Understanding the use of two integration methods on separable first order differential equations
arXiv:0902.0748, submitted to Physical Review Special Topics - Physics Education Research
Katrina E. Black, Michael C. Wittmann
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.