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Algebra Teaching around the World pp 17–37Cite as

Solving Linear Equations

A Balanced Approach

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Abstract

Concerted efforts at improving student performance in algebra demonstrate that “children throughout the elementary grades are capable of learning powerful unifying ideas of mathematics that are the foundation of both arithmetic and algebra” (Carpenter, Franke, & Levi, 2003, p. xi). In New Zealand, Britt and Irwin’s (2005) investigation of the Numeracy Development Project found that those students who acquired flexibility in using a range of general arithmetical strategies also developed the ability to express the structure of those strategies in symbolic forms.

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References

  • Aczel, J. (1998). Learning algebraic strategies using a computerised balance model. In A. Oliver & K. Newstead (Eds.), Proceedings of the 22nd conference of the International group for the Psychology of Mathematics Education (Vol. 2, pp. 1–16). Stellenbosch: PME.

    Google Scholar 

  • Anthony, G. (2013). Student perceptions of the ‘good’ teacher and ‘good’ learning in New Zealand mathematics classrooms In B. Kaur, G. Anthony, M. Otani & D. J. Clarke (Eds.), Students’ voice in mathematics classrooms around the world (pp. 209–226). Rotterdam: Sense Publishers.

    Google Scholar 

  • Ball, D. (1993). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. The Elementary School Journal, 93(4), 373–397.

    Article  Google Scholar 

  • Britt, M. S., & Irwin, K. C. (2005). Algebraic thinking in the numeracy project: Year one of a three-year study. In P. Clarkson, S. Downton, D. Gronn, M. Horne, A. McDonough, R. Pierce, & A. Roche (Eds.), Building connections: theory, research and practice. (Proceedings of the 28th annual conference of Mathematics Education Research Group, pp. 169–176). Sydney: MERGA.

    Google Scholar 

  • Brown, T., Eade, F., & Wilson, D. (1999). Semantic innovation: Arithmetical and algebraic metaphors with narratives of learning. Educational Studies in Mathematics, 40, 53–70.

    Article  Google Scholar 

  • Caglayan, G., & Olive, J. (2010). Eighth grade students’ representations of linear equations based on a cups and tiles model. Educational Studies in Mathematics, 74(2), 143–162.

    Article  Google Scholar 

  • Carpenter, T., Franke, M., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Portsmouth, MH: Heinemann.

    Google Scholar 

  • Chazan, D. (2008). The shifting landscape of school algebra in the United States. In C. E. Greenes (Ed.), Algebra and algebraic thinking in school mathematics (pp. 19–33). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Clarke, D. (2006). The LPS design. In D. J. Clarke, C. Keitel, & Y. Shimizu (Eds.), Mathematics classrooms in twelve countries: The insider’s perspective (pp. 15–36). Rotterdam: Sense Publishers.

    Google Scholar 

  • Cobb, P., Gresalfi, M., & Hodge, L. L. (2009). An interpretive scheme for analyzing the identities that students develop in mathematics classrooms. Journal for Research in Mathematics Education, 40(1), 40–68.

    Google Scholar 

  • Cuoco, A. (2008). Introducing extensible tools in high school algebra. In C. E. Greenes (Ed.), Algebra and algebraic thinking in school mathematics (pp. 51–62). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Davis. B., & Simmt, E. (2003). Understanding learning systems: Mathematics education and complexity science. Journal for Research in Mathematics Education, 34(2), 137–167.

    Article  Google Scholar 

  • Filloy, E., & Rojano, T. (1989). Solving equations: the transition from arithmetic to algebra. For the Learning of Mathematics, 9(2), 19–25.

    Google Scholar 

  • Filloy, E., & Sutherland, R. (1996). Designing curricula for teaching and learning algebra. In A. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (Vol. 1, pp. 139–160). Dordrecht: Kluwer.

    Google Scholar 

  • Herscovics, N., & Linchevski, L. (1994). A cognitive gap between arithmetic and algebra. Educational Studies in Mathematics, 27, 59–78.

    Article  Google Scholar 

  • Johnson, D. (Ed.). (1989). Children’s mathematical frameworks 8-13: A study of classroom teaching. Windsor: NFER -Nelson.

