Abstract
Current reforms in mathematics education advocate the development of mathematical learning communities in which students have opportunities to engage in mathematical discourse and classroom practices which underlie algebraic reasoning. This article specifically addresses the pedagogical actions teachers take which structure student engagement in dialogical discourse and activity which facilitates early algebraic reasoning. Using videotaped recordings of classroom observations, the teacher and researcher collaboratively examined the classroom practices and modified the participatory practices to develop a learning environment which supported early algebraic reasoning. Facilitating change in the classroom environment was a lengthy process which required consistent and ongoing attention initially to the social norms and then to the socio-mathematical norms. Specific pedagogical actions such as the use of specifically designed tasks, materials and representations and a constant press for justification and generalisation were required to support students to link their numerical understandings to algebraic reasoning.
Similar content being viewed by others
References
Anthony, G., & Hunter, J. (2008). Developing algebraic generalization strategies. In O. Figueras, J. Cortina, S. Alatoree, T. Rojano, & A. Sepulveda (Eds.), Proceedings of the 32nd conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 65–72). Morelia: PME.
Blanton, M. (2008). Algebra and the elementary classroom: transforming thinking, transforming practice. Portsmouth: Heinemann.
Blanton, M., & Kaput, J. (2005). Characterizing a classroom practice that promotes algebraic reasoning. Journal for Research in Mathematics Education, 36, 412–446.
Carpenter, T., Franke, M., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Portsmouth: Heinemann.
Carraher, D., Schliemann, A. D., Brizuela, B., & Earnest, D. (2006). Arithmetic and algebra in early mathematics education. Journal for Research in Mathematics Education, 37(2), 87–115.
Cobb, P. (1995). Cultural tools and mathematical learning: a case study. Journal for Research in Mathematics Education, 26(4), 362–385.
Cobb, P. (2000). Conducting teaching experiments in collaboration with teachers. In A. Kelly & R. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 307–333). Mahwah: Lawrence Erlbaum.
Cobb, P., Wood, T., Yackel, E., & McNeal, B. (1992). Characteristics of classroom mathematics traditions: an interactional analysis. American Educational Research Journal, 29(3), 73–604.
Department for Education and Employment (DfEE). (1999). National Numeracy Strategy: framework for teaching mathematics from reception to year 6. Cambridge: CUP.
Goos, M. (2004). Learning mathematics in a classroom community of inquiry. Journal for Research in Mathematics Education, 35(4), 258–291.
Hunter, J. (2007). Developing early algebraic reasoning in a mathematical community of inquiry. Unpublished masters thesis, Massey University, Palmerston North, New Zealand.
Hunter, J. (2010). You might say you’re 9 years old but you’re actually B years old because you’re always getting older: Facilitating young children’s understanding of variables. In L. Sparrow, B. Kissane, & C. Hurst (Eds.), Shaping the future of mathematics education: Proceedings of the 33 rd annual conference of the Mathematics Education Research Group of Australasia (Vol. 2, pp. 256–267). Fremantle: MERGA.
Hunter, J., & Anthony, G. (2008). Developing relational thinking in an inquiry environment. In O. Figueras, J. Cortina, S. Alatorre, T. Rojano & A. Sepulveda (Eds.), Proceedings of the 32 nd conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 193–200). Morelia: PME.
Hunter, R. (2009). Teachers developing communities of mathematical inquiry. Auckland: Massey University.
Kaput, J. (1999). Teaching and learning a new algebra. In E. Fennema & T. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 133–155). Mahwah: Lawrence Erlbaum.
Kazemi, E. (1998). Discourse that promotes conceptual understanding. Teaching Children Mathematics, 4(7), 410–414.
Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12, 317–326.
Kuchemann, D. (1981). Algebra. In K. M. Hart, M. L. Brown, D. E. Kuchemann, D. Kerslake, G. Ruddock, & M. McCartney (Eds.), Children's understanding of mathematics: 11–16 (pp. 102–119). Oxford: John Murray.
Lampert, M., & Cobb, P. (2003). Communication and learning in the mathematics classroom. In J. Kilpatrick & D. Shifter (Eds.), Research companion to the NTCM Standards (pp. 237–249). Reston: National Council of Teachers of Mathematics.
Littleton, K., Mercer, N., Dawes, L., Wegerif, R., Rowe, D., & Sams, C. (2005). Thinking together at Key Stage 1. Early Years: An International Journal of Research and Development, 25(2), 165–180.
MacGregor, M., & Stacey, K. (1997). Students' understanding of algebraic notation. Educational Studies in Mathematics, 33, 1–19.
Manoucheri, A., & St John, S. (2006). From classroom discussions to group discourse. Mathematics Teacher, 99(8), 544–552.
McCrone, S. (2005). The development of mathematical discussions: an investigation of a fifth-grade classroom. Mathematical Thinking and Learning, 7(2), 111–133.
Mercer, N. (2000). Words and minds. London: Routledge.
Mercer, N., Littleton, K., & Wegerif, R. (2004). Methods for studying the processes of interaction and collaborative activity in computer-based educational activities. Technology, Pedagogy and Education, 13(2), 193–209.
Mercer, N., & Sams, C. (2006). Teaching children how to use language to solve maths problems. Language and Education, 20(6), 507–528.
Ministry of Education. (2007). The New Zealand Curriculum. Wellington: Learning Media.
Monaghan, F. (2005). Don't think in your head, think aloud: ICT and exploratory talk in the primary school mathematics classroom. Research in Mathematics Education, 7, 83–100.
National Council of Teachers of Mathematics, (2000). Principles and standards for school mathematics. Reston, VA: Author.
O'Connor, M. C., & Michaels, S. (1996). Shifting participant frameworks: orchestrating thinking practices in group discussion. In D. Hicks (Ed.), Child discourse and social learning (pp. 63–102). Cambridge: Cambridge University.
Rojas-Drummond, S., & Zapata, M. (2004). Exploratory talk, argumentation and reasoning in Mexican primary school children. Language and Education, 18(6), 539–557.
Sherin, M. G. (2002). A balancing act: developing a discourse community in a mathematics classroom. Journal of Mathematics Teacher Education, 5, 205–233.
Stacey, K., & Chick, H. (2004). Solving the problem with algebra. In K. Stacey, H. Chick, & M. Kendal (Eds.), The future of the teaching and learning of algebra (pp. 1–20). Dordrecht: Kluwer.
Stein, C. (2007). Let's talk: promoting mathematical discourse in the classroom. Mathematics Teacher, 101(4), 285–289.
Weingrad, P. (1998). Teaching and learning politeness for mathematical argument in school. In M. Lampert & M. L. Blunk (Eds.), Talking mathematics in school: studies of teaching and learning (pp. 213–237). Cambridge: University Press.
Whitenack, J., & Yackel, E. (2002). Making mathematical arguments in primary grades: the importance of explaining and justifying ideas. Teaching Children Mathematics, 8(9), 524–528.
Wood, T., & McNeal, B. (2003). Complexity in teaching and children's mathematical thinking. In N. L. Pateman, B. J. Dougherty, & J. Zilliox (Eds.), Proceedings of the 27th annual conference of the International group for the Psychology of Mathematics Education (Vol. 4, pp. 435–443). Honolulu: PME.
Zack, V. (1999). Everyday and mathematical language in children's argumentation about proof. Educational Review, 51(2), 129–146.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hunter, J. Developing learning environments which support early algebraic reasoning: a case from a New Zealand primary classroom. Math Ed Res J 26, 659–682 (2014). https://doi.org/10.1007/s13394-013-0093-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13394-013-0093-4