D. K., & Hill, H. (2001). Learning policy: When state education reform works. New Haven, CT: Yale University Press.Google Scholar
  13. Creswell, J. W. (2003). Research design: Qualitative, quantitative, quantitative, and mixed approaches. Thousand Oaks, CA: Sage.Google Scholar
  14. Creswell, J. W., & Plano Clark, V. L. (2006). Designing and conducting mixed methods research. Thousand Oaks, CA: Sage.Google Scholar
  15. Creswell, J. W., Plano Clark, V. L., Guttmann, M. L., & Hanson, E. E. (2003). Advanced nixed methods research design. In A. Tashakkori & C. Teddlie (Eds.), Handbook of mixed methods in social and behavioral research (pp. 209–240). Thousand Oaks, CA: Sage.Google Scholar
  16. Davydov, V. V. (1990). Types of generalization in instruction. Reston, VA: National Council of Teachers of Mathematics.Google Scholar
  17. Davydov, V. V. (1991). On the objective origin of the concept of fractions. Focus on Learning Problem in Mathematics, 13(1), 13–64.Google Scholar
  18. Davydov, V. V. (1995). The influence of L. S. Vygotsky on education theory, research, and practice. Educational Researcher, 24, 12–21.Google Scholar
  19. Davydov, V. V. (1998). The concept of developmental teaching. Journal of Russian and East European Psychology, 36(4), 11–36.CrossRefGoogle Scholar
  20. Doolittle, P. (1997). Vygotsky’s zone of proximal development as a theoretical foundation for cooperative learning. Journal on Excellence in College Teaching, 8(1), 83–103.Google Scholar
  21. Gall, M. D., Gall, J. P., & Borg, W. R. (2010). Applying educational research. Boston: Pearson.Google Scholar
  22. Garet, M. S., Porter, A. C., Desimore, L., Birman, B. F., & Yoon, K. S. (2001). What makes professional development effective? Results from a national sample of teachers. American Educational Research Journal, 38(4), 915–945.CrossRefGoogle Scholar
  23. Gay, L. R., & Airasian, P. (1996). Educational research: Competencies for analysis and application. Upper Saddle River, NJ: Merrill.Google Scholar
  24. Goos, M. (1999). Scaffolds for learning: A sociocultural approach to reforming mathematics teaching and teacher education. Mathematics Teacher Education and Development, 1, 4–21.Google Scholar
  25. Goos, M. (2004). Learning mathematics in a classroom community of inquiry. Journal for Research in Mathematics Education, 35, 258–291.CrossRefGoogle Scholar
  26. Goos, M. (2005). A sociocultural analysis of the development of pre-service beginning teachers’ pedagogical identities as users of technology. Journal of Mathematics Teacher Education, 8(1), 35–59.CrossRefGoogle Scholar
  27. Greene, J. C., Caracelli, V. J., & Graham, W. F. (1989). Toward a conceptual framework for mixed-method evaluation designs. Educational Evaluation and Policy Analysis, 11(3), 255–274.Google Scholar
  28. Hill, H. C. (2004). Professional development standards and practices in elementary school mathematics. The Elementary School Journal, 104, 345–363.CrossRefGoogle Scholar
  29. Hill, H. C., & Ball, D. (2004). Learning mathematics for teaching results from California’s mathematics professional development institutes. Journal for Research in Mathematics Education, 35, 330–351.CrossRefGoogle Scholar
  30. Hogan, K., & Pressley, M. (1997). Scaffolding scientific competencies within classroom communities of inquiry. In K. Hogan & M. Pressley (Eds.), Scaffolding student learning: Instructional approaches and issues (pp. 74–107). Cambridge, MA: Brookline Books.Google Scholar
  31. Janesick, V. J. (1994). The dance of qualitative research design: Metaphor, methodology, and meaning. In N. K. Denzin & Y. S. Lincoln (Eds.), Handbook of qualitative research (pp. 209–219). Thousand Oaks, CA: Sage Publications, Inc.Google Scholar
  32. Jennings, C., & Di, X. (1996). Collaborative learning and thinking: The Vygotskian approach. In L. Dixon-Krauss (Ed.), Vygotsky in the classroom: Mediated literacy instruction and assessment (pp. 77–91). New York: Longman Publishers.Google Scholar
  33. Johnson, R. B., & Onwuegbuzie, A. J. (2004). Mixed methods research: A research paradigm whose time has come. Educational Researcher, 33(7), 14–26.CrossRefGoogle Scholar
  34. Kozulin, A. (1998). Psychological tools: A sociocultural approach to education. Cambridge, MA: Harvard University Press.Google Scholar
  35. Kumpulainen, K., & Mutanen, M. (2000). Mapping the dynamics of peer group interaction: A method of analysis of socially shared learning processes. In H. Cowie & G. van der Aalsvoort (Eds.), Social interaction in learning and instruction: The meaning of discourse for the construction of knowledge (pp. 144–160). Amsterdam: Pergamon.Google Scholar
