In J. P. Ponte & J. F. Matos (Eds.), Proceedings of the 18th International Conference for the Psychology of Mathematics Education, vol. III. (pp.376-383). Lisbon:
University of Lisbon.
Summary
In this paper, we analyze the usefullness of diagrams in mathematical problem
solving from standpoint that diagrams can be changing gradually during solving
processes. The aim of this paper is to present one function of diagrams, i.e.
generating new elements by integrating information at hand. After considering
examples from the previous research, students' solutions will be analyzed in
order to find an empirical evidence for this function. The analysis will also
suggest that, even if diagrams can show new elements to a solver, the decision
about what sense should be given to those elements is left to the solver.
In I. Hirabayashi et al. (Eds.), Proceedings ofthe17th International
Conference for the Psychology of Mathematics
Educaiton, vol. III .(pp.49-56). Tsukuba: University of Tsukuba
@Summary
The aim of this study is to explore problem-solving processes and find some
characteristic activities by expert problem solver. The video-taped and audio-
taped records are analyzed and interpreted from the viewpoint of the solver's
structures of the problem situation. From this analysis, the following
characteristic activities are found; (1) During the problem solving process a solver
constructs prospective structures of the problem situation; (2) even if the prospective
structure proves to be inappropriate, trying to elaborate the prospective structure
can produce the useful information to the solver. Existence of prospective structures
is also justified by the recent views in philosophy of mathematics.