「メタ知識」を視点とした授業改善へのアプローチ : 「指示の文脈」と「記号体系」との間の相互作用

抄録

The research focus of this study is to explore the ways in which teachers can make their everyday teaching more fruitful from a metaknowledge perspective. For the study, qualitative, hermeneutical and micro-ethnographical case studies are utilized. Two teaching episodes (episode I and episode II) are analyzed from an epistemological point of view. The two episodes are taken from an 8th grade mathematics classroom; in both episodes, the context is the teaching of basic triangle congruence theorems. Episode I is a transcript from a standard classroom setting; episode II is a transcript from a similar setting but in a co-operative teaching experiment, which seems more fruitful from a metaknowledge perspective. An epistemological triangle is used as a theoretical perspective to analyze the two episodes. It is not fixed but is kept flexible to enable further improvement of the analysis. That is, there is an interactive relationship between the developing epistemological triangle as a theoretical perspective and the interpretation of the two episodes, especially the differences between them. Analysis of the two episodes from the perspective of the epistemological triangle reveals that in episode II there are clear interactions between developing the students' reference context and developing the students' symbol system. However, there are no such interactions in episode I. It becomes more clearly from a metaknowledge perspective how do the differences between them influence the students' mathematics learning and is episode II more fruitful. It is observed that the teacher's instructional approach in episode II is a complete contrast to the teacher's approach in episode I. The teacher in episode I attempted to teach the new symbol system directly through language without developing the students' reference context. The teacher in episode II attempted to create a productive 'tension' between the symbol system and a structural reference context and to develop and maintain this tension (Steinbring, H. 1997, p.79). To achieve these goals, the teacher in episode II attempted: (1) to try to understand the extent of the student's reference context and work on it by presenting geometrical constructions, which would put the students' reference context off its balance (2) to encourage the students to formulate their own conceptions of the reference context structure (3) to introduce a 'free element' into the subject matter, where the word "free' means the teacher is no "obligation for action', which is typical of institutionalized educational processes (Bauersfeld, H. 1988, p.37). These three actions are significant elements in fostering the interactions between developing the students' reference context and developing their symbol system.