### Mathematical Biosciences and Engineering

2013, Issue 5&6: 1437-1453. doi: 10.3934/mbe.2013.10.1437

# The role of multiple modeling perspectives in students' learning of exponential growth

• Received: 01 October 2012 Accepted: 29 June 2018 Published: 01 August 2013
• MSC : Primary: 97M60, 97M30; Secondary: 92B05.

• The exponential is among the most important family functions in mathematics; the foundation for the solution of linear differential equations, linear difference equations, and stochastic processes. However there is little research and superficial agreement on how the concepts of exponential growth are learned and/or should be taught initially. In order to investigate these issues, I preformed a teaching experiment with two high school students, which focused on building understandings of exponential growth leading up to the (nonlinear) logistic differential equation model. In this paper, I highlight some of the ways of thinking used by participants in this teaching experiment. From these results I discuss how mathematicians using exponential growth routinely make use of multiple --- sometimes contradictory --- ways of thinking, as well as the danger that these multiple ways of thinking are not being made distinct to students.

Citation: Carlos Castillo-Garsow. The role of multiple modeling perspectives in students' learning of exponential growth[J]. Mathematical Biosciences and Engineering, 2013, 10(5&6): 1437-1453. doi: 10.3934/mbe.2013.10.1437

### Related Papers:

• The exponential is among the most important family functions in mathematics; the foundation for the solution of linear differential equations, linear difference equations, and stochastic processes. However there is little research and superficial agreement on how the concepts of exponential growth are learned and/or should be taught initially. In order to investigate these issues, I preformed a teaching experiment with two high school students, which focused on building understandings of exponential growth leading up to the (nonlinear) logistic differential equation model. In this paper, I highlight some of the ways of thinking used by participants in this teaching experiment. From these results I discuss how mathematicians using exponential growth routinely make use of multiple --- sometimes contradictory --- ways of thinking, as well as the danger that these multiple ways of thinking are not being made distinct to students.

 [1] Third edition, Blackwell Science, 1996. [2] Springer, New York, 2000. [3] Ph.D thesis, Arizona State University, Tempe, AZ, 2010. [4] in "Quantitative Reasoning and Mathematical Modeling: A Driver for STEM Integrated Education and Teaching in Context" (eds. R. Mayes, R. Bonillia, L. L. Hatfield and S. Belbase), WISDOMe Monographs, Vol. 2, University of Wyoming Press, Laramie, WY, 2012. [5] Educational Studies in Mathematics, 26 (1994), 135-164. [6] Journal for Research in Mathematics Education, 26 (1995), 66-86. [7] Falmer Press, London, 1995. [8] In "Proceedings of the 20th Annual meeting of PME-NA," ERIC, Columbus, 1998. [9] Review of Educational Research, 60 (1990), 1-64. [10] Sixth edition, John Murray, London, 1826. [11] Ph.D thesis, Arizona State University, 2010. [12] in "Quantitative reasoning and Mathematical modeling: A driver for STEM Integrated Education and Teaching in Context" (eds. R. Mayes, R. Bonillia, L. L. Hatfield and S. Belbase), WISDOMe Monographs, Vol. 2, University of Wyoming Press, Laramie, WY, 2012. [13] in "Research Design in Mathematics and Science Education" (eds. R. Lesh and A. E. Kelly), Erlbaum, Hillsdale, NJ, (2000), 267-307. [14] Ph.D thesis, Arizona State University, 2008. [15] in "Proceedings of the Annual Meeting of the International Group for the Psychology of Mathematics Education" (eds. O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano and A. Sepulveda), Vol. 1, PME, Morelia, Mexico, (2008), 45-64. [16] in "Vital Directions for Mathematics Education Research" (ed. K. Leatham), Springer, New York, 2013.
###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

1.285 1.3