UC Berkeley

Learning is typically thought of as a change in a student's understanding within a single context. The term context is used here to describe a domain or subdomain of knowledge. Students' previous understandings of the context are known to play a considerable role in such learning. Another important kind of learning is reasoning across contexts. Through reasoning across contexts, students' understanding of one context influences understanding of another context. This dissertation investigated the role of students' previous understandings in this reasoning process.

Psychology research has employed one type of experimental design to investigate reasoning across contexts. This has resulted in focus on a particular way of reasoning across contexts, called analogical transfer, in which participants' previous understandings play a minimal role. In contrast, this dissertation employed a case study design for the purpose of investigating the role of participants' previous understandings in reasoning across contexts.

Participants' previous understandings of contexts were discovered to play a considerable role in their reasoning across contexts. Three categories of ways of reasoning across contexts in which students' previous understandings play a role were identified. In the first of these, a participant's new understanding of a context is a combination of ideas used previously to understand the same context and ideas used to understand another context. In the second, an idea from either the participant's previous understanding or from the participant's understanding of another context is modified to contribute to a new understanding. In the third, an idea from the participant's previous understanding is brought into different focus through comparison with a corresponding idea from another context. These three are termed combining, modifying, and refocusing interactions, respectively.

Understanding of these different possible roles for students' previous understandings in reasoning across contexts can inform instruction in which a general concept is instructed through particular contexts. An example of such a general concept is the concept of equilibration considered here.