本研究從實務應用之觀點，將學科認知屬性與錯誤類型和認知診斷模式結合，本研究使用數學科「分數」與「圖形的縮放」作為範例，編製認知診斷測驗，透過認知診斷模式估計學生之認知屬性和錯誤類型。研究結果顯示: 「分數」單元的信度是0.82，「圖形的縮放」信度是0.83。本研究使用專家判讀結果作為效標，「分數」與「圖形的縮放」認知診斷模式估計的結果與專家的一致性約0.85，顯示認知診斷模式能提供有效的回饋給學生和老師，作為補救教學之依據。

　　This paper incorporates both attribute and error pattern into the cognitive diagnostic model and takes two math topics, which were Fraction and Proportional Reasoning, as examples to construct the cognitive diagnostic assessments that would eventually evaluate students’ attribute and error pattern. As shown in the result, the reliability of “Fraction” and “Proportional Reasoning” are respectively 0.82 and 0.83. Also, this paper utilizes judgements from experts as criteria and the consistency between such criteria and the results of the cognitive diagnostic model for “Fration” and “Proportional Reasoning” is both about 0.85, indicating the cognitive diagnostic model could offer valid feedback to students as well as teachers and serve as guidance of remedial instruction.