本研究主要想探討IRT與CTT何者更能清楚反映出學生的真實情況，並進而分析現階段國小學童在同分母分數加減概念上之表現情形。本研究以問卷調查法進行，針對桃園縣一所國民小學進行研究，並選取該校四、五年級各一班的學童作為研究樣本，總計有效樣本數54位。研究工具則採用自編之「分數加減法概念問卷」，其測驗內容包含能力維度與運算維度等兩大維度。
根據資料顯示，本研究主要發現如下：（1）IRT的試題難易度與CTT之試題難易度在試題上之排序達一致性。（2）IRT之試題鑑別度值越高，確實更可以清楚區隔出學生能力的差異。（3）IRT之鑑別度除具可加性外，所導出的能力值更能合理地呈現出學生的能力，並且可以合理地分辨出學生程度的差異。（4）學童學習分數加減計算時，「假分數計算」是屬於較為簡單之計算類型，因此也較容易被學童所接受、學習。學童熟不熟練「帶分數與假分數互換」或「帶分數拆解」，對於學習分數加減概念是具有關鍵性的影響。（5）學童在分數應用題的列式上有不錯之表現。（6）學童在分數的加減運算上，「假分數＋假分數」的運算是屬於比較簡單之運算類型，而「假分數＋帶分數、帶分數－假分數」則是屬於較為困難的運算類型。

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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