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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 99004-2418, 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 Castillo-Chavez, "Mathematical Models in Population Biology and Epidemiology,", Springer, (2000).
|
[3] |
Carlos William Castillo-Garsow, "Teaching the Verhulst Model: A Teaching Experiment in Covariational Reasoning and Exponential Growth,", Ph.D thesis, (2010). Google Scholar |
[4] |
Carlos William Castillo-Garsow, 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. |
[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. |
[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: 10.1007/978-1-4614-6977-3_4. |
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 Castillo-Chavez, "Mathematical Models in Population Biology and Epidemiology,", Springer, (2000).
|
[3] |
Carlos William Castillo-Garsow, "Teaching the Verhulst Model: A Teaching Experiment in Covariational Reasoning and Exponential Growth,", Ph.D thesis, (2010). Google Scholar |
[4] |
Carlos William Castillo-Garsow, 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. |
[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. |
[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: 10.1007/978-1-4614-6977-3_4. |
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