  36. Larkin, M. J. (2001). Providing support for student independence through scaffolded instruction. Teaching Exceptional Children, 34, 30–34.Google Scholar
  37. Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis. Thousand Oaks, CA: SAGE Publications.Google Scholar
  38. Murray, D. E., & McPherson. (2006). Scaffolding instruction for reading the web. Language Teaching Research, 10, 131–156.CrossRefGoogle Scholar
  39. National Research Council. (2002). Scientific research in education. Washington, DC: National Academy of Sciences.Google Scholar
  40. Nevills, P. (2003, Winter). Cruising the cerebral superhighway. Journal of Staff Development, 24(1), 20–23.Google Scholar
  41. Osana, H., & Folger, T. (2000). Negotiated meaning in small group conversation: Talk in a schools for thought classroom. Paper presented at the 2000 annual meeting of the American Educational Research Association, New Orleans, LA.Google Scholar
  42. Palinscar, A. (1986). The role of dialogue in providing scaffolded instruction. Educational Psychologist, 21(1–2), 73–98.Google Scholar
  43. Palinscar, A., & Brown, A. (1988). Teaching and practicing thinking skills to promote comprehension in the context of group problem solving. RASE, 9(1), 33–39.Google Scholar
  44. Prawat, R. S. (1996). Learning community, commitment, and school reform. Journal of Curriculum Studies, 28(1), 91–110.CrossRefGoogle Scholar
  45. Roehler, L., & Cantlon, D. (1997). Scaffolding: A powerful tool in social constructivist classrooms. In K. Hogan & M. Pressley (Eds.), Scaffolding student learning: Instructional approaches and issues (pp. 6–42). Cambridge, MA: Brookline Books.Google Scholar
  46. Rojas-Drummond, S. (2000). Guided participation, discourse and the construction of knowledge in Mexican classrooms. In H. Cowie & G. van der Aalsvoort (Eds.), Social interaction in learning and instruction: The meaning of discourse for the construction of knowledge (pp. 193–213). Amsterdam: Pergamon.Google Scholar
  47. Rosenshine, B., & Meister, C. (1992, April). The use of scaffolds for teaching higher-level cognitive strategies. Educational Leadership, 49, 26–33.Google Scholar
  48. Thorne, S., Kirkham, S. R., & O’Flynn-Magee, K. (2004). The analytic challenge in interpretive description. International Journal of Qualitative Methods, 3(1), 1–11.Google Scholar
  49. Thornton, S. (1995). Children solving problems. Cambridge, MA: Harvard University Press.Google Scholar
  50. Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.Google Scholar
  51. Vygotsky, L. S. (1994). The problem of the environment. In R. Van Der Veer & J. Valsiner (Eds.), The Vygotsky reader (pp. 338–354). Cambridge, MA: Blackwell.Google Scholar
  52. Vygotsky, L. S., & Luria, A. (1994). Tool and symbol in child development. In R. Van Der Veer & J. Valsiner (Eds.), The Vygotsky reader (pp. 99–174). Cambridge, MA: Blackwell.Google Scholar
  53. Wasser, J., & Bresler, L. (1996). Working in the interpretive zone: Conceptualizing collaboration in qualitative research teams. Educational Researcher, 25, 5–15.Google Scholar
  54. Wegerif, R., & Mercer, N. (2000). Language for thinking: A study of children solving reasoning test problems together. In H. Cowie & G. van der Aalsvoort (Eds.), Social interaction in learning and instruction: The meaning of discourse for the construction of knowledge (pp. 179–192). Amsterdam: Pergamon.Google Scholar
  55. Wells, G. (1999). Dialogic inquiry: Towards a sociocultural practice and theory of education. New York: Cambridge University Press.CrossRefGoogle Scholar
  56. Wells, G. (2000). Dialogic inquiry in education: Building on the legacy of Vygotsky. In C. D. Lee & P. Smagorinsky (Eds.), Vygotskian perspectives on literacy research (pp. 51–85). New York: Cambridge University Press.Google Scholar
  57. Wertsch, J. V. (1979). From social interaction to higher psychological processes: A classification and application of Vygotsky’s theory. Human Development, 22, 1–22.CrossRefGoogle Scholar
  58. Wertsch, J. V. (1980). The significance of dialogue in Vygotsky’s account of social, egocentric, and inner speech. Contemporary Educational Psychology, 5, 150–162.CrossRefGoogle Scholar
  59. Wood, D., Bruner, J., & Ross, G. (1976). The role of tutoring in problem solving. Journal of Child Psychology and Psychiatry, 17, 89–100.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Lillie R. Albert
    • 1
  1. 1.Lynch School of EducationBoston CollegeChestnut HillUSA

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