Together yet separate: Students’ associating amounts of change in quantities involved in rate of change
Together yet separate: Students’ associating amounts of change in quantities involved in rate of change
复制标题
在一起但又分开：学生将变化量与变化率所涉及的数量联系起来
DOI：
--
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
H. Johnson
中科院分区：
文献类型：
--
作者：
H. Johnson
本文推广了有关变化率协变量的定量推理工作。它报告了一个多案例研究的三个学生的推理量的变化率时，工作的任务，包括多种表示的协变量。当解释相关金额之间的关系时，学生们确定了部分（例如，图表上的间隔），在此期间，他们可以比较数量的变化量。虽然这样的推理对于将笛卡尔图解释为共变量的表示是有用的，但是它没有促进对共变量的变化强度的变化的关注（例如，减少的增长）。关注学生在协变量变化量之间的关系可能会进一步深入了解学生如何对变化率有一个强有力的理解。
This paper extends work about quantitative reasoning related to covarying quantities involved in rate of change. It reports a multiple case study of three students’ reasoning about quantities involved in rate of change when working on tasks incorporating multiple representations of covarying quantities. When interpreting relationships between associated amounts, students identified sections (e.g., an interval on a graph) in which they could make comparisons between amounts of change in quantities. Although such reasoning is useful for interpreting a Cartesian graph as a representation of covarying quantities, it does not foster attention to variation in the intensity of change in covarying quantities (e.g., a decreasing increase). Focusing on the kinds of relationships students make between amounts of change in covarying quantities might provide further insight into how students could develop a robust understanding of rate of change.