# Understanding Equivalence of Symbolic Expressions in a Spreadsheet-Based Environment

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## Abstract

Use of spreadsheets in a beginning algebra course was investigated mainly with regard to their potential to promote generalization of patterns. Less is known about their use in promoting understanding and learning of transformational activities. The overall purpose of this paper is to consider the conceptual aspects of learning a transformational skill (use of the distributive law to produce equivalent algebraic expressions) in a learning sequence composed of both spreadsheets and paper-and-pencil activities. We conducted a sequence of classroom activities in several classes, and analyzed the students’ work on a spreadsheet activity and on an assessment activity by both qualitative and quantitative methods. The findings indicate both encouraging benefits and some potential sources of difficulties caused by the use of spreadsheets at initial stages of learning symbolic transformations.

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## Notes

1. In this case and in the case of two other expressions (see Table 3), we used the original spreadsheet notation, since these two formulas employ quantities from different lines, and dropping the line indexes (as we did in the other cases) cannot adequately describe these solutions.

## References

• Ainley, J. (1996). Purposeful contexts for normal notation in spreadsheet environment. Journal of Mathematics Behavior, 15, 405–422.

• Baker, J. E., & Sugden, S. J. (2003). Spreadsheets in education: The first 25 years. Spreadsheets in Education, 1(1). Retrieved on March 2007, from http://www.sie.bond.edu.au/

• Dettori, G., Garuti, R., & Lemut, E. (2001). From arithmetic to algebraic thinking by using a spreadsheet. In R. Sutherland, T. Rojano, A. Bell, & R. Lins (Eds.), Perspectives on school algebra (pp. 191–208). Dordrecht, The Netherlands: Kluwer Academic Publishers.

• Drouhard, J. P., & Teppo, A. R. (2004). Symbols and language. In K. Stacey, H. Chick, & M. Kendal (Eds.), The future of the teaching and learning of algebra (pp. 227–266). The 12th ICMI study. Dordrecht, The Netherlands: Kluwer Academic Publishers.

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

• Friedlander, A. (1999). Cognitive processes in a spreadsheet environment. In O. Zaslavsky (Ed.), Proceedings of the 23rd Meeting of the PME Conference (Vol. 2, pp. 337–344), Haifa, Israel.

• Friedlander, A., & Stein, H. (2001). Students’ choice of tools in solving equations in a technological learning environment. In M. Heuvel-Panhuizen (Ed.), Proceedings of the 25th International Conference for the Psychology of Mathematics Education (Vol. 2, pp. 441–448). Utrecht, The Netherlands.

• Friedlander, A., & Tabach, M. (2001a). Promoting multiple representations in algebra. In A. A. Cuoco & F. R. Curcio (Eds.), The roles of representation in school mathematics, 2001 yearbook of the National Council of Teachers of Mathematics (pp. 173–185). Reston, VA: NCTM.

• Friedlander, A., & Tabach, M. (2001b). Developing a curriculum of beginning algebra in a spreadsheet environment. In H. Chick, K. Stacey, J. Vincent, & J. Vincent (Eds.), Proceedings of the 12th ICMI Study Conference, The Future of Teaching and Learning of Algebra (pp. 252–257). Melbourne, Australia: University of Melbourne.

• Haspekian, M. (2005). An “instrumental approach” to study the integration of computer tool into mathematics teaching: The case of spreadsheets. International Journal of Computers for Mathematics Learning, 10, 109–141.

• Heid, M. K. (1995). Curriculum and evaluation standards for school mathematics, Addenda series: Algebra in a technological world. Reston, VA: NCTM.

• Hershkowitz, R., Dreyfus, T., Ben-Zvi, D., Friedlander, A., Hadas, N., Resnick, N., Tabach M., & Schwarz, B. B. (2002). Mathematics curriculum development for computerized environments: a designer-researcher-learner-activity. In L. D. English (Ed.), Handbook of the international research in mathematics education (pp. 657–694). Mahwah, New Jersey: Lawrence Erlbaum Associates.

• Hershkowitz, R., & Schwarz, B. B. (1999). The emergent perspective in a rich learning environment: Some roles of tools and activities in the construction of sociomathematical norms. Educational Studies in Mathematics, 39, 149–166.

• Kieran, C. (2004). The core of algebra: Reflections on its main activities. In K. Stacey, H. Chick, & M. Kendal (Eds.), The future of teaching and learning of algebra: 12th ICMI Study (pp. 21–34). Dordrecht, The Netherlands: Kluwer Academic Publishers.

• Rojano, T., & Sutherland, R. (2001). Arithmetic world – Algebra world. In H. Chick, K. Stacey, J. Vincent, & J. Vincent (Eds.), Proceedings of the 12th ICMI Study Conference, The Future of Teaching and Learning of Algebra (pp. 515–522). Melbourne, Australia: University of Melbourne.

• Sutherland, R., & Balacheff, N. (1999). Didactical complexity of computational environments for the learning of mathematics. International Journal of Computers for Mathematical Learning, 4, 1–26.

• Sutherland, R., & Rojano, T. (1993). A spreadsheet approach to solving algebra problems. Journal of Mathematical Behavior, 12, 353–383.

• Tabach, M., & Friedlander, A. (2004). Levels of student responses in a spreadsheet-based environment. Proceedings of the 28th International Conference for the Psychology of Mathematics Education (Vol. 2, pp. 423–430). Bergen, Norway.

• Tabach, M., & Friedlander, A. (2006). Solving equations in a spreadsheets environment. In C. Hoyles, J. B. Lagrange, L. H. Son, & N. Sinclair (Eds.), Proceedings of the 17th ICMI Study Conference “Technology Revisited” (pp. 539–545). Hanoi, Vietnam: Hanoi University of Technology. (CD-ROM).

• Tabach, M., Hershkowitz, R., Arcavi, A., & Dreyfus, T. (in press). Computerized environments in mathematics classrooms: A research - design view. To appear in L. D. English (Ed.), Handbook for international research in mathematics education, 2nd ed. Mahwah, NJ: Lawrence Erlbaum.

• Tabach, M., Hershkowitz, R., & Schwarz, B. B. (2006). Constructing and consolidating of algebraic knowledge within dyadic processes: A case study. Educational Studies in Mathematics, 63(3), 235–258.

• Wilson, K., Ainley, J., & Bills, L. (2005). Naming a column on a spreadsheet: Is it more algebraic? In D. Hewitt & A. Noyes (Eds.), Proceedings of the Sixth British Congress of Mathematics Education (pp. 184–191). Warwick, U.K.

• Yerushalmy, M., & Chazan, D. (2002). Flux in school algebra: Curricular change, graphing technology, research on students learning and teacher knowledge. In L. D. English (Ed.), Handbook of international research in mathematics education (pp. 725–755). Mahwah, NJ: Lawrence Erlbaum.

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Correspondence to Michal Tabach.

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Tabach, M., Friedlander, A. Understanding Equivalence of Symbolic Expressions in a Spreadsheet-Based Environment. Int J Comput Math Learning 13, 27–46 (2008). https://doi.org/10.1007/s10758-008-9125-7