The Identification of Partially Correct Constructs
Gila Ron, Rina Hershkowitz, Tommy Dreyfus · 2008
We show how the RBC model for abstraction in context can be used to follow the emergence of a learner’s knowledge constructs and to identify in detail the learner’s partially correct constructs (PaCCs). These PaCCs are used to explain the learner’s inconsistent answers and provide added insight into processes of knowledge construction. The research process is illustrated by means of an example from elementary probability. We thus demonstrate the analytic power of the RBC model for abstraction in context. Abstraction has been a central issue in mathematics and science education for many years. The classic work by Piaget, Davydov, Skemp and others has in recent years been succeeded by research fora, symposia and discussion groups at various conferences, as well as several special issues of research journals, most recently the Mathematics Education Research Journal (Mitchelmore & White, 2007). One of the approaches to research on abstraction presented on these occasions is abstraction in context, or AiC (Hershkowitz, Schwarz & Dreyfus, 2001). This approach considers abstraction as a process of emergence of knowledge constructs that are new to the learner. In order to describe such processes at a fine-grained level, abstraction in context makes use of a model, the RBC model, which is based on three epistemic actions to be described below. The RBC model has been used for this purpose by different research teams with students of different ages learning about different mathematical topics (including square roots, algebra, probability, rate