Commenced in January 2007
Paper Count: 31108
Theory of Fractions in College Algebra Course
Authors: Alexander Y. Vaninsky
Abstract:The paper compares the treatment of fractions in a typical undergraduate college curriculum and in abstract algebra textbooks. It stresses that the main difference is that the undergraduate curriculum treats equivalent fractions as equal, and this treatment eventually leads to paradoxes and impairs the students- ability to perceive ratios, proportions, radicals and rational exponents adequately. The paper suggests a simplified version of rigorous theory of fractions suitable for regular college curriculum.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1331329Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1283
 I. Arnon, P. Nesher, and R. Nirenburg. " What can be learnt about fractions only with computers." In: O. Zaslavsky 23rd Conference of the International Group for the Psychology of Mathematics Education (PME-23, 1999). 2, 33-40.
 W. Baker, "The Complexities of Complex numbers." Working paper. Mathematics Journal, Spring 2006, 1-2. Hostos Community College, Bronx, NY.
 P. Bland, The Basics of Abstract Algebra. NY: W.H. Freeman, 2002.
 S. Gordon, S. " What-s Wrong with College Algebra." Primus, 2008, 18(6), 516 - 541.
 R. Philipp, B. Schappelle. "Algebra as Generalized Arithmetic: Starting with the Known for a Change. Preview." Mathematics Teacher, 1999, 92(4), 310 - 316.
 E. Sheinerman. Mathematics. A Discrete Introduction. 2nd Ed. CA: Thomson Brooks/Cole, 2006.
 T. Shifrin. Abstract Algebra: A Geometric Approach. NJ: Prentice Hall, 1996.
 L. Streefland, Fractions in Realistic Mathematics Education: A Paradigm of Developmental Research. MA: Kluwer. 1991
 H. Wu. "The Mis-Education of Mathematics Teachers." Notices of the American Mathematical Society, 2011, 58(2), 372 - 384.