Skip to main content
Log in

To Define Or Not To Define: The Case Of (-8)1/3

  • Published:
Educational Studies in Mathematics Aims and scope Submit manuscript

Abstract

This paper discusses two possible approaches to (-8)1/3. The first is that (-8)1/3 = 3√(-8) = -2. The second is that (-8)1/3 is undefined. The pros and cons of each of these approaches are considered and some implications to teacher education are specified.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  • Borasi, R.: 1992, Learning Mathematics Through Inquiry, Protsmouth, NH: Heinemann Educational Books.

    Google Scholar 

  • Dugopolski, M.: 1995, College Algebra, Addison-Wesley.

  • Even, R. and Tirosh, D.: 1995, ‘Subject-matter knowledge and knowledge about students as sources of teacher presentations of the subject matter’, Educational Studies in Mathematics 29, 1–19.

    Article  Google Scholar 

  • Goel, S.K. and Robillard, M.S.: 1996, ‘The equation \(- 2 = ( - 8)^{\tfrac{1} {3}} = ( - 8)^{\tfrac{2} {6}} = [( - 8)^2 ]^{\tfrac{1} {6}} = 2\)’, Educational Studies in Mathematics.

  • Goren, J.: 1990, Algebra (1st edition), Tel-Aviv, Israel: Goren's Pub (in Hebrew).

    Google Scholar 

  • Goren, J.: 1994, Algebra (2nd edition), Tel-Aviv, Israel: Goren's Pub (in Hebrew).

    Google Scholar 

  • Larson, R.E. and Hostetler, R.P.: 1993, College Algebra (3rd edition), D.C.: Heath.

    Google Scholar 

  • Sfard, A., Katorza, D., Amitsur, S. and Maschler, M.: 1983, Analysis. Jerusalem, Israel: The Israeli Center of Science Education, The Hebrew University (in Hebrew).

    Google Scholar 

  • Senk, S.L., Thompson, D.T., Viktora, S.S., Rubenstein, R.N., Halvorson, J., Flanders, J., Jakucyn, N., Pillsbury, G. and Usiskin, Z.: 1990, Advanced Algebra (1st edition), Glenview, Illinois: Scott, Foresman and Company.

    Google Scholar 

  • Senk, S.L., Thompson, D.T., Viktora, S.S., Usiskin, Z., Ahbel, N.P., Levin, S., Weinhold, M.L., Rubenstein, R.N., Halvorson, J., Flanders, J., Jakucyn, N. and Pillsbury: 1996, Advanced Algebra (2nd edition), Glenview, Illinois: Scott, Foresman and Company.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tirosh, D., Even, R. To Define Or Not To Define: The Case Of (-8)1/3 . Educational Studies in Mathematics 33, 321–330 (1997). https://doi.org/10.1023/A:1002916606955

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1002916606955

Keywords

Navigation