算数・数学の授業における「知的責任の委譲」の実現の問題 : 「教授学的シツエーションモデル」の構築とモデルによる授業過程の分析

抄録

In our country, it has been an important and difficult task for many of the teachers to achieve 'the class where the students thinking is dominant' or 'the class where the students work actively or independently'. One of the causes seems to be that we understand the class intuitively and the characteristic is not clear. We need the view point or framework which enables us to see it in the mathematics class interaction. The research focuses of this paper are following two points: (1) To construct the framework to see the feature of the class described above. (2) To examine the effectiveness of the framework and to identify some important elements to realize the class. To be more specific we regard 'actively or independently' described above as "Devolution of the Intellectual Responsibility" and further "adidactical situation" which are the central concepts of French mathematics didactics. We assume that there are some steps or levels from the didactical situation to adidactical situation, we developed a framework 'Didactical Situation Model (DSM)' based on mainly two ideas. One is a model developed by Mellin-Olsen (1991) identifying the level of knowledge control in a didactical situation. The other is the types of "MATOME" identified by Iwasaki and Steinbring (2009). To examine the framework DSM, 5 mathematics lessons were taken from a sixth grade mathematics classroom. Analysis of the third lesson revealed that: (1) The DSM enables us to catch "the Devolution of the Intellectual Responsibility" in the each of the didactical situation in the lesson more concretely. (2) For realizing "the Devolution of the Intellectual Responsibility" in the interaction, it is important for teachers to evaluate the student's idea from the view point of the problem concerned instead of evaluating student's idea from the view point of teacher's expectation. (3) To achieve 'the class where the students work actively or independently', it is extremely important that students can have the goal level of control of the DSM.