Skip to main content
Log in

Algebraic procedures and creative thinking

  • Original Article
  • Published:
ZDM Aims and scope Submit manuscript

Abstract

Simplifying symbolic expressions is usually perceived in middle school algebra as an algorithmic activity, achieved by performing sequences of short drill-and-practice tasks, which have little to do with conceptual learning or with creative mathematical thinking. The aim of this study is to explore possible ways by which ninth-grade students can be encouraged to apply flexible and creative thinking in the context of a task that requires students to design a multiple-choice questionnaire on equivalent algebraic expressions. Fifty-six ninth-grade students answered Take-a-Quiz and Make-a-Quiz questionnaires. The findings indicate that students can be engaged in a satisfactory way in these kinds of non-routine tasks. Also, about two-thirds of the participating students were able to display a medium or high level of originality in their construction of equivalent expressions. In addition, an analysis of the non-equivalent expressions suggested by the participating students as distractors indicated a relatively high level of awareness to the most common errors that might occur in this type of activity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1

Similar content being viewed by others

References

  • Booth, L. R. (1988). Children’s difficulties in beginning algebra. In A. F. Coxford & A. P. Shulte (Eds.), The ideas of algebra K-12, 1988 yearbook of teachers of mathematics (NCTM) (pp. 20–32). Reston: NCTM.

    Google Scholar 

  • Borasi, R. (1994). Capitalizing on errors as “springboards for inquiry”: A teaching experiment. Journal for Research in Mathematics Education, 25, 166–208.

    Article  Google Scholar 

  • Borasi, R. (1996). Reconceiving mathematics instruction: A focus on errors. Greenwood Publishing Group.

  • Ervynck, G. (1991). Mathematical creativity. In D. Tall (Ed.), Advanced mathematical thinking (pp. 42–53). Dordrecht: Kluwer.

    Google Scholar 

  • Friedlander, A., & Arcavi, A. (2012). Practicing algebraic skills, a conceptual approach. Mathematics Teacher, 105(8), 608–614.

    Article  Google Scholar 

  • Guilford, J. P. (1967). The nature of human intelligence. New York: McGraw-Hill.

    Google Scholar 

  • Kieran, C. (1992). The learning and teaching of school algebra. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 390–419). New York: Macmillan.

    Google Scholar 

  • Kieran, C., & Sfard, A. (1999). Seeing through symbols: The case of equivalent expressions. Focus on learning problems in mathematics, 21(1), 1–17.

    Google Scholar 

  • Leikin, R. (2009). Exploring mathematical creativity using multiple solution tasks. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 129–135). Rotterdam: Sense Publishers.

    Google Scholar 

  • Leikin, R., & Lev, M. (2007). Multiple solution tasks as a magnifying glass for observation of mathematical creativity. In J. H. Woo, H. C. Lew, K. S. Park, & D. Y. Seo (Eds.), Proceedings of the 31st International Conference for the Psychology of Mathematics Education (Vol. 3, pp. 161–168). Seoul: The Korea Society of Educational Studies in Mathematics.

    Google Scholar 

  • Leikin, R., & Pitta-Pantazi, D. (Eds.) (2013). Creativity and mathematics education: the state of the art. ZDM - The International Journal on Mathematics Education, 45(2), 159–166.

  • Macgregor, M., & Stacey, K. (1997). Students’ understanding of algebraic notation: 11–15. Educational Studies in Mathematics, 33(1), 1–19‏.

    Article  Google Scholar 

  • Matz, M. (1982). Towards a process model for high-school algebra errors. In D. Sleeman & J. S. Brown (Eds.), Intelligent tutoring systems (pp. 25–50). London: Academic Press.

    Google Scholar 

  • Rojano, T., & Sutherland, R. (2001). Algebraic reasoning with spreadsheets. In Proceedings of the international seminar “Reasoning explanation and proof in school mathematics and their place in the intended curriculum”. Qualifications and Curriculum Authority (pp. 1–16). Cambridge, UK.‏

  • Sak, U., & Maker, C. J. (2006). Developmental variations in children’s creative mathematical thinking as a function of schooling, age, and knowledge. Creativity Research Journal, 18(3), 279–291.

    Article  Google Scholar 

  • Singer, F. M., Ellerton, N., & Cai, J. (Eds.) (2013). Problem-posing research in mathematics education: new questions and directions. Educational Studies in Mathematics, 83(1), 1–7. doi: 10.1007/s10649-013-9478-2.

  • Sternberg, R. J., & Lubart, T. I. (1996). Investing in creativity. American Psychologist, 51, 677–688.

    Article  Google Scholar 

  • Tabach, M., & Friedlander, A. (2008a). Understanding equivalence of symbolic expressions in a spreadsheet-based environment. International Journal of Computers for Mathematical Learning, 13(1), 27–46.

    Article  Google Scholar 

  • Tabach, M., & Friedlander, A. (2008b). The role of context in learning beginning algebra. In C. E. Greens (Ed.), Algebra and algebraic thinking in school mathematics, 2008 yearbook (pp. 223–232). Reston: The National Council of Teachers of Mathematics.

    Google Scholar 

  • Tabach, M., & Friedlander, A. (2013). School mathematics and creativity at the elementary and middle grade level: How are they related? ZDM - The International Journal on Mathematics Education, 45, 227–238. doi:10.1007/s11858-012-0471-5.

    Article  Google Scholar 

  • Tirosh, D., Even, R., & Robinson, N. (1998). Simplifying algebraic expressions: Teacher awareness and teaching approaches. Educational studies in mathematics, 35(1), 51–64.

    Article  Google Scholar 

  • Torrance, E. P. (1974). Torrance tests of creative thinking. Bensenville: Scholastic Testing Service.

    Google Scholar 

  • Usiskin, Z. (1988). Conceptions of school algebra and uses of variables. In A. F. Coxford & A. P. Shulte (Eds.), The ideas of algebra K-12, 1988 yearbook of teachers of mathematics (NCTM) (pp. 8–19). Reston: NCTM.

    Google Scholar 

  • Zazkis, R., & Leikin, R. (2007). Generating examples: From pedagogical tool to a research tool. For the Learning of Mathematics, 27(2), 15–21.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Michal Tabach.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tabach, M., Friedlander, A. Algebraic procedures and creative thinking. ZDM Mathematics Education 49, 53–63 (2017). https://doi.org/10.1007/s11858-016-0803-y

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-016-0803-y

Keywords

Navigation