An Exponential Growth Learning Trajectory: Students' Emerging Understanding of Exponential Growth Through Covariation
An Exponential Growth Learning Trajectory: Students' Emerging Understanding of Exponential Growth Through Covariation
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DOI：
10.1080/10986065.2016.1183090
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发表时间：
2016-01-01
影响因子：
1.6
通讯作者：
Amidon, Joel
中科院分区：
文献类型：
--
作者：
Ellis, Amy B.;Ozgur, Zekiye;Amidon, Joel
本文提出了一种指数增长学习轨迹(EGLT)，该轨迹识别和表征了初中生由于强调协变而对指数增长的初始和发展理解。EGLT解释了学生随着时间的推移对一系列任务和活动的思考和学习，这些任务和活动是为了产生一种指数增长的观点，即两个连续协变的量之间的关系。从两个早期青少年的教学实验中发展出来的EGLT确定了学生概念发展的三个主要阶段：前功能推理、协变观点和对应观点。学习轨迹与三个学生在轨迹中的进展一起展示，以此来说明参与者如何理解指数增长的想法。
This article presents an Exponential Growth Learning Trajectory (EGLT), a trajectory identifying and characterizing middle grade students' initial and developing understanding of exponential growth as a result of an instructional emphasis on covariation. The EGLT explicates students' thinking and learning over time in relation to a set of tasks and activities developed to engender a view of exponential growth as a relation between two continuously covarying quantities. Developed out of two teaching experiments with early adolescents, the EGLT identifies three major stages of students' conceptual development: prefunctional reasoning, the covariation view, and the correspondence view. The learning trajectory is presented along with three individual students' progressions through the trajectory as a way to illustrate the variation present in how the participants made sense of ideas about exponential growth.