And the Rest is Just Algebra pp 3-18 | Cite as

# Algebra Underperformances at College Level: What Are the Consequences?

Chapter

First Online:

## 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

- Adelman, C. (2006).
*The toolbox revisited: Paths to degree completion from high school through college*. Washington, DC: U.S. Department of Education.Google Scholar - Ashlock, R. B. (2010).
*Error patterns in computation: Using error patterns to improve instruction*. Boston: Allyn & Bacon.Google Scholar - 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 - 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 - 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 - 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 - Cornu, B. (1991). Limits. In D. Tall (Ed.),
*Advanced mathematical thinking*(pp. 153–166). Boston: Kluwer.Google Scholar - De Morgan, A. (1910).
*On the study and difficulties of mathematics*. Chicago: Open Court.Google Scholar - 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 - 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 - Harel, G., Fuller, E., & Rabin, J. (2008). Attention to meaning by algebra teachers.
*The Journal of Mathematical Behavior, 27*, 116–127.CrossRefGoogle Scholar - 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 - 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 - 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 - Mason, J. (2002).
*Mathematics teaching practice: A guidebook for university and college lecturers*. Chichester: Horwood.CrossRefGoogle Scholar - 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 - Rice, J. A. (2007).
*Mathematical statistics and data analysis*(3rd ed.). California: Thomson, Brooks/Cole.Google Scholar - 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 - 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 - 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 - Stewart, J. (2014).
*Calculus*(8th ed.). Boston: Cengage Learning.Google Scholar - 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 - Williams, S. (1991). Models of limit held by college calculus students.
*Journal for Research in Mathematics Education, 22*, 219–236.CrossRefGoogle Scholar - Wu, H. (2001). How to prepare students for algebra.
*American Educator, 25*(2), 10–17.Google Scholar

## Copyright information

© Springer International Publishing Switzerland 2017