理解两种积分方法在可分一阶微分方程中的应用
Understanding the use of two integration methods on separable first order differential equations
摘要：
我们提出的证据，从三个学生的互动，其中两种类型的常见的解决方法，用于解决简单的一阶微分方程。我们使用资源的语言来描述这些，考虑认知游戏作为沿着包含链接的程序和概念资源的资源图的解决方案的特定途径。使用成绩单数据，我们定义了几个程序资源，显示它们如何可以组织成两个方面的先前描述的认知游戏，并产生一个资源图，允许可视化的认知游戏的这一部分。通过代表两个正确的数学程序的共享资源，我们帮助澄清的思维类型，学生从事学习时，将数学推理应用到物理和说明如何“失败连接”两个想法往往会阻碍学生的成功解决问题。
英文摘要：
We present evidence from three student interactions in which two types of common solution methods for solving simple first-order differential equations are used. We describe these using the language of resources, considering epistemic games as particular pathways of solutions along resource graphs containing linked procedural and conceptual resources. Using transcript data, we define several procedural resources, show how they can be organized into two facets of a previously described epistemic game, and produce a resource graph that allows visualization of this portion of the epistemic games. By representing two correct mathematical procedures in terms of shared resources, we help clarify the types of thinking in which students engage when learning to apply mathematical reasoning to physics and illustrate how a "failure to connect" two ideas often hinders students' successful problem solving.
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