Young children's ability to use the balance strategy to solve for unknowns

Mathematics Education Research Journal

Volumn 17, Issue 1, 2005, Pages 58-72

  Warren, Elizabeth ^a   Cooper, Tom ^b  

^a AUSTRALIAN CATHOLIC UNIVERSITY   (Australia)

^b QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 67349233175     PISSN: 10332170     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF03217409     Document Type: Article

References (29)

1. 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
2. Baroody, A. J., & Ginsburg, H. P. (1983). The effects of instruction on children's understanding of the equals sign. Elementary School Journal, 84, 199-212
3. Behr, M., Erlwanger, S., & Nichols, E. (1980). How children view the equals sign. Mathematics Teaching, 92, 13-18
4. Berenson, S. (1997). Language, diversity, and assessment in mathematics learning. Focus on Learning Problems in Mathematics, 19(4), 1-10
5. Boulton-Lewis, G., Cooper, T. J., Atweh, B., Pillay, H., & Wills, L. (1998). Arithmetic, pre-algebra and algebra: A model of transition. In C. Kanes, M. Goos, & E. Warren (Eds.), Teaching mathematics in new times (Proceedings of the 21st annual conference of the Mathematics Education Research Group of Australasia, Vol. 1, pp. 114-120). Gold Coast: MERGA
6. Carpenter, T. P., & Franke, M. (2001). Developing algebraic reasoning in the elementary school: Generalisation and proof. In H. Chick, K. Stacey, J. Vincent, & J. Vincent (Eds.), The future of the teaching and learning of algebra. Proceedings of the 12th ICMI study conference (Vol. 1, pp. 155-162). Dordrecht, The Netherlands: Kluwer Academic
7. Carpenter, T., Franke, M., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Portsmouth: Heinemann
8. Carpenter, T. P., & Levi, L. (2000). Developing conceptions of algebraic reasoning in the primary grades. Wisconsin Center for Educational Research. Retrieved 12 March, 2005 from http://www. wcer. wisc. edu/ncisla/publications/reports/RR-002. PDF
9. Confrey, J., & Lachance, A. (2000). Transformative teaching experiments through conjecture-driven research design. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 231-265). Mahwah, NJ: Lawrence Erlbaum
10. English, L. D., & Sharry, P. (1996). Analogical reasoning and the development of algebraic abstraction. Educational Studies in Mathematics, 30, 135-157
11. Filloy, E., & Rojano, T. (1989). Solving equations: The transition from arithmetic to algebra. For the Learning of Mathematics, 9(2), 19-25
12. 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 Academic
13. Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht: Reidel Publication
14. Kaput, J., & Blanton, M. (2001). Algebrafying the elementary mathematics experience. In H. Chick, K. Stacey, J. Vincent, & J. Vincent (Eds.), The future of the teaching and learning of algebra. Proceedings of the 12th ICMI study conference (Vol. 1, pp. 344-352). Dordrecht, The Netherlands: Kluwer Academic
15. Kieran, K., & Chalouh, L. (1992). Prealgebra: The transition from arithmetic to algebra. In T. D. Owens (Ed.), Research ideas for the classroom: Middle grades mathematics (pp. 179-198). New York: Macmillan
16. Linchevski, L., & Herscovics, N. (1996). Crossing the cognitive gap between arithmetic and algebra: Operating on the unknown in the context of equations. Educational Studies in Mathematics, 30, 39-65
17. Luria, A. (1981). Language and cognition. Washington, DC: V. H. Winston
18. Malara, N., & Navarra, G. (2003). ArAl Project: Arithmetic pathways towards favouring pre-algebraic thinking. Bologana: Pitagora Editrice
19. Pirie, S. E. B., & 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
20. Rojana, T., & Sutherland, R. (1994). Towards an algebraic notion of function. The role of spreadsheets. In D. Kirshner, (Ed.), Proceedings of the 16th annual meeting of the North American Chapter of the International Group of the Psychology of Mathematics Education (pp. 278-284). Baton Rouge: Louisiana State University
21. Saenz-Ludlow, A., & Walgamuth, C. (1998). Third graders' interpretation of equality and the equal symbol. Educational Studies in Mathematics, 35, 153-187
22. Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1-36
23. Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 267-306). Mahwah, NJ: Lawrence Erlbaum
24. Steinberg, R. M., Sleeman, D. H., & Ktoriza, D. (1991). Algebra students' knowledge of equivalence of equations. Journal for Research in Mathematics Education, 22, 112-121
25. Tall, D. (1991). The psychology of advanced mathematical thinking. In D. Tall (Ed.), Advanced mathematical thinking (pp. 3-24). Dordrecht, The Netherlands: Kluwer Academic
26. Warren, E. (2001). Algebra understanding: The importance of learning in the early years. In H. Chick, K. Stacey, J. Vincent, & J. Vincent (Eds.), The future of the teaching and learning of algebra. Proceedings of the 12th ICMl study conference (Vol. 2, pp. 633-640). Dordrecht, The Netherlands: Kluwer Academic
27. Warren, E. (2002). Unknowns, arithmetic to algebra: Two exemplars. In A. Cockbum & E. Nardi (Eds.), Proceedings of the 26th conference of the international group for the psychology of mathematics education (Vol. 4, pp. 369-376). Norwich: PME
28. Warren, E., (2003). Young children's understanding of equals: A longitudinal study. In N. Pateman, G. Dougherty, & J. Zilliox (Eds.), Proceedings of the 27th conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 379-387). Hawaii: PME
29. Warren, E., & Cooper, T. (2001). Theory and practice: Developing an algebra syllabus for P-7. In H. Chick, K. Stacey, J. Vincent, & J. Vincent (Eds.), The future of the teaching and learning of algebra. Proceedings of the 12th ICMI study conference (Vol. 2, pp. 641-648). Dordrecht, The Netherlands: Kluwer Academic