| Abstract: | This article examines the issue of why students fail to activate and use mathematical knowledge during problem solving when it is known that they possess the required knowledge. This issue is explored by analyzing problem-solving attempts of a high-achieving student and a low-achieving student in the domain of plane geometry. On the basis of these data and other literature, three major sources of mathematical knowledge-access difficulties are identified that might be considered by classroom teachers, including a student's (1) dispositional state, (2) management of the problem-solving process, and (3) state of organization of his or her mathematical knowledge. It is argued that teaching practices that place emphasis on careful management of problem-solving activity could help students activate and extend the use of mathematical knowledge acquired in lesson activities. |
