以提供受試者學習強項與弱點診斷回饋訊息之認知診斷評量可被用以評估受試者之分數學習情況，以提升教學與學習品質。但現僅有少數認知診斷評量可供應用，如何編製一個認知診斷評量以給予可用的診斷訊息，是一個值得討論的問題。
本研究旨在發展國小五年級數學異分母分數加減單元認知診斷評量，探討運用DINA模式、G-DINA模式與DINO模式於參與此認知診斷評量的547位五、六年級學生之作答反應資料中作診斷分析，透過模式適配指標的分析及比較，找出最適合於解釋此認知診斷評量診斷測驗結果之認知診斷模式，以此認知診斷模式進行試題鑑別度分析。並依據30位受試者的訪談對話內容逐字稿探究及檢驗此認知診斷評量之分類準確率。
研究結果顯示DINA模式較適宜被用以詮釋受試者作答反應資料與推論受試者認知屬性可能精熟狀態，且於此認知診斷模式下，多數認知診斷試題之整體試題鑑別度達0.5以上。除此之外，透過訪談資料獲知的受試者真實學習狀態驗證DINA模式推測得到的受試者認知屬性可能精熟狀態，兩者之間的一致性達0.75，顯示DINA模式之推論結果具有一定之效度。

Cognitive diagnostic assessments aim to provide formative diagnostic feedback of test takers’ learning strengths and weaknesses. It could be used to evaluate test takers’ fraction learning situation and to improve the quality of teaching and learning. However, few cognitive diagnostic assessments are specifically designed for providing diagnostic feedback. How to construct a cognitive diagnostic assessment to provide effective feedback is worth discussing.
The purpose of the research is to develop a mathematical cognitive diagnostic assessment of addition and subtraction of fractions with different denominators for fifth graders by applying deterministic-input noisy “and” gate(DINA) model, generalized deterministic inputs, noisy “and” gate(G-DINA) model and deterministic input “or” gate(DINO) model. Five hundred and forty-seven students’ response data i s explored and diagnosed to find out the most suitable cognitive diagnostic model which could best interpret test takers’ response through the analysis and comparison of the fit of the model to the data. With this cognitive diagnostic model, the global item discrimination index of every diagnostic item could be computed. Thirty interviewees’ interview transcripts are also used to investigate and examine the classification accuracy of this cognitive diagnostic assessment.
The results showed that DINA model was more suitable for interpreting test takers’ response data and for inferring their possible mastery states of attributes. In DINA model, most of the diagnostic items’ global item discrimination indices were above 0.5. Besides, according to the true learning states of the test takers, known from the interview, the accuracy of the test takers’ possible mastery states of attributes inferred through the DINA model could be proved. The consistency between them is 0.75, showing that DINA model had quite validity.

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