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.
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REFERENCES
Borasi, R.: 1992, Learning Mathematics Through Inquiry, Protsmouth, NH: Heinemann Educational Books.
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.
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).
Goren, J.: 1994, Algebra (2nd edition), Tel-Aviv, Israel: Goren's Pub (in Hebrew).
Larson, R.E. and Hostetler, R.P.: 1993, College Algebra (3rd edition), D.C.: Heath.
Sfard, A., Katorza, D., Amitsur, S. and Maschler, M.: 1983, Analysis. Jerusalem, Israel: The Israeli Center of Science Education, The Hebrew University (in Hebrew).
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.
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.
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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
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DOI: https://doi.org/10.1023/A:1002916606955