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Journal of Mathematics Teacher Education

, Volume 16, Issue 4, pp 293–318 | Cite as

Teaching mathematical problem-solving from an emergent constructivist perspective: the experiences of Irish primary teachers

  • John O’Shea
  • Aisling M. Leavy
Article

Abstract

The primary school mathematics curriculum in Ireland is based upon a constructivist philosophy of learning. As constructivism is a theory of learning and not teaching, implementing a constructivist approach in the classroom requires teachers to identify the implications and applications of constructivist philosophy for teaching. In this research, case study is employed to reveal the extent to which teachers’ detailed understanding of emergent constructivism and its implications for classroom practice informed their teaching practices, all within the context of teaching problem-solving lessons in the senior primary school mathematics classroom. Results highlight the challenges and opportunities faced by primary teachers as an attempt is made to allow an understanding of learning from an emergent constructivist perspective inform teaching practice. Throughout this research, it emerged that teachers’ beliefs and attitudes regarding appropriate mathematical constructions did not correlate with what students may have deemed appropriate. Teachers need to understand their beliefs and those of their students and to work on changing both if necessary. The study affirms that teacher knowledge, beliefs, identify, school contexts and school curriculum are all important factors to consider.

Keywords

Mathematical problem-solving Constructivism Primary mathematics Ireland 

References

  1. Airsian, P. W., & Walsh, M. E. (1997). Constructivist Cautions. Phi Delta Kappan, 78(6), 444–449.Google Scholar
  2. Bauersfeld, H. (1992). Classroom culture from a social constructivist’s perspective. Educational Studies in Mathematics, 23, 467–481.CrossRefGoogle Scholar
  3. Cobb, P., & Bauersfeld, H. (1995). The emergence of mathematical meaning: Interaction in classroom cultures. New Jersey: Hillsdale.Google Scholar
  4. Cobb, P. E., & Wood, Y. T. (1993). Discourse, mathematical thinking and classroom practice. In E. Forman, N. Minick, & C. Addison Stone (Eds.), Contexts for learning: Sociocultural dynamics in childrens development (pp. 336–356). Oxford: Oxford University Press.Google Scholar
  5. Cobb, P., Wood, T., Yackel, E., & McNeal, B. (1992). Characteristics of classroom mathematics traditions: An interactional analysis. American Educational Research Journal, 29, 573–604.CrossRefGoogle Scholar
  6. Cobb, P., & Yackel, E. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458–477.CrossRefGoogle Scholar
  7. Cockcroft, W. H. (1982). Mathematics Counts. HMSO: Report of Inquiry into the Teaching of Mathematics in Schools.Google Scholar
  8. Cohen, D. (1990). A revolution in one classroom: The case of Mrs Oublier. Educational Evaluation and Policy Analysis, 12(3), 311–329.Google Scholar
  9. Confrey, J. (1990). What constructivism implies for teaching. In R. B. Davis, C. A. Maher, & N. Noddings (Eds.), Constructivist views on the teaching and learning of mathematics (JRME monograph 4) National Council of Teachers of Mathematics (pp. 107–122). VA: Reston.Google Scholar
  10. Confrey, J. (1994a). A theory of intellectual development: Part 1. For the Learning of Mathematics, 14, 2–8.Google Scholar
  11. Confrey, J. (1994b). A theory of intellectual development: Part 2. For the Learning of Mathematics, 15, 38–48.Google Scholar
  12. Confrey, J. (1995). A theory of intellectual development: Part 2. For the Learning of Mathematics, 15, 36–45.Google Scholar
  13. Cuban, L. (1988). A fundamental puzzle of school reform. Phi Delta Kappan, 69, 341–344.Google Scholar
  14. Draper, R. (2002). Every teacher a literacy teacher? An analysis of the literacy-related messages in secondary methods textbooks. Journal of Literacy Research, 34, 357–384.CrossRefGoogle Scholar
  15. Elmore, R., Peterson, P., & McCarthy, S. (1996). Restructuring in the classroom: Teaching, Learning, and School Organization. San Francisco: Jossey-Bass.Google Scholar
  16. Francisco, J. M., & Maher, C. A. (2005). Conditions for promoting reasoning in problem solving: Insights from a longitudinal study. Journal of Mathematical Behaviour, 24, 361–372.CrossRefGoogle Scholar
  17. Gallimore, G., & Tharp, R. G. (1989). Rousing minds to life: Teaching learning and schooling in the social context. Cambridge: Cambridge University Press.Google Scholar
  18. Garofalo, J., & Lester, F. (1985). Metacognition, cognitive monitoring and mathematical performance. Journal for Research in Mathematics Education, 16, 163–176.CrossRefGoogle Scholar
  19. Government of Ireland. (1971). Curaclam na Bunscoile. Dublin: Stationary Office.Google Scholar
  20. Government of Ireland. (1999a). Mathematics curriculum: Teacher guidelines. Dublin: Stationary Office.Google Scholar
  21. Government of Ireland. (1999b). Mathematics Curriculum. Dublin: Stationary Office.Google Scholar
  22. Greer, B. (1997). Modelling reality in mathematics classrooms: The case of word problems. Learning and Instruction, 7(4), 293–307.CrossRefGoogle Scholar
