
Previous Article
Some recent developments on linear determinacy
 MBE Home
 This Issue

Next Article
The basic reproduction number $R_0$ and effectiveness of reactive interventions during dengue epidemics: The 2002 dengue outbreak in Easter Island, Chile
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 
[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 
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 
[1] 
Dalibor Pražák. Exponential attractor for the delayed logistic equation with a nonlinear diffusion. Conference Publications, 2003, 2003 (Special) : 717726. doi: 10.3934/proc.2003.2003.717 
[2] 
Farid Tari. Geometric properties of the integral curves of an implicit differential equation. Discrete & Continuous Dynamical Systems  A, 2007, 17 (2) : 349364. doi: 10.3934/dcds.2007.17.349 
[3] 
Michael Scheutzow. Exponential growth rate for a singular linear stochastic delay differential equation. Discrete & Continuous Dynamical Systems  B, 2013, 18 (6) : 16831696. doi: 10.3934/dcdsb.2013.18.1683 
[4] 
Luis Caffarelli, Serena Dipierro, Enrico Valdinoci. A logistic equation with nonlocal interactions. Kinetic & Related Models, 2017, 10 (1) : 141170. doi: 10.3934/krm.2017006 
[5] 
Ulrike Kant, Werner M. Seiler. Singularities in the geometric theory of differential equations. Conference Publications, 2011, 2011 (Special) : 784793. doi: 10.3934/proc.2011.2011.784 
[6] 
J. GarcíaMelián, Julio D. Rossi. A logistic equation with refuge and nonlocal diffusion. Communications on Pure & Applied Analysis, 2009, 8 (6) : 20372053. doi: 10.3934/cpaa.2009.8.2037 
[7] 
John A. D. Appleby, John A. Daniels. Exponential growth in the solution of an affine stochastic differential equation with an average functional and financial market bubbles. Conference Publications, 2011, 2011 (Special) : 91101. doi: 10.3934/proc.2011.2011.91 
[8] 
Qingxu Dou, Jesús Cuevas, J. C. Eilbeck, Francis Michael Russell. Breathers and kinks in a simulated crystal experiment. Discrete & Continuous Dynamical Systems  S, 2011, 4 (5) : 11071118. doi: 10.3934/dcdss.2011.4.1107 
[9] 
Antonio Suárez. A logistic equation with degenerate diffusion and Robin boundary conditions. Communications on Pure & Applied Analysis, 2008, 7 (5) : 12551267. doi: 10.3934/cpaa.2008.7.1255 
[10] 
JianWen Sun, WanTong Li, ZhiCheng Wang. A nonlocal dispersal logistic equation with spatial degeneracy. Discrete & Continuous Dynamical Systems  A, 2015, 35 (7) : 32173238. doi: 10.3934/dcds.2015.35.3217 
[11] 
Eugenio Montefusco, Benedetta Pellacci, Gianmaria Verzini. Fractional diffusion with Neumann boundary conditions: The logistic equation. Discrete & Continuous Dynamical Systems  B, 2013, 18 (8) : 21752202. doi: 10.3934/dcdsb.2013.18.2175 
[12] 
Anna Doubova, Enrique FernándezCara. Some geometric inverse problems for the linear wave equation. Inverse Problems & Imaging, 2015, 9 (2) : 371393. doi: 10.3934/ipi.2015.9.371 
[13] 
AnneSophie de Suzzoni. Continuity of the flow of the BenjaminBonaMahony equation on probability measures. Discrete & Continuous Dynamical Systems  A, 2015, 35 (7) : 29052920. doi: 10.3934/dcds.2015.35.2905 
[14] 
Samia Challal, Abdeslem Lyaghfouri. Hölder continuity of solutions to the $A$Laplace equation involving measures. Communications on Pure & Applied Analysis, 2009, 8 (5) : 15771583. doi: 10.3934/cpaa.2009.8.1577 
[15] 
Nikolay A. Gusev. On the onedimensional continuity equation with a nearly incompressible vector field. Communications on Pure & Applied Analysis, 2019, 18 (2) : 559568. doi: 10.3934/cpaa.2019028 
[16] 
Shouwen Fang, Peng Zhu. Differential Harnack estimates for backward heat equations with potentials under geometric flows. Communications on Pure & Applied Analysis, 2015, 14 (3) : 793809. doi: 10.3934/cpaa.2015.14.793 
[17] 
Eugenii Shustin. Exponential decay of oscillations in a multidimensional delay differential system. Conference Publications, 2003, 2003 (Special) : 809816. doi: 10.3934/proc.2003.2003.809 
[18] 
Hammamia Mohamed Ali, Lassaad Mchiria, Sana Netchaoui, Stefanie Sonner. Pullback exponential attractors for differential equations with variable delays. Discrete & Continuous Dynamical Systems  B, 2017, 22 (11) : 119. doi: 10.3934/dcdsb.2019183 
[19] 
Kei Matsuura, Mitsuharu Otani. Exponential attractors for a quasilinear parabolic equation. Conference Publications, 2007, 2007 (Special) : 713720. doi: 10.3934/proc.2007.2007.713 
[20] 
Luis Silvestre. Hölder continuity for integrodifferential parabolic equations with polynomial growth respect to the gradient. Discrete & Continuous Dynamical Systems  A, 2010, 28 (3) : 10691081. doi: 10.3934/dcds.2010.28.1069 
2018 Impact Factor: 1.313
Tools
Metrics
Other articles
by authors
[Back to Top]