Advertisement

Algebra Underperformances at College Level: What Are the Consequences?

  • Sepideh StewartEmail author
  • Stacy Reeder
Chapter

Abstract

Many college instructors consider the final problem-solving steps in their respective disciplines as “just algebra”; however, for many college students, a weak foundation in algebra seems to be a source of significant struggle with solving a variety of mathematics problems. The purpose of this chapter is to reveal some typical algebra errors that subsequently plague students’ abilities to succeed in higher-level mathematics courses. The early detection and mindfulness of these errors will aid in the creation of a model for intervention that is specifically designed for students’ needs in each course.

Keywords

Algebra Common errors Undergraduate mathematics Student difficulties, calculus, college mathematics 

References

  1. Adelman, C. (2006). The toolbox revisited: Paths to degree completion from high school through college. Washington, DC: U.S. Department of Education.Google Scholar
  2. Ashlock, R. B. (2010). Error patterns in computation: Using error patterns to improve instruction. Boston: Allyn & Bacon.Google Scholar
  3. Benander, L., & Clement, J. (1985). Catalogue of error patterns observed in courses on basic mathematics. Working Draft. Massachusetts: (ERIC Document Reproduction Service No. ED 287 672).Google Scholar
  4. Booth, J. L., Barbieri, C., Eyer, F., & Paré-Blagoev, E. J. (2014). Persistent and pernicious errors in algebraic problem solving. The Journal of Problem Solving, 7(1), 3.CrossRefGoogle Scholar
  5. Booth, J. L., & Newton, K. J. (2012). Fractions: Could they really be the gatekeeper’s doorman? Contemporary Educational Psychology, 37(4), 247–253.CrossRefGoogle Scholar
  6. Brown, G., & Quinn, R. J. (2007). Fraction proficiency and success in algebra: What does research say? Australian Mathematics Teacher, 63(3), 23–30.Google Scholar
  7. Cornu, B. (1991). Limits. In D. Tall (Ed.), Advanced mathematical thinking (pp. 153–166). Boston: Kluwer.Google Scholar
  8. De Morgan, A. (1910). On the study and difficulties of mathematics. Chicago: Open Court.Google Scholar
  9. Drouhard, J. P., & Teppo, A. R. (2004). Symbols and language. In The future of the teaching and learning of algebra the 12th ICMI study (pp. 225–264). Boston: Kluwer.CrossRefGoogle Scholar
  10. Harel, G. (2007). The DNR system as a conceptual framework for curriculum development in instruction. In R. Lesh, J. Kaput, & E. Hamilton (Eds.), Foundations for the future in mathematics education. New Jersey: Erlbaum.Google Scholar
  11. Harel, G., Fuller, E., & Rabin, J. (2008). Attention to meaning by algebra teachers. The Journal of Mathematical Behavior, 27, 116–127.CrossRefGoogle Scholar
  12. Harel, G., & Sowder, L. (2005). Advanced mathematical-thinking at any age: Its nature and its development. Mathematical Thinking and Learning, 7, 27–50.CrossRefGoogle Scholar
  13. Hoch, M., & Dreyfus, T. (2004). Structure sense in high school algebra: The effects of brackets. In M. J. Hoines & A. B. Fuglestad (Eds.), Proceedings of the 28th conference of the international group for the psychology of mathematics education (Vol. 3, pp. 49–56). Bergen, Norway: PME.Google Scholar
  14. 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
  15. Mason, J. (2002). Mathematics teaching practice: A guidebook for university and college lecturers. Chichester: Horwood.CrossRefGoogle Scholar
  16. Oehrtman, M. (2002). Collapsing dimensions, physical limitation, and other student metaphors for limit concepts: An instrumentalist investigation into calculus students’ spontaneous reasoning, Ph.D. dissertation.Google Scholar
  17. Rice, J. A. (2007). Mathematical statistics and data analysis (3rd ed.). California: Thomson, Brooks/Cole.Google Scholar
  18. Sfard, A., & Linchevski, L. (1994). The gains and the pitfalls of reification—The case of algebra. Educational Studies in Mathematics, 26(2), 191–228.CrossRefGoogle Scholar
  19. Stacey, K., Chick, H., & Kendal, M. (Eds.). (2004). The future of the teaching and learning of algebra: The 12th ICMI study (Vol. 8). New York: Springer.Google Scholar
  20. Stein, M. K., Kaufman, J. H., Sherman, M., & Hillen, A. F. (2011). Algebra a challenge at the crossroads of policy and practice. Review of Educational Research, 81(4), 453–492.Google Scholar
  21. Stewart, J. (2014). Calculus (8th ed.). Boston: Cengage Learning.Google Scholar
  22. U.S. Department of Education, National Center for Education Statistics. (2004). The condition of education 2004 (NCES 2004–077). Washington, DC: U.S. Government Printing Office.Google Scholar
  23. Williams, S. (1991). Models of limit held by college calculus students. Journal for Research in Mathematics Education, 22, 219–236.CrossRefGoogle Scholar
  24. Wu, H. (2001). How to prepare students for algebra. American Educator, 25(2), 10–17.Google Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of OklahomaNormanUSA
  2. 2.University of OklahomaNormanUSA

Personalised recommendations