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.
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Airsian, P. W., & Walsh, M. E. (1997). Constructivist Cautions. Phi Delta Kappan, 78(6), 444–449.
Bauersfeld, H. (1992). Classroom culture from a social constructivist’s perspective. Educational Studies in Mathematics, 23, 467–481.
Cobb, P., & Bauersfeld, H. (1995). The emergence of mathematical meaning: Interaction in classroom cultures. New Jersey: Hillsdale.
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.
Cobb, P., Wood, T., Yackel, E., & McNeal, B. (1992). Characteristics of classroom mathematics traditions: An interactional analysis. American Educational Research Journal, 29, 573–604.
Cobb, P., & Yackel, E. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458–477.
Cockcroft, W. H. (1982). Mathematics Counts. HMSO: Report of Inquiry into the Teaching of Mathematics in Schools.
Cohen, D. (1990). A revolution in one classroom: The case of Mrs Oublier. Educational Evaluation and Policy Analysis, 12(3), 311–329.
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.
Confrey, J. (1994a). A theory of intellectual development: Part 1. For the Learning of Mathematics, 14, 2–8.
Confrey, J. (1994b). A theory of intellectual development: Part 2. For the Learning of Mathematics, 15, 38–48.
Confrey, J. (1995). A theory of intellectual development: Part 2. For the Learning of Mathematics, 15, 36–45.
Cuban, L. (1988). A fundamental puzzle of school reform. Phi Delta Kappan, 69, 341–344.
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.
Elmore, R., Peterson, P., & McCarthy, S. (1996). Restructuring in the classroom: Teaching, Learning, and School Organization. San Francisco: Jossey-Bass.
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.
Gallimore, G., & Tharp, R. G. (1989). Rousing minds to life: Teaching learning and schooling in the social context. Cambridge: Cambridge University Press.
Garofalo, J., & Lester, F. (1985). Metacognition, cognitive monitoring and mathematical performance. Journal for Research in Mathematics Education, 16, 163–176.
Government of Ireland. (1971). Curaclam na Bunscoile. Dublin: Stationary Office.
Government of Ireland. (1999a). Mathematics curriculum: Teacher guidelines. Dublin: Stationary Office.
Government of Ireland. (1999b). Mathematics Curriculum. Dublin: Stationary Office.
Greer, B. (1997). Modelling reality in mathematics classrooms: The case of word problems. Learning and Instruction, 7(4), 293–307.
Halmos, P. (1980). The heart of mathematics. American Mathematical Monthly, 87, 519–524.
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.
Inhelder, B., & Piaget, J. (1958). The growth of logical thinking from childhood to adolescence. New York: Basic Books.
Lerman, S. (1996). Intersubjectivity in mathematics learning: A challenge to the radical constructivist paradigm? Journal for Research in Mathematics Education, 27(2), 133–150.
Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis (2nd edition). Thousand Oaks: Sage Publications.
Murray, H., (1992). Learning Mathematics Through Social Interaction. Paper presented to Working Group 4, ICME 7 Conference, Quebec, August 1992.
National Council for Curriculum and Assessment, (2008). ‘Primary Curriculum Review: Phase 2’. www.ncca.ie, Accessed 10-01-2011.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. VA: National Council of Teachers of Mathematics.
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.
OECD. (2009). Take the test: Sample questions from OECD’S PISA assessment. Paris: OECD.
Petersen, P. L. (1988). Teachers’ and students’ cognitional knowledge for classroom teaching and learning. Educational Researcher, 17(5), 5–14.
Pirie, S., & Kieran, T. (1992). Creating constructivist environments and constructing creative mathematics. Educational Studies in Mathematics, 23, 505–528.
Polya, G. (1945). How to Solve It. NJ: Princeton University.
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.
Schoenfeld, A. H. (1994). Mathematical thinking and problem solving. NJ: LEA.
Schoenfeld, A. H. (2004). The math wars. Educational Policy, 18(1), 253–286.
Shavelson, R., McDonnell, L. M., & Oakes, J. (1989). Indicators for monitoring mathematics and science education: A sourcebook. Santa Monica: RAND Corporation.
Shiel, G., & Kelly, D. (2001). The 1999 national assessment of mathematics achievement. Dublin: ERC.
Stake, R. (1995). The Art of Case Research. Thousand Oaks: Sage Publications.
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.
Steffe,L.P & P.W.Thompson, (2000). Radical constructivism in action. Building on the pioneering work of Ernst von Glasersfeld (1–9)., Routledge, London.
Surgenor, P., Shiel, G., Close, S., & Millar, D. (2006). Counting on success: Mathematics achievement in Irish primary schools. Dublin: Stationary Office.
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.
Von Glasersfeld, E. (1989). Constructivism in education. In T. Husen & N. Postlethwaite (Eds.), International encyclopedia of education (pp. 162–163). Oxford: Pergamon.
Von Glasersfeld, E. (1992). On manifestly (or, at least, apparently) timeless objectivity. Philosophy of Mathematics Education Newsletter, 6, 12–13.
Von Glasersfeld, E. (1995). Radical constructivism: A way of knowing and learning. London: The Falmer Press.
Wilburne, J. M. (2006). Preparing preservice elementary school teachers to teach problem solving. Teaching Children Mathematics, 12(9), 454–463.
Windschitl, M. (1999). The challenges of sustaining a constructivist classroom culture. Phi Delta Kappan, 80, 751–755.
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.
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O’Shea, J., Leavy, A.M. Teaching mathematical problem-solving from an emergent constructivist perspective: the experiences of Irish primary teachers. J Math Teacher Educ 16, 293–318 (2013). https://doi.org/10.1007/s10857-013-9235-6
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DOI: https://doi.org/10.1007/s10857-013-9235-6