Mathematical memory revisited: Mathematical problem solving by high-achieving students

The present study deals with the role of the mathematical memory in problem solving. To examine that, two problem-solving activities of high achieving students from secondary school were observed one year apart -the proposed tasks were non-routine for the students, but could be solved with similar methods. The study shows that even if not recalling the previously solved task, the participants' individual ways of approaching both tasks were identical. Moreover, the study displays that the participants used their mathematical memory mainly at the initial phase and during a small fragment of the problem-solving process, and indicates that students who apply algebraic methods are more successful than those who use numerical approaches.