A study of formation rules of mathematical terms, problematic terms, and applications to mathematical equcation.

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We studied the terms and sentence styles used in the mathematical education in Japanese from the three points of view as follows :(i)Problematic terms and sentences.(ii)Formation rules of terms from Chinese characters.(iii)Fundamental sentence styles and grammars for mathematical expressions in Japanese.1. Concerning (i), we found many examples, such as :(1)Some old words, whose meanings are now very difficult for pupils to understand, are used in textbooks as fondamental words.(2)There are some differences in meaning and in usage for such logical words as Japanese "to", which corresponds to English "and", and Japanese "ka", which corresponds to English "or". Unfortunately, teachers have missed to notice this until now.(3)There are some problems in teaching "Necessary conditions" and "Sufficient conditions".(4)English notion "limit" has been translated into two Japanese words, "kyokugen" and "kyokugenti", while the latter word is not well treated in classrooms.2. Concerning (ii), we collected 145 Chinese characters as fundamental characters of Japanese mathematical terms and gave explanations how to use them in mathematics.3. Concerning (iii), we collected sentence style of Definitions, Theorems and Proofs. We studied the usages of logical words used in them.