The role of multiple modeling perspectives in students' learning of exponential growth
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 a...
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| Format: | Article |
| Language: | English |
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AIMS Press
2013-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1437 |
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| author | Carlos Castillo-Garsow |
| author_facet | Carlos Castillo-Garsow |
| author_sort | Carlos Castillo-Garsow |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-9223c37749c2424e8466b9988c6968eb |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-9223c37749c2424e8466b9988c6968eb2025-01-24T02:26:34ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-07-01105&61437145310.3934/mbe.2013.10.1437The role of multiple modeling perspectives in students' learning of exponential growthCarlos Castillo-Garsow0Mathematics Department, Kingston Hall 216, Eastern Washington University, Cheney, WA 99004-2418The 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.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1437logisticcontinuitycovariation.geometricdifferential equationexponentialteaching experiment |
| spellingShingle | Carlos Castillo-Garsow The role of multiple modeling perspectives in students' learning of exponential growth Mathematical Biosciences and Engineering logistic continuity covariation. geometric differential equation exponential teaching experiment |
| title | The role of multiple modeling perspectives in students' learning of exponential growth |
| title_full | The role of multiple modeling perspectives in students' learning of exponential growth |
| title_fullStr | The role of multiple modeling perspectives in students' learning of exponential growth |
| title_full_unstemmed | The role of multiple modeling perspectives in students' learning of exponential growth |
| title_short | The role of multiple modeling perspectives in students' learning of exponential growth |
| title_sort | role of multiple modeling perspectives in students learning of exponential growth |
| topic | logistic continuity covariation. geometric differential equation exponential teaching experiment |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1437 |
| work_keys_str_mv | AT carloscastillogarsow theroleofmultiplemodelingperspectivesinstudentslearningofexponentialgrowth AT carloscastillogarsow roleofmultiplemodelingperspectivesinstudentslearningofexponentialgrowth |