摘要 近年來測驗的編製逐漸朝向階層式的評量架構，期能測得學生較高階的能力值，加上使用適當的模式進行分析，不僅可同時獲得欲求得的能力估計值，還能獲得較多的訊息量。本研究根據NAEP的數學評量架構，編製一份六年級數學小數的除法測驗，利用實徵資料比較HIRT、MIRT和UIRT三種估計模式對學生小數除法的能力值估計是否有差異，影響如何？以作為階層式評量架構之測量模式選用依據。 本研究測驗的結果顯示此份測驗具備良好的信度（Cronbach α係數值為0.79）、效度和鑑別度；透過實徵方式在模式適配度指標（model fit indexes）AIC、BIC、DIC三種指標值都顯示HIRT之完整模式較適合用於估計階層式評量架構；HIRT模式中小數的除法能力及概念、程序、問題解決間的迴歸係數在0.8以上，尤其概念在解釋小數的除法能力時影響力最大；HIRT之完整模式也可以提供較多訊息，且估計效果較佳。

Abstract In resent years, for estimating students’ higher abilities, the framework of assessment gradually turns into large-scale standardized assessment framework. Suitable model not only tells us the ability estimates wanted, and gets the better estimation result. By means of empirical study, the main purpose of the study is to compare if there is difference in mathematical ability estimation by HIRT(hierarchical item response theory), MIRT (multidimensional item response theory) and UIRT (unidimensional item response theory) and what their influences are as the reference of mathematical assessment model. The assessment on Decimal division is designed for six-grade students based on the mathematical assessment framework of NAEP. The reliability on the assessment is 0.79. The result is analyzed and compared by HIRT, MIRT and UIRT models. According to the model fit indexes (AIC, BIC and DIC), it shows that HIRT model is suitable to large-scale standardized assessment framework. In HIRT pattern, the coefficients of Decimal division, and conceptual understanding, procedural knowledge, problem solving inference regression are higher than 0.7, especially conceptual understanding influence the Decimal division. Therefore, the result of the empirical study confirms HIRT model can provide more information and has better estimation.