PARTIAL KNOWLEDGE CONSTRUCTS FOR THE PROBABILITY AREA MODEL

We present the learning process of a pair of grade 8 students, who learn a topic in elementary probability. The students successfully accomplish a sequence of several tasks without apparent difficulty. When working on a further task, which seems to require only actions they have previously carried out well, they run into difficulty. In order to explain this difficulty, we analyze their learning process during the task sequence, and identify some partial knowledge. SOME THEORETICAL ASPECTS Students ' incorrect answers sometimes overshadow meaningful knowledge they have constructed. On the other hand, correct answers often hide knowledge gaps. In both cases, we can speak of partial knowledge. Partial knowledge constructs are the main focus of this paper. The RBC model (Hershkowitz, Schwarz, & Dreyfus, 2001) will be used as the main methodological tool. Processes of knowledge construction are expressed in the model by means of three observable and identifiable epistemic actions, Recognizing, Building-with, and Constructing (whence RBC). Constructing of new knowledge i