学校数学の証明の構成における蓋然的な論の検討の方法 : argumentationを視点として

抄録

In constructing a proof, students need to examine the probable arguments they found when devising a plan of proof. However, many students do not seem to acquire effective methods of making such an examination. In order to provide ideas for improving the learning and teaching of proving, this paper aims at deliberating how to examine probable arguments in constructing a proof from an argumentative perspective. Towards this aim, this paper elaborates the nature of argumentation based on Toulmin (1958/2003), who focused on the probability of practical arguments and the essential aspects of using such arguments. Based on the nature of argumentation and the relationship between constructing a proof and devising a plan of proof, this paper theoretically characterizes how to examine probable arguments as the following: a) clarifying the probability of arguments by changing their types; b) improving arguments by identifying and justifying the condition under which the arguments hold; c) exploring alternative arguments by utilizing dismissed arguments; and d) modifying arguments by justifying the truth of their warrants. Finally, this paper discusses the validity of the characterization and derives an implication for teachers' means to facilitate students' examination of probable arguments.