Using Resource Theory to Understand How Students Think About Indexing.

Students struggle with how to loop through lists in Python, often mixing and matching their strategies between looping by value and looping by index. At the heart of this issue is the concept of indexing, which can be a challenging abstraction for students. This work uses Resource Theory, a cognitive framework based on DiSessa's Knowledge in Pieces, to identify concepts and procedures that students activate when solving problems involving indexing. Resource theory posits that there are elements of understanding--called resources--that students activate when solving problems. We have conducted think-aloud interviews with students, asking them to solve tasks that involved indexing a multi-dimensional list, and used the resource theory framework to analyze how students conceptualize indexing. From our analysis, we have identified three resources (Item, Position Value, and Retrieval) that encapsulate the pieces of understanding that students bring to bear when they use indexing to solve problems. These resources can provide a new way for instructors to think about the critical cognitive components of the abstract concept of indexing. We propose strategies for using analogies to refocus student intuition to emphasize the relationship between these three resources and how and when to apply them.