Understanding the use of two integration methods on separable first order differential equations

TL;DR

This study investigates how students use two common solution methods for simple first-order differential equations, analyzing their reasoning processes and identifying challenges in connecting ideas during problem solving.

Contribution

It introduces a resource-based framework to analyze student interactions with differential equation solution methods, highlighting the importance of connecting procedural and conceptual resources.

Findings

Students use two types of solution methods involving shared resources.

A resource graph visualizes the epistemic pathways students follow.

Failure to connect ideas impedes successful problem solving.

Abstract

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.