Research on judgment of suitability concerning descriptions of definition of terms in mathematics textbooks for lower secondary school

The purpose of this study is to examine teachers' judgment concerning descriptions of definition of terms composed by the author and based on mathematics textbooks for lower secondary school. For this purpose the author asked 306 lower secondary school mathematics teachers to be participants of this research. Findings revealed that (1) Concrete examples are necessary in case of defining“variables based on constant''. But in case of“substitution”，a concrete example is not necessary. And necessity of concrete examples depends on the context in which the terms are used．(2)“congruence”，should not be defined in two grades. It should be defined in only 7th. Teachers think that descriptions of definition based on the one used in elementary school mode and expressed in symbol is not proper in lower secondary school in case of“parallel”．(3) As to the basic mathematics concept such as“invariable''，teachers think that in case of“constant”,“fixed number”or letters representing“fixed number”is proper. In case of “Theorem of circumference angle”，“all（angles) are equal”is proper. Thus, proper descriptions of“invariable，'depend on the context in which they are used. (4) Those who use the textbook A think that in case of“Absolute value"，descriptions based on their textbooks are proper. In contrast with this，in case of“Prime number”they think that the description is not proper. Teachers do not necessarily prefer the descriptions based on their textbooks familiar to them