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Some recent developments on linear determinacy
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:
[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 
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Carlos William CastilloGarsow, "Teaching the Verhulst Model: A Teaching Experiment in Covariational Reasoning and Exponential Growth,", Ph.D thesis, (2010). Google Scholar 
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Carlos William CastilloGarsow, Continuous quantitative reasoning,, in, (2012). Google Scholar 
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Jere Confrey and Erick Smith, Exponential functions, rates of change, and the multiplicative unit,, Educational Studies in Mathematics, 26 (1994), 135. Google Scholar 
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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 
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E. V. Glasersfeld, "Radical Constructivism: A Way of Knowing and Learning,", Falmer Press, (1995). Google Scholar 
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Fernando Hitt and Orlando Planchart, Graphing discrete versus continuous functions: A case study,, In, (1998). Google Scholar 
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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 
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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 
[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 
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Patrick W Thompson, In the absence of meaning,, in, (2013). doi: 10.1007/9781461469773_4. Google Scholar 
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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