| Summary: | 碩士 === 國立新竹教育大學 === 數理教育研究所 === 98 === The purpose of the study is to investigate which one can truly reveal students’ real situation, IRT or CTT ? Furthermore, we wanted to know if elementary school students can do addition and subtraction on fraction on the same denominator. The subjects of our research are 4th and 5th students from an elementary school in Taoyuan. The number of sample is 54. A questionnaire about addition and subtraction of fractions was used as our research tool, in which two dimensions are included, mathematical ability and mathematical operation.
The main findings of the study were:
（1）There is consistency between the rank of the item difficulty of IRT and the one of CTT.
（2）The higher value of the item discrimination can differentiate more exaclty between students having abilities.
（3）The value of the discrimination of IRT not only can differentiates between students having abilities,but also has additivity and the value of ability calculated by IRT can represents student’s ability more reasonably.
（4）On Fractional problems,improper fractional calculation is easier calculational type for students to study.Mastery of the skills of mixed number to improper fraction and partitioning whole numbers is important for students to study addition and subtraction problems of fractional numbers.
（5）Students are doing well on writing down the formula of fractional applications.
（6）On fractional operations,the kind of 「improper fraction＋improper fraction」is easier operational type.But,these kinds of「improper fraction＋mixed number,mixed number－improper fraction」are more difficult.
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