A characterization of dynamic reasoning: Reasoning with time as parameter |
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Authors: | Karen Allen Keene |
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Affiliation: | Department of Mathematics, Science & Technology Education, North Carolina State University, Raleigh, NC 27695, United States |
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Abstract: | Students incorporate and use the implicit and explicit parameter time to support their mathematical reasoning and deepen their understandings as they participate in a differential equations class during instruction on solutions to systems of differential equations. Therefore, dynamic reasoning is defined as developing and using conceptualizations about time as a parameter that implicitly or explicitly coordinates with other quantities to understand and solve problems. Students participate in the following types of mathematical activity related to dynamic reasoning: making time an explicit quantity, using the metaphor of time as “unidimensional space”, using time to reason both quantitatively and qualitatively, using three-dimensional visualization of time related functions, fusing context and representation of time related functions, and using the fictive motion metaphor for function. The purpose of this article is to present a characterization of dynamic reasoning and promote more explicit attention to this type of reasoning by teachers in K-16 mathematics in order to improve student understanding in time related areas of mathematics. |
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Keywords: | Undergraduate mathematics Differential equations Mathematics education Time Motion Dynamic reasoning Parameter |
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