A RESEARCH INTO TERMS AND SENTENCE STYLES OF MATHEMATICAL TEXTBOOKS

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We investigated into the mathematical terms and mathematical notions used in the mathematical education of the elementary and the middle level. We found many concrete examples of terms and notions incompletely or insufficiently defined.One example of such is "ippan-kaku", which is a Japanese word for English "general angle". It is not clear if this notion is a generalized notion for angles or a generalized notion for expressing the measure of angles, and so, it is not clear if the expression as 40ﾟ can be regarded as " ippan-kaku" or not. If the expression as 40ﾟ +n*360ﾟ (n=0, <plus-minus>1, <plus-minus>2, <plus-minus>3, ・・・) is "ippan-kaku", then this is neither an angle nor an expression for an angle, but something else. This makes pupils confused when they are asked in examinations "to answer the problem using ippan-We published three books to explain these linguistic problems.