認知診斷模式之理論與實務

Cognitive Diagnostic Model-Theory and Practice

吳慧珉(Huey-Min Wu)；鄭俊彥(Chun-Yen Cheng)；施淑娟(Shu-Chuan Shih)

Q矩陣 ； 分數加減 ； 無參數 ； 認知診斷模式 ； adding and subtracting fractions ； cognitive diagnostic model ； non-parametric ； Q-matrix

測驗學刊

62卷4期（2015 / 12 / 01）

303 - 328

繁體中文

本研究介紹認知診斷模式之理論與實例分析。參數型認知診斷模式有明確的參數定義，可描述試題特性或認知屬性特性，但估計演算法則複雜且須考慮模式適配與樣本大小之問題。無參數型認知診斷模式透過距離與加權，估計學生認知屬性組型，理論簡單易懂，沒有樣本大小之限制，但無法呈現試題之特性，應用較受限制。目前多數的研究聚焦於理論的探討與模擬研究，理論須落實於實務方能有用，本研究以實例「分數的加減」作為範例，探討認知診斷模式於實務分析之成效。在與專家的一致性比較方面，參數型DINA、R-RUM與無參數型Panelized的加權具有良好的一致性。教師可根據認知屬性的分布率，了解學生的學習成效，學生能根據診斷的結果，得到詳細的回饋。文末對實務應用提出Q矩陣設計、題目的編製、模式分析之建議。

Cognitive diagnostic models are introduced in this paper. The “Adding and Subtracting Fractions” unit for 4th grade math was used as an example. Parametric cognitively diagnostic models utilize parameters to define test questions or attribute characteristics therefore users can easily master the features of the questions. However, parametric cognitively diagnostic models also have limitations such as the parameter estimation algorithm is very complex, and issue such as goodness-of-fit and sample size require careful evaluation. Non-parametric cognitively diagnostic models model which overcomes issues with goodness-of-fit and sample size, and this model is capable of estimating the pattern of the attribute profile of the examinees by using a simple distance algorithm. However, application of this model is rather restricted due to the lack of parameters to explain the characteristics of its test questions. Most studies, using either parametric or non-parametric cognitively diagnostic models, focus on exploring simulation experiments and rarely examine empirical data. Theoretical models, however, need to be implemented in actual situations to realize their utility. Therefore, this study investigates the effectiveness of parametric and non-parametric cognitive diagnostic models in empirical data analysis. Using the experts’ decision as criteria, DINA, RRUM, and weighted panelized models represented good consistency with experts’ decision. Cognitively diagnostic models can provide teachers and students with detailed assessment information. The suggestions related to Q-matrix, item developing, and model fitting in practical settings are provided.

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