Reasoning about variation in the intensity of change in covarying quantities involved in rate of change
Reasoning about variation in the intensity of change in covarying quantities involved in rate of change
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DOI：
10.1016/j.jmathb.2012.01.001
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发表时间：
2012-09-01
影响因子：
1.7
通讯作者：
Johnson, Heather L.
中科院分区：
文献类型：
--
作者：
Johnson, Heather L.
本文扩展了与变化率相关的定量推理领域的工作，通过研究涉及多个共变量表示的任务中涉及变化率的共变量的数值和非数值推理。研究结果表明，通过系统地改变一个量，一个人可以同时参加的变化强度的变化，在一个量，表明协变量之间的关系。结果记录了一个中学生如何在微积分正式教学之前，以数学上强大但不基于比率的方式，对变化率中涉及的协变量进行数值和非数值推理。我将讨论如何协调协变和转换推理支持参加变化的变化率中所涉及的数量的变化强度。(C)2012 Elsevier Inc. All rights reserved.
This paper extends work in the area of quantitative reasoning related to rate of change by investigating numerical and nonnumerical reasoning about covarying quantities involved in rate of change via tasks involving multiple representations of covarying quantities. The findings suggest that by systematically varying one quantity, an individual could simultaneously attend to variation in the intensity of change in a quantity indicating a relationship between covarying quantities. The results document how a secondary student, prior to formal instruction in calculus, reasoned numerically and nonnumerically about covarying quantities involved in rate of change in a way that was mathematically powerful and yet not ratio-based. I discuss how coordinating covariational and transformational reasoning supports attending to variation in the intensity of change in quantities involved in rate of change. (C) 2012 Elsevier Inc. All rights reserved.