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Improving Teachers’ Mathematical Content Knowledge Through Scaffolded Instruction

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Rhetorical Ways of Thinking

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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.

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Notes

  1. 1.

    The actual name of the state comprehensive assessment test is not given because to name the test would provide some identification of the Catholic archdiocese district. This might lead to identification of schools and teachers and would violate the human subject agreement with participants that all identifying information would be excluded in dissemination of results.

  2. 2.

    The four roles identified in this chapter were also evidence in prior research on children collaborative learning (Albert & McKee, 2001).

References

  • Albert, L. R. (2000). Outside in, inside out: Seventh grade students’ mathematical thought processes. Educational Studies in Mathematics, 41, 109–142.

    Article  Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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 

  • Bakhtin, M. (1984). Problems of Dostoevsky’s poetics. Minneapolis, MN: University of Minnesota Press.

    Google Scholar 

  • 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 

  • 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 

  • 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.

    Chapter  Google Scholar 

  • Cobb, P. (1994). Where is the mind? Constructivist and sociocultural perspectives on mathematical development. Educational Researcher, 23(7), 13–20.

    Google Scholar 

  • Cohen, E. (1994). Designing group work: Strategies for the heterogeneous classroom. New York: Teachers College Press.

    Google Scholar 

  • Cohen, D. K., & Hill, H. (2001). Learning policy: When state education reform works. New Haven, CT: Yale University Press.

    Google Scholar 

  • Creswell, J. W. (2003). Research design: Qualitative, quantitative, quantitative, and mixed approaches. Thousand Oaks, CA: Sage.

    Google Scholar 

  • Creswell, J. W., & Plano Clark, V. L. (2006). Designing and conducting mixed methods research. Thousand Oaks, CA: Sage.

    Google Scholar 

  • 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 

  • Davydov, V. V. (1990). Types of generalization in instruction. Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • 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 

  • Davydov, V. V. (1995). The influence of L. S. Vygotsky on education theory, research, and practice. Educational Researcher, 24, 12–21.

    Google Scholar 

  • Davydov, V. V. (1998). The concept of developmental teaching. Journal of Russian and East European Psychology, 36(4), 11–36.

    Article  Google Scholar 

  • 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 

  • Gall, M. D., Gall, J. P., & Borg, W. R. (2010). Applying educational research. Boston: Pearson.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Gay, L. R., & Airasian, P. (1996). Educational research: Competencies for analysis and application. Upper Saddle River, NJ: Merrill.

    Google Scholar 

  • 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 

  • Goos, M. (2004). Learning mathematics in a classroom community of inquiry. Journal for Research in Mathematics Education, 35, 258–291.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • Hill, H. C. (2004). Professional development standards and practices in elementary school mathematics. The Elementary School Journal, 104, 345–363.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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 

  • 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 

  • Johnson, R. B., & Onwuegbuzie, A. J. (2004). Mixed methods research: A research paradigm whose time has come. Educational Researcher, 33(7), 14–26.

    Article  Google Scholar 

  • Kozulin, A. (1998). Psychological tools: A sociocultural approach to education. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • 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 

  • Larkin, M. J. (2001). Providing support for student independence through scaffolded instruction. Teaching Exceptional Children, 34, 30–34.

    Google Scholar 

  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis. Thousand Oaks, CA: SAGE Publications.

    Google Scholar 

  • Murray, D. E., & McPherson. (2006). Scaffolding instruction for reading the web. Language Teaching Research, 10, 131–156.

    Article  Google Scholar 

  • National Research Council. (2002). Scientific research in education. Washington, DC: National Academy of Sciences.

    Google Scholar 

  • Nevills, P. (2003, Winter). Cruising the cerebral superhighway. Journal of Staff Development, 24(1), 20–23.

    Google Scholar 

  • 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 

  • Palinscar, A. (1986). The role of dialogue in providing scaffolded instruction. Educational Psychologist, 21(1–2), 73–98.

    Google Scholar 

  • 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 

  • Prawat, R. S. (1996). Learning community, commitment, and school reform. Journal of Curriculum Studies, 28(1), 91–110.

    Article  Google Scholar 

  • 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 

  • 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 

  • Rosenshine, B., & Meister, C. (1992, April). The use of scaffolds for teaching higher-level cognitive strategies. Educational Leadership, 49, 26–33.

    Google Scholar 

  • 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 

  • Thornton, S. (1995). Children solving problems. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • 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 

  • 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 

  • Wasser, J., & Bresler, L. (1996). Working in the interpretive zone: Conceptualizing collaboration in qualitative research teams. Educational Researcher, 25, 5–15.

    Google Scholar 

  • 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 

  • Wells, G. (1999). Dialogic inquiry: Towards a sociocultural practice and theory of education. New York: Cambridge University Press.

    Book  Google Scholar 

  • 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 

  • Wertsch, J. V. (1979). From social interaction to higher psychological processes: A classification and application of Vygotsky’s theory. Human Development, 22, 1–22.

    Article  Google Scholar 

  • Wertsch, J. V. (1980). The significance of dialogue in Vygotsky’s account of social, egocentric, and inner speech. Contemporary Educational Psychology, 5, 150–162.

    Article  Google Scholar 

  • Wood, D., Bruner, J., & Ross, G. (1976). The role of tutoring in problem solving. Journal of Child Psychology and Psychiatry, 17, 89–100.

    Article  Google Scholar 

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Authors and Affiliations

  1. Lynch School of Education, Boston College, Chestnut Hill, MA, USA

    Lillie R. Albert Ph.D.

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  1. Lillie R. Albert Ph.D.
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Albert, L.R. (2012). Improving Teachers’ Mathematical Content Knowledge Through Scaffolded Instruction. In: Rhetorical Ways of Thinking. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4065-5_4

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