Study on Self-Referential-Activities in Mathematical Problem Solving (V) : An Analysis of Self-Referential-Activities in Problem Solving Processes during a Class for Problem Solving

Abstract

The purpose of a series of our studies is to examine the role of "self-referential-activity" on mathematical problem solving. The term "self-referential-activity" means solver's activities that he/she refers to his/her own solving processes or products during or after problem solving. In study (I), we proposed the theoretical framework for analyzing self-referential activity. And, in study (II) and (III), we elaborated the variable "OG/NOG" and "M-SE/SE-C" respectively. In this article, we examined a student's problem solving process observed in a class which purpose was to construct a square from two given smaller squares (e.g. 7cm and 3cm). The student's solving activity was analyzed from our theoretical framework. As a result, the solving process was characterized as "Fail to pursue an approach but continue to pursue it" activity. We had theoretically assumed the existence of this kind of Local-Bad-Judge in study (IV), so this finding supports our theoretical assumption and its powerfulness of our framework. In addition, we discussed the possibility of translation from unsuccessful situation to successful one, and from these perspective we proposed teacher's suggestions or comments for the student to improve these kinds of unsuccessful situation to successful ones. The variables in our theoretical framework help us to consider such suggestions or comments. And, it is suggested that such suggestions or comments do not always need to be general one but be oriented to current situation.