抄録
The purpose of a series of our studies is to investigate the role of "self-referential activity" in mathematical problem solving. The term "self-referential activity" means solver's activities that she/he refers to her/his own solving processes or products during or after problem solving. For example, in study (I), we proposed the theoretical framework for analyzing self-referential activity. And, in study (II) and (Ill), we elaborated the variable "OG/NOG" and "M-SE/SE-C" respectively. In studies (VII), we theoretically examined the role of "looking-back" activity in the phase after problem solving, and we identified six roles of "looking-back" activity. In addition, we investigated "looking-back" activity after solving "Telephone-Line Problem" to examine the effectiveness of some kind of treatments to develop solver's solution. The purpose of this article is to investigate the development of solution through some looking-back activities after solving other kind of problem ("Paper-Rock-Scissors Problem"). In order to investigate whether there is any development of solution after a specific looking-back activity, the control group and the three experimental groups were set up. All groups solved two types of paper-rock-scissors problems; the two problems (Problem 1 and 2) had same problem structure, but the second Problem 2 with more broad problem space was more complicated and relatively difficult. And, the subjects in each experimental group had to reply a question between solving Problem 1 and Problem 2. The question statement was intended for implementing a specific looking-back activity with the corresponding function to "checking your own solution" (Check-Solution Treatment), "inquiring into better solution" (Better-Solution Treatment), and "examining generalization of your own solution" (Generalization Treatment) respectively. As a result, we could find the following points. (1) It seemed to be difficult to improve solver's misunderstanding or inappropriate problem representation with/without treatments. (2) "Unsophisticated solution" founded in the control group had a tendency to be fixed even if the problem became more complicated. (3) There was not a significant difference among control group and treatment groups, but each of the treatments seemed to contribute to the development of solution. This tendency suggests that some general and content-free treatments such as ones treated in this article may play an important role in mathematics classroom situation in terms of whole-class problem solving.
