事象の数学化に及ぼす言語の影響 ―概念的相対主義・言語相対論の視座からみた「かけ算・たし算の順序問題」の分析を通して ―

抄録

　　The purpose of this paper is to clarify the effect of differences in the structure of natural language and mathematical language at the stage of “mathematisation” where the translation from the language in the real world to the language in the mathematical world.  To achieve the purpose, three sub-tasks were set in this paper; (1) How have language problems been dealt with in mathematics education and their research? (2) What kind of suggestions can be obtained from linguistics in order to qualitatively realize the structure and cognitive process of Japanese and mathematical languages? (3) From the perspective of linguistics, how does the differences in structure between Japanese and mathematical languages affect learners’ thinking?  

　　The results corresponding to the sub-tasks are as follows; (1) It is organized from an international perspective and a Japanese perspective.  In particular, while language problems have been attracting attention internationally in mathematical modeling research in recent years, the reason why it was difficult to study language problems in Japan was clarified.  (2) We pointed out that the field of linguistics, which has a high affinity with mathematics education and its research, is cognitive linguistics, and organized basic ideas of cognitive linguistics.  Furthermore, based on cognitive linguistics, we organized two relativist perspectives: “relativism of interpretation between individuals (conceptual relativism)” and “relativism of languages  (linguistic relativism)”. And we also theoretically argued that these relativism provide a new perspective that are different from the existing framework of mathematical modelling research.  (3) We conducted a survey and empirically verified that the perspectives of “conceptual relativism” and “linguistic relativism” are effective frameworks for capturing the influence of language on mathematisation.

　　The content of this paper may also be useful as a basic study that examining the possibility of using cognitive linguistics in mathematics education and research.  This is the significance of this paper.