適用於小班教學現場之部分連結神經網路認知診斷模式

A Cognitive Diagnosis Model Based on Partially Connected Neural Network and Its Application on Small-Class Teaching

認知診斷模式已經被應用到不同學科領域中，以細部了解學生在技能概念的精熟與否。然而，常見的參數型認知診斷模式，如DINA（Deterministic Input, Noisy ''And'' Gate）模式和廣義DINA（Generalized DINA, GDINA）模式，都需要一定數量的訓練樣本，才能有好的預測效果，故DINA與GDINA不太適用於目前小班制的教學現場。本研究提出一個部分連結的神經網路模式，不同於傳統的全連結神經網路模式，透過試題與技能對應的Q矩陣，來決定試題與概念之間的連結。也就是說，學生的特定技能概念具備與否，應該只與需要使用到該技能概念的試題對錯有關。最後再利用理想作答反應來訓練網路連結的權重，這種訓練方式不需要使用到學生的真實作答反應，只要在命題時，設計好該試卷的Q矩陣，便可以透過Q矩陣推得的理想作答反應來求得網路連結權重。由模擬資料和「分數乘法」實證資料實驗結果顯示，部分連結神經網路認知診斷模式在小樣本的情況下，分類一致性優於DINA模式與GDINA模式。因此，此模式可以適用於目前小班教學現場，甚至可以搭配網路教學平臺進行個人化診斷評量，即在單一學生情況下，也可以進行概念精熟診斷。

Cognitive diagnosis models (CDMs) classify examinees' mastery skill profiles according to their test performance and Q matrix, the mapping between items and skills. They have been applied to many but different research areas such as language assessment, psychology, and international testing. Moreover, they are also be applied to adaptive learning or personalized learning. DINA (Deterministic Input, Noisy ''And'' Gate Model) and its generalized version, GDINA (Generalized DINA) are two well-known models in CDMs. However, both of them need a certain amount of examinees' responses to train and pre-determine appropriate models' parameters. Hence, they are not suitable for small-class teaching. In this study, a partially connected neural network for cognitive diagnostic (PNNCD) was proposed. The connections between nodes in the input layer and nodes in the output layer are determined by the Q matrix. The reason is that only items required specific skill can influence the mastery level of the skill. Moreover, the ideal responses, directly determined by the Q matrix of the test, are used to train the model weights. That is, the proposed model is not trained by examinees' responses, and, hence, it can be directly applied to only one examinee situation. According to experiments on both simulated data sets and a real data set, the proposed PNNCD outperforms than DINA and GDINA in small sample size. Therefore, PNNCD is more appropriate to apply in the small-class teaching.