Abstract
The aim of this study is to characterise students’ understanding of the function-derivative relationship when learning economic concepts. To this end, we use a fuzzy metric (Chang 1968) to identify the development of economic concept understanding that is defined by the function-derivative relationship. The results indicate that the understanding of these economic concepts is linked to students’ capacity to perform conversions and treatments between the algebraic and graphic registers of the function-derivative relationship when extracting the economic meaning of concavity/convexity in graphs of functions using the second derivative.
Similar content being viewed by others
References
Ariza, A., & Llinares, S. (2009). The usefulness of derivative concept in learning economic concepts by high school and university students. Enseñanza de las Ciencias, 27(1), 121–136.
Arnold, I. J. M., & Straten, J. T. (2012). Motivation and math skills as determinants of first-year performance in economics. The Journal of Economic Education, 43(1), 33–47.
Arnon, I., Cottrill, J., Dubinksy, E., Oktaç, A., Roa Fuentes, S., Trigueros, M., & Weller, K. (2014). APOS Theory. A framework for research and curriculum development in mathematics education. London: Springer.
Ballard, C. L., & Johnson, F. (2004). Basic math skills and performance in an introductory economics class. The Journal of Economic Education, 35(1), 3–23.
Butler, J. S., Finegan, T. A., & Siegfried, J. J. (1998). Does more calculus improve student learning in intermediate micro-and macroeconomic theory? Journal of Applied Econometrics, 13(2), 185–202.
Chang, C. L. (1968). Fuzzy topological spaces. Journal of Mathematical Analysis and Applications, 24(1), 182–190.
De Bock, D., Van Dooren, W., Janssens, D., & Verschaffel, L. (2007). The illusion of linearity. From analysis to improvement. London: Springer.
Dubinsky, E. (1991). Reflective abstraction in advanced mathematical thinking. In D. Tall (Ed.), Advanced mathematical thinking (pp. 95–123). Dordrecht: Kluwer Academic Publishers.
Duval, R. (1995). Sémiosis et pensée humaine: registres sémiotiques et apprentissages intellectuels Paris: Peter lang [traducción : Semiosis y pensamiento humano. Registros semióticos y aprendizajes intelectuales
Elia, I. (2006). How students conceive function: a triadic conceptual- semiotic model of the understanding of a complex concept. The Montana Mathematics Enthusiast, 3(2), 256–272.
Gagatsis, A., & Shiakalli, M. (2004). Ability to translate from one representation of the concept of function to another and mathematical problem solving. Educational Psychology, 24(5), 645–657.
Gagatsis, A., Elia, I., & Mousoulides, N. (2006). Are registers of representations and problem solving processes on functions compartmentalized in students thinking? Department of Education: University of Cyprus.
Gamer, B., & Gamer, L. (2001). Retention of concepts and skills in traditional and reformed applied calculus. Mathematics Education Research Journal, 13(3), 165–184.
García, M., Llinares, S., & Sánchez-Matamoros, G. (2011). Characterizing thematized derivative schema by the underlying emergent structures. International Journal of Science and Mathematics Education, 9, 1023–1045.
George, A., & Veeramani, P. V. (1994). On some results in fuzzy metric spaces. Fuzzy Sets and Systems, 64, 395–399.
Gery, F. W. (1970). Mathematics and the understanding of economic concepts. The Journal of Economic Education, 2(1), 100–104.
Habre, S., & Abboud, M. (2006). Student’s conceptual understanding of a function and its derivative in an experimental calculus course. The Journal of Mathematical Behavior, 25, 57–72.
Haciomeroglu, E. S., Aspinwall, L., & Presmerg, N. C. (2010). Contrasting cases of calculus Students’ understanding of derivative graphs. Mathematical Thinking and Learning, 12(2), 152–176.
Hey, J. D. (2005). I teach economics, Not algebra and calculus. The Journal of Economic Education, 36(3), 292–304.
Piaget, J. and Garcia, R. (1989). Psychogenesis and the history of science (H. Feider, Trans.). New York: Columbia University Press. (Original work published 1983).
Sánchez-Matamoros, G., García, M., & Llinares, S. (2013). Some indictors of the development of derivative schema. BOLEMA, 27(45), 281–302.
Stamatis, D.H. (2014). Understanding Mathematical Concepts in Finance and Economics. Bookstand Publishing
Vrancken, S., Engler, A. and Müller, D. (2011). Una propuesta para la introducción del concepto de derivada desde la variación: análisis de resultados. Facultad de Ciencias Agrarias - Universidad Nacional del Litoral-Santa Fe (Argentina)
Yoon, Y., & Thomas, M. (2015). Graphical construction of a local perspective on differentiation and integration. Mathematics Education Research Journal, 27(2), 183–200.
Zadeh, L. A. (1965). Fuzzy sets. Inform. Control, 8, 338–353.
Zandieh, M. (2000). A theoretical framework for analyzing student understanding of the concept of derivate. In E. Dubinsky; A. Shoenfeld; J. Kaput (Eds.), Research in Collegiate Mathematics Education IV CBMS Issues in Mathematics Education. Providence, RI: American Mathematical Society, 2000, 103–127.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ariza, A., Llinares, S. & Valls, J. Students’ understanding of the function-derivative relationship when learning economic concepts. Math Ed Res J 27, 615–635 (2015). https://doi.org/10.1007/s13394-015-0156-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13394-015-0156-9