    Google Scholar 

  • Irwin, K. C., & Britt, M. S. (2005). The algebraic nature of students’ numerical manipulation in the New Zealand numeracy project. Educational Studies in Mathematics, 58, 169–188.

    Article  Google Scholar 

  • Kieran, C. (2004). Algebraic thinking in the early grades: What is it? The Mathematics Educator, 8, 139–151.

    Google Scholar 

  • Kaput, J., Blanton, M., & Moreno, L. (2008). Algebra from a symbolization point of view. In J. Kaput, D. Carraher, & M. Blanton (Eds.), Algebra in the early grades (pp. 19–55). New York, NY: Lawrence Erlbaum Associates.

    Google Scholar 

  • Lima, R. N., & Tall, D. (2008). Procedural embodiment and magic in linear equations. Educational Studies in Mathematics, 67, 3–18.

    Article  Google Scholar 

  • Linchevski, L., & Herscovics, N. (1996). Closing the cognitive gap between arithmetic and algebra: Operating on the unknown in the context of equations. Educational Studies in Mathematics, 30, 39–65.

    Article  Google Scholar 

  • Linsell, C. (2009). Students’ knowledge and strategies for solving equations. In Findings from the New Zealand Secondary Numeracy Project 2008 (pp. 29–43). Wellington, New Zealand: Learning Media.

    Google Scholar 

  • National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education.

    Google Scholar 

  • Ministry of Education. (2006). Numeracy Professional Development Projects 2006, Book 3 Getting Started. Wellington, New Zealand: The Ministry of Education.

    Google Scholar 

  • Norton, S., & Windsor, W. (2008). Students’ attitude towards using materials to learn algebra: A year 7 case study. In M. Goos, R. Brown, & K. Makar (Eds.), Navigating currents and carting directions (Proceedings of the 31st annual conference of the Mathematics Education Research group of Australasia, pp. 369–376). Brisbane: MERGA.

    Google Scholar 

  • Pirie, S., & Kieren, T. (1994). Growth in mathematical understanding: How can we characterise it and how can we represent it? Educational Studies in Mathematics, 26, 165–190.

    Article  Google Scholar 

  • Pirie, S., & Martin, L. (1997). The equation, the whole equation and nothing but the equation! One approach to the teaching of linear equations. Educational Studies in Mathematics, 34, 159–181.

    Article  Google Scholar 

  • Sfard, A., & Linchevski, L. (1994). The gains and the pitfalls of reification—the case of algebra. Educational Studies in Mathematics, 26, 191–228.

    Article  Google Scholar 

  • Star, J. R., & Newton, K. J. (2009). The nature and development of experts’ strategy flexibility for solving equations. ZDM Mathematics Education, 41, 557–567.

    Article  Google Scholar 

  • Vlassis, J. (2002). The balance model: Hindrance or support for the solving of linear equations with one unknown. Educational Studies in Mathematics, 49, 341–359.

    Article  Google Scholar 

  • Walshaw, M. (2010). Pedagogical change: Rethinking identity and reflective practice. Journal of Mathematics Teacher Education, 13(6), 487–497.

    Article  Google Scholar 

  • Warren, E., & Cooper, T. J. (2005). Young children’s ability to use the balance strategy to solve for unknowns. Mathematics Education Research Journal, 17(1), 58–72.

    Article  Google Scholar 

  • Watson, A. (2009). Algebraic reasoning. In Key understandings in mathematics learning. Oxford: Nuffield Foundation.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Massey University, New Zealand

    Glenda Anthony

  2. Massey University, New Zealand

    Tim Burgess

Authors
  1. Glenda Anthony
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  2. Tim Burgess
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Editor information

Editors and Affiliations

  1. The University of Hong Kong, Hong Kong

    Frederick K. S. Leung

  2. Hongik University, Korea

    Kyungmee Park

  3. University of Melbourne, Australia

    Derek Holton

  4. University of Melbourne, Australia

    David Clarke

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© 2014 Sense Publishers

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Anthony, G., Burgess, T. (2014). Solving Linear Equations. In: Leung, F.K.S., Park, K., Holton, D., Clarke, D. (eds) Algebra Teaching around the World. Series Preface. SensePublishers, Rotterdam. https://doi.org/10.1007/978-94-6209-707-0_2

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