Abstract
This paper suggests that consistently referring to variables as placeholders is an effective countermeasure for addressing a number of the difficulties students’ encounter in learning mathematics. The suggestion is supported by examples discussing ways in which variables are used to express unknown quantities, define functions and express other universal statements, and serve as generic elements in mathematical discourse. In addition, making greater use of the term “dummy variable” and phrasing statements both with and without variables may help students avoid mistakes that result from misinterpreting the scope of a bound variable.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Dieudonné, J.: Abstraction in mathematics and the evolution of algebra. In: Lamon, W. (ed.) Learning and the Nature of Mathematics, pp. 102–103. SRA Associates, Inc., Chicago (1972)
Frege, G.: The Basic Laws of Arithmetic: Exposition of the System (Translated and edited by M. Furth). University of California Press, Berkeley (1964)
Klein, F.: Elementary Mathematics from an Advanced Standpoint (Translated from the 3rd German edition by Hedrick, E.R. and Noble, C.A.). Dover Publications, New York (1924)
Quine, W.V.O.: Methods of Logic, 4th edn. Harvard University Press, Cambridge (1982)
Tarski, A.: Intrtoduction to Logic and to the Methodology of Deductive Sciences. Oxford University Press, New York (1941)
Whitehead, A.N.: An Introduction to Mathematics. Henry Holt and Co., New York (1911)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Epp, S.S. (2011). Variables in Mathematics Education. In: Blackburn, P., van Ditmarsch, H., Manzano, M., Soler-Toscano, F. (eds) Tools for Teaching Logic. TICTTL 2011. Lecture Notes in Computer Science(), vol 6680. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21350-2_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-21350-2_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21349-6
Online ISBN: 978-3-642-21350-2
eBook Packages: Computer ScienceComputer Science (R0)