Abstract
Mathematical modelling begins in the early primary grades even though the language and ideas of mathematical modelling are not employed. The common arithmetic operations are mathematical models for various counting and measure situations found in the real world. These models parallel the theoretical properties of the operations and provide the basis for more sophisticated mathematical models found in algebra, geometry, analysis, and statistics. The advantages of drawing attention early in instruction to modelling acts involving arithmetic operations are outlined.
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
Blum, W. (1991). Applications and modelling in mathematics teaching: A review of arguments and instructional aspects. In M. Niss, W. Blum, & I. Huntley (Eds.), Teaching of mathematical modelling and applications (pp. 10–29). Chichester: Ellis Horwood.
Davis, P.J., & Hersh, R. (1981). The mathematical experience. Boston: Birkhauser.
De Bock, D., Van Dooren, W., & Janssens, D. (2005). Studying and remedying students’ modelling competencies: Routine versus adaptive expertise. This volume, Chapter 3.3.3.
Dossey, J.A., McCrone, S., Giordano, F.R., & Weir, M.D. (2002). Mathematics methods and modelling for today’s mathematics classroom. Pacific Grove, CA: Brooks/Cole.
Greer, B. (1992). Multiplication and division as models of situations. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 276–295). New York: Macmillan.
Harel, G., & Confrey, J. (Eds.). (1994). The development of multiplicative reasoning in the learning of mathematics. Albany, NY: State University of New York Press.
Meerschaert, M. M. (1993). Mathematical modeling. New York: Academic Press.
Nesher, P. (1980). The stereotyped nature of school word problems. For the Learning of Mathematics 1(1), 41–48.
Sutherland, E. (1947). One-step problem patterns and their relation to problem solving in arithmetic. Contributions to Education, No 925. New York: Teachers College, Columbia University.
University of Chicago School Mathematics Project (2002): Transition mathematics. Glenview, IL: Prentice Hall.
Usiskin, Z., & Bell, M. (1983). Applying arithmetic: A handbook of applications of arithmetic. Volume II: Operations. Arithmetic and Its Applications Project, ERIC document ED 264 088, Chicago, IL.
Verschaffel, L. (2002). Taking the modelling perspective seriously at the elementary school level: Promises and pitfalls [Plenary talk]. In A.D. Cockburn, & E. Nardi (Eds.), Proceedings of the 26th Annual Conference of the International Group for the Psychology of Mathematics Educatio. Norwich, England: University of East Anglia.
Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Lisse, The Netherlands: Swets and Zeitlinger.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Usiskin, Z. (2007). The Arithmetic Operations as Mathematical Models. In: Blum, W., Galbraith, P.L., Henn, HW., Niss, M. (eds) Modelling and Applications in Mathematics Education. New ICMI Study Series, vol 10. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-29822-1_27
Download citation
DOI: https://doi.org/10.1007/978-0-387-29822-1_27
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-29820-7
Online ISBN: 978-0-387-29822-1
eBook Packages: Humanities, Social Sciences and LawEducation (R0)