  23. Halmos, P. (1980). The heart of mathematics. American Mathematical Monthly, 87, 519–524.CrossRefGoogle Scholar
  24. Hoffman, B., & A. Spatariu, (2007). The effect of self-efficacy and metacognitive prompting on math problem-solving efficiency. Paper presented at the annual meeting of the American Psychological Association, San Francisco, August 19, 2007.Google Scholar
  25. Inhelder, B., & Piaget, J. (1958). The growth of logical thinking from childhood to adolescence. New York: Basic Books.CrossRefGoogle Scholar
  26. Lerman, S. (1996). Intersubjectivity in mathematics learning: A challenge to the radical constructivist paradigm? Journal for Research in Mathematics Education, 27(2), 133–150.CrossRefGoogle Scholar
  27. Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis (2nd edition). Thousand Oaks: Sage Publications.Google Scholar
  28. Murray, H., (1992). Learning Mathematics Through Social Interaction. Paper presented to Working Group 4, ICME 7 Conference, Quebec, August 1992.Google Scholar
  29. National Council for Curriculum and Assessment, (2008). ‘Primary Curriculum Review: Phase 2’. www.ncca.ie, Accessed 10-01-2011.
  30. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. VA: National Council of Teachers of Mathematics.Google Scholar
  31. O’Shea, J., (2010). Endeavouring to Teach Mathematical Problem Solving from a Constructivist Perspective: The Experiences of Primary Teachers. Unpublished Doctoral Dissertation: University of Limerick.Google Scholar
  32. OECD. (2009). Take the test: Sample questions from OECD’S PISA assessment. Paris: OECD.Google Scholar
  33. Petersen, P. L. (1988). Teachers’ and students’ cognitional knowledge for classroom teaching and learning. Educational Researcher, 17(5), 5–14.CrossRefGoogle Scholar
  34. Pirie, S., & Kieran, T. (1992). Creating constructivist environments and constructing creative mathematics. Educational Studies in Mathematics, 23, 505–528.CrossRefGoogle Scholar
  35. Polya, G. (1945). How to Solve It. NJ: Princeton University.Google Scholar
  36. Purple, D. E., & Shapiro, H. S. (1995). Beyond liberation and excellence: A discourse for education as transformation. In H. S. Shapiro & D. E. Purple (Eds.), Critical social issues in American education: Transformation in a post-modern world (pp. 373–409). NJ: Lawrence Erlbaum.Google Scholar
  37. Schoenfeld, A. H. (1994). Mathematical thinking and problem solving. NJ: LEA.Google Scholar
  38. Schoenfeld, A. H. (2004). The math wars. Educational Policy, 18(1), 253–286.CrossRefGoogle Scholar
  39. Shavelson, R., McDonnell, L. M., & Oakes, J. (1989). Indicators for monitoring mathematics and science education: A sourcebook. Santa Monica: RAND Corporation.Google Scholar
  40. Shiel, G., & Kelly, D. (2001). The 1999 national assessment of mathematics achievement. Dublin: ERC.Google Scholar
  41. Stake, R. (1995). The Art of Case Research. Thousand Oaks: Sage Publications.Google Scholar
  42. Stanic, G., & Kilpatrick, J. (1989). Historical perspectives on problem solving in the mathematics curriculum. In R. I. Charles & E. A. Silver (Eds.), The teaching and assessing of mathematical problem solving (pp. 1–22). VA: National Council of Teachers of Mathematics.Google Scholar
  43. Steffe,L.P & P.W.Thompson, (2000). Radical constructivism in action. Building on the pioneering work of Ernst von Glasersfeld (1–9)., Routledge, London.Google Scholar
  44. Surgenor, P., Shiel, G., Close, S., & Millar, D. (2006). Counting on success: Mathematics achievement in Irish primary schools. Dublin: Stationary Office.Google Scholar
  45. Tobin, K., & Tippins, D. J. (1993). Constructivism as a referent for teaching and learning. In K. Tobin (Ed.), The practice of Constructivism in science education (pp. 51–69). Hillsdale: Lawrence Erlbaum Associates.Google Scholar
  46. Von Glasersfeld, E. (1989). Constructivism in education. In T. Husen & N. Postlethwaite (Eds.), International encyclopedia of education (pp. 162–163). Oxford: Pergamon.Google Scholar
  47. Von Glasersfeld, E. (1992). On manifestly (or, at least, apparently) timeless objectivity. Philosophy of Mathematics Education Newsletter, 6, 12–13.Google Scholar
  48. Von Glasersfeld, E. (1995). Radical constructivism: A way of knowing and learning. London: The Falmer Press.CrossRefGoogle Scholar
  49. Wilburne, J. M. (2006). Preparing preservice elementary school teachers to teach problem solving. Teaching Children Mathematics, 12(9), 454–463.Google Scholar
  50. Windschitl, M. (1999). The challenges of sustaining a constructivist classroom culture. Phi Delta Kappan, 80, 751–755.Google Scholar
  51. Wolffe, R. J., & McMullen, D. W. (1996). The constructivist connection: Linking theory, best practice and technology. Journal of Computing in Teacher Education, 12(2), 25–28.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Reflective Practice and Early Childhood StudiesMary Immaculate CollegeLimerickIreland
  2. 2.Department of Language, Literacy and Mathematics EducationMary Immaculate CollegeLimerickIreland

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