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The role of multiple modeling perspectives in students' learning of exponential growth
1.  Mathematics Department, Kingston Hall 216, Eastern Washington University, Cheney, WA 990042418, United States 
References:
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Fred Brauer and Carlos CastilloChavez, "Mathematical Models in Population Biology and Epidemiology,", Springer, (2000). Google Scholar 
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E. V. Glasersfeld, "Radical Constructivism: A Way of Knowing and Learning,", Falmer Press, (1995). Google Scholar 
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T. R. Malthus, "An Essay on the Principle of Population,", Sixth edition, (1826). Google Scholar 
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Kevin C. Moore, "The Role of Quantitative Reasoning in Precalculus Students Learning Central Concepts of Trigonometry,", Ph.D thesis, (2010). Google Scholar 
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Kevin C. Moore, Coherence, quantitative reasoning, and the trigonometry of students,, in, (2012). Google Scholar 
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L. P. Steffe and Patrick W Thompson, Teaching experiment methodology: Underlying principles and essential elements,, in, (2000), 267. Google Scholar 
[14] 
April Strom, "A Case Study of a Secondary Mathematics Teacher'S Understanding of Exponential Function: An Emerging Theoretical Framework,", Ph.D thesis, (2008). Google Scholar 
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Patrick W. Thompson, Conceptual analysis of mathematical ideas: Some spadework at the foundation of mathematics education,, in, (2008), 45. Google Scholar 
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show all references
References:
[1] 
M. Begon, J. L. Harper and C. R. Townsend, "Ecology: Individuals, Populations and Communities,", Third edition, (1996). Google Scholar 
[2] 
Fred Brauer and Carlos CastilloChavez, "Mathematical Models in Population Biology and Epidemiology,", Springer, (2000). Google Scholar 
[3] 
Carlos William CastilloGarsow, "Teaching the Verhulst Model: A Teaching Experiment in Covariational Reasoning and Exponential Growth,", Ph.D thesis, (2010). Google Scholar 
[4] 
Carlos William CastilloGarsow, Continuous quantitative reasoning,, in, (2012). Google Scholar 
[5] 
Jere Confrey and Erick Smith, Exponential functions, rates of change, and the multiplicative unit,, Educational Studies in Mathematics, 26 (1994), 135. Google Scholar 
[6] 
Jere Confrey and Erick Smith, Splitting, covariation, and their role in the development of exponential functions,, Journal for Research in Mathematics Education, 26 (1995), 66. doi: 10.2307/749228. Google Scholar 
[7] 
E. V. Glasersfeld, "Radical Constructivism: A Way of Knowing and Learning,", Falmer Press, (1995). Google Scholar 
[8] 
Fernando Hitt and Orlando Planchart, Graphing discrete versus continuous functions: A case study,, In, (1998). Google Scholar 
[9] 
G. Leinhardt, O. Zaslavsky and M. K. Stein, Functions, graphs, and graphing: Tasks, learning, and teaching,, Review of Educational Research, 60 (1990), 1. doi: 10.3102/00346543060001001. Google Scholar 
[10] 
T. R. Malthus, "An Essay on the Principle of Population,", Sixth edition, (1826). Google Scholar 
[11] 
Kevin C. Moore, "The Role of Quantitative Reasoning in Precalculus Students Learning Central Concepts of Trigonometry,", Ph.D thesis, (2010). Google Scholar 
[12] 
Kevin C. Moore, Coherence, quantitative reasoning, and the trigonometry of students,, in, (2012). Google Scholar 
[13] 
L. P. Steffe and Patrick W Thompson, Teaching experiment methodology: Underlying principles and essential elements,, in, (2000), 267. Google Scholar 
[14] 
April Strom, "A Case Study of a Secondary Mathematics Teacher'S Understanding of Exponential Function: An Emerging Theoretical Framework,", Ph.D thesis, (2008). Google Scholar 
[15] 
Patrick W. Thompson, Conceptual analysis of mathematical ideas: Some spadework at the foundation of mathematics education,, in, (2008), 45. Google Scholar 
[16] 
Patrick W Thompson, In the absence of meaning,, in, (2013). doi: 10.1007/9781461469773_4. Google Scholar